ATTN Jesse; on a separate thread

[Alan Grayson]

Please define what you mean by local events, with some examples. And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG

[Alan Grayson]

You'll notice that the author doesn't expressly state what the paradox is, but clearly suggests it's the discrepancy between what the frames predict re: car fitting or not in the garage as predicted by the frames.  But he then makes a claim that "The resolution of the paradox is that if the front end of the car stops simultaneously to the back end from one "reference frame", that will not be true in the other." Can you state exactly how this resolves the issue?  TY, AG

http://insti.physics.sunysb.edu/~siegel/sr.html

A famous "paradox" is trying to park a relativistic car in a garage: From the point of view of the car, the garage has "Lorentz contracted", and the car will no longer fit. But from the point of view of the garage, the car is now shorter, and so will fit even better. The resolution of the paradox is that if the front end of the car stops simultaneously to the back end from one "reference frame", that will not be true in the other. If both ends do not stop at the same time, the car changes length. (This has often been observed nonrelativistically, for cars stopped by trees or other cars.)

[Alan Grayson]

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

[Jesse Mazer]

On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <agrays...@gmail.com> wrote:

Please define what you mean by local events, with some examples.

I did that in my last two comments on the other thread, the first of which you had said you were going to respond to in more detail. In my second-to-last post see the two paragraphs beginning with the sentence 'But are you asking a different question about what is the motive for demanding that any claims about how things work in different frames needs to pass the test of giving identical local predictions, in order to qualify as good physics?' with the example of the mini bomb and the glass of water, and in my last post see the paragraphs beginning with '"The car fits" or "the car fits" are not statements about local events, i.e. statements about things that happen at a single spacetime point in one of Brent's diagrams'--in that comment I then went on to give examples involving endpoints of the car and garage crossing paths with clock readings and ruler markings given at those specific crossing points in spacetime. Can you re-read those carefully, and if you're still unclear ask follow-up questions to either of those comments?

Note that in these kinds of problems we idealize things like clocks and endpoints of the car as being like point particles that only have a single position coordinate at a single time coordinate (likewise the bomb and the glass of water), which I assume you won't have a problem with if you are willing to similarly idealize the car and garage as 1-dimensional. But if you were to treat clocks etc. as having an extension in space that was tiny compared to the lengths of the car/garage, and passing by the ends of the car garage at a similarly tiny distance, this would differ only negligibly from the idealized calculation of treating them as points.

Jesse

 

And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG

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[Alan Grayson]

On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <agrays...@gmail.com> wrote:

Please define what you mean by local events, with some examples.

I did that in my last two comments on the other thread, the first of which you had said you were going to respond to in more detail. In my second-to-last post see the two paragraphs beginning with the sentence 'But are you asking a different question about what is the motive for demanding that any claims about how things work in different frames needs to pass the test of giving identical local predictions, in order to qualify as good physics?' with the example of the mini bomb and the glass of water, and in my last post see the paragraphs beginning with '"The car fits" or "the car fits" are not statements about local events, i.e. statements about things that happen at a single spacetime point in one of Brent's diagrams'--in that comment I then went on to give examples involving endpoints of the car and garage crossing paths with clock readings and ruler markings given at those specific crossing points in spacetime. Can you re-read those carefully, and if you're still unclear ask follow-up questions to either of those comments?

Note that in these kinds of problems we idealize things like clocks and endpoints of the car as being like point particles that only have a single position coordinate at a single time coordinate (likewise the bomb and the glass of water), which I assume you won't have a problem with if you are willing to similarly idealize the car and garage as 1-dimensional. But if you were to treat clocks etc. as having an extension in space that was tiny compared to the lengths of the car/garage, and passing by the ends of the car garage at a similarly tiny distance, this would differ only negligibly from the idealized calculation of treating them as points.

Jesse

I don't have a problem with idealizations and it's clear that we're using them in this issue. I didn't want to reply on the other thread in order not to mess up your long post which I will eventually respond to. And I realize that the simultaneous endpoints of a perfectly fitting car are not local events but why does the fact that they're not simultaneous in the car frame solve this apparent paradox? And you'll notice the author I quoted doesn't state exactly what the paradox is. AG 

[Alan Grayson]

On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote:

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG 

[Alan Grayson]

On Friday, December 20, 2024 at 5:09:12 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote:

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG 

In further consideration, it's OK. My equation does cross x-axis at x=7, when t=0. AG 

[Jesse Mazer]

On Fri, Dec 20, 2024 at 7:21 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 5:09:12 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote:

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG 

In further consideration, it's OK. My equation does cross x-axis at x=7, when t=0. AG 

Yep, that's right. And if we had a second object whose worldline was described by some different equation like x(t) = 9 + 3*t, and we asked the question "where is each object located at t=8 ?", then in terms of a graph we could solve this by drawing a horizontal line that crossed the 8 mark on the vertical time axis, and seeing where it intersects the two lines x(t) = 7 + 12*t and x(t) = 9 + 3*t -- in other words, where a 1D line of simultaneity intersects the worldlines. That's the same basic idea in relativity, except that in relativity a given frame will have its simultaneity lines tilted at an angle when it's plotted in the coordinates of a different frame.

Jesse

 

On Friday, December 20, 2024 at 4:14:30 AM UTC-7 Alan Grayson wrote:

Please define what you mean by local events, with some examples. And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG

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[Jesse Mazer]

What I'm saying is that "solving the paradox" requires understanding that despite the disagreement over fit, there is no actual disagreement about local events like the ones I mentioned with rulers and clocks at different positions. But to understand conceptually how it can be possible that they can disagree on fitting but still agree on all details about local events, you really need to look at the way the frames have differing definitions of simultaneity. As I pointed out on the other thread, if you imagine a hypothetical world where there is *no* disagreement over simultaneity but each frame still predicts that objects moving in that frame are Lorentz-contracted, then two frames that make different claims about whether the car fit would automatically *also* be disagreeing over clock readings at some local events.

As for the other author you quoted, that person is dealing with a different version of the car/garage paradox where the car is supposed to instantaneously accelerate to come to rest relative to the garage when the front end reaches the back of the garage, and they're saying that this would lead to different physical scenarios depending on whether all points in the car accelerate simultaneously in the car frame, or if they accelerate simultaneously in the garage frame. In the first scenario the back end of the car will come to rest relative to the garage when it's outside the garage (so the car never fit in either frame) and in the second scenario the back end of the car will come to rest when it's inside the garage (so the car did fit in both frames). This wouldn't be a mere difference between frames as in Brent's scenario where there's no acceleration, these would be two physically different options for how to accelerate the car.

Jesse

 

 

And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG

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[Alan Grayson]

On Friday, December 20, 2024 at 7:36:49 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 7:21 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 5:09:12 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote:

 

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG 

In further consideration, it's OK. My equation does cross x-axis at x=7, when t=0. AG 

Yep, that's right. And if we had a second object whose worldline was described by some different equation like x(t) = 9 + 3*t, and we asked the question "where is each object located at t=8 ?", then in terms of a graph we could solve this by drawing a horizontal line that crossed the 8 mark on the vertical time axis, and seeing where it intersects the two lines x(t) = 7 + 12*t and x(t) = 9 + 3*t -- in other words, where a 1D line of simultaneity intersects the worldlines. That's the same basic idea in relativity, except that in relativity a given frame will have its simultaneity lines tilted at an angle when it's plotted in the coordinates of a different frame.

Jesse

You claimed that local events are frame invariant under the LT. So if we consider the endpoints of the car, and each event is frame invariant, then presumably the events, having the same time in the garage frame, will have the same time in the car frame, and thus must be simultaneous. But the claim is they're NOT simultaneous and somehow this solve the apparent paradox. I still don't get it. AG 

[Alan Grayson]

On Friday, December 20, 2024 at 7:47:47 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:53 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <agrays...@gmail.com> wrote:

Please define what you mean by local events, with some examples.

I did that in my last two comments on the other thread, the first of which you had said you were going to respond to in more detail. In my second-to-last post see the two paragraphs beginning with the sentence 'But are you asking a different question about what is the motive for demanding that any claims about how things work in different frames needs to pass the test of giving identical local predictions, in order to qualify as good physics?' with the example of the mini bomb and the glass of water, and in my last post see the paragraphs beginning with '"The car fits" or "the car fits" are not statements about local events, i.e. statements about things that happen at a single spacetime point in one of Brent's diagrams'--in that comment I then went on to give examples involving endpoints of the car and garage crossing paths with clock readings and ruler markings given at those specific crossing points in spacetime. Can you re-read those carefully, and if you're still unclear ask follow-up questions to either of those comments?

Note that in these kinds of problems we idealize things like clocks and endpoints of the car as being like point particles that only have a single position coordinate at a single time coordinate (likewise the bomb and the glass of water), which I assume you won't have a problem with if you are willing to similarly idealize the car and garage as 1-dimensional. But if you were to treat clocks etc. as having an extension in space that was tiny compared to the lengths of the car/garage, and passing by the ends of the car garage at a similarly tiny distance, this would differ only negligibly from the idealized calculation of treating them as points.

Jesse

I don't have a problem with idealizations and it's clear that we're using them in this issue. I didn't want to reply on the other thread in order not to mess up your long post which I will eventually respond to. And I realize that the simultaneous endpoints of a perfectly fitting car are not local events but why does the fact that they're not simultaneous in the car frame solve this apparent paradox? And you'll notice the author I quoted doesn't state exactly what the paradox is. AG 

What I'm saying is that "solving the paradox" requires understanding that despite the disagreement over fit, there is no actual disagreement about local events like the ones I mentioned with rulers and clocks at different positions. But to understand conceptually how it can be possible that they can disagree on fitting but still agree on all details about local events, you really need to look at the way the frames have differing definitions of simultaneity. As I pointed out on the other thread, if you imagine a hypothetical world where there is *no* disagreement over simultaneity but each frame still predicts that objects moving in that frame are Lorentz-contracted, then two frames that make different claims about whether the car fit would automatically *also* be disagreeing over clock readings at some local events.

As for the other author you quoted, that person is dealing with a different version of the car/garage paradox where the car is supposed to instantaneously accelerate to come to rest relative to the garage when the front end reaches the back of the garage, and they're saying that this would lead to different physical scenarios depending on whether all points in the car accelerate simultaneously in the car frame, or if they accelerate simultaneously in the garage frame. In the first scenario the back end of the car will come to rest relative to the garage when it's outside the garage (so the car never fit in either frame) and in the second scenario the back end of the car will come to rest when it's inside the garage (so the car did fit in both frames). This wouldn't be a mere difference between frames as in Brent's scenario where there's no acceleration, these would be two physically different options for how to accelerate the car.

There's nothing in that scenario which models it as accelerating (actually decelerating) to get a perfect fit. In fact, the author states that the car fits in the garage from the garage frame, but not in the garage in the car frame. He then states that simultaneity fails in car frame and this is the alleged solution. At least he seems to agree with my concept of what constitutes a paradox. AG

Jesse

[Alan Grayson]

Wrong. The author does have the car stopping to get a perfect fit, but I don't think this matters. We can assume the car is in constant motion and get the same result re; differerence in simultaneity between frames. AG 

Jesse

[Jesse Mazer]

On Fri, Dec 20, 2024 at 9:48 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 7:36:49 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 7:21 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 5:09:12 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote:

 

Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG

No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG 

In further consideration, it's OK. My equation does cross x-axis at x=7, when t=0. AG 

Yep, that's right. And if we had a second object whose worldline was described by some different equation like x(t) = 9 + 3*t, and we asked the question "where is each object located at t=8 ?", then in terms of a graph we could solve this by drawing a horizontal line that crossed the 8 mark on the vertical time axis, and seeing where it intersects the two lines x(t) = 7 + 12*t and x(t) = 9 + 3*t -- in other words, where a 1D line of simultaneity intersects the worldlines. That's the same basic idea in relativity, except that in relativity a given frame will have its simultaneity lines tilted at an angle when it's plotted in the coordinates of a different frame.

Jesse

You claimed that local events are frame invariant under the LT. So if we consider the endpoints of the car, and each event is frame invariant, then presumably the events, having the same time in the garage frame, will have the same time in the car frame, and thus must be simultaneous.

How do you figure? No, only the set of things happening at any *single* point in spacetime (like clock readings and ruler markers and other events like two worldlines crossing) will be frame-invariant, and I already said when I talk about "local events" I am talking about single points in spacetime. Any time you are talking about relationships between *different* points in spacetime, whether temporal relations like simultaneity/non-simultaneity or spatial relations like distance, that is *not* a claim about local events at a single point in spacetime, and so not frame-invariant.

Jesse

On Friday, December 20, 2024 at 4:14:30 AM UTC-7 Alan Grayson wrote:

Please define what you mean by local events, with some examples. And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG

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[Jesse Mazer]

There are different ways of formulating the paradox, and as you seem to acknowledge, the author you linked at http://insti.physics.sunysb.edu/~siegel/sr.html does talk about the car stopping, and notes there are different possible physical scenarios for when the back of the car stops if the front stops when it reaches the back wall (i.e. whether the back of the car stops simultaneously with the front according to the car frame's definition of simultaneity or the garage frame's definition of simultaneity). Of course you can also formulate the paradox in terms of different frames' perspective on a car moving inertially through the garage without stopping as Brent did (that's the way the paradox is usually formulated), but then why did you specifically ask about a page that has a completely different version of the problem? 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events, so it's just the same physical scenario described in different coordinate systems; in the version on the website you need to consider simultaneity for a very different reason, because it's specified that the car's back end can stop simultaneously with the front end in either the car frame and the garage frame, resulting in genuinely different physical scenarios. 

Jesse

[Alan Grayson]

That scenario was posted, IIRC, by Quentin, in part his demonstration of how simple the solution, and how stupid I am. I prefer the scenario where the car doesn't cease its motion, and IIUC, the alleged solution is the same, which I don't understand; disagreement about simultaneity. AG 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

[Jesse Mazer]

I also prefer to talk about an inertial scenario with no stopping, so let's drop the discussion of that webpage.

 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

Did you read the comment before the one you are responding to here? I don't understand why you think agreement on local events would have anything to do with simultaneity, I explained why it doesn't there. Do you think you can define simultaneity in a way that only refers to facts about what's happening at a single point in space time, with no reference to any relation between that point and any other point in spacetime? If you think you can, tell me what specific local facts you are referring to, given a particular choice of point in spacetime (say, the point where the worldline of the back of the car crosses the worldline of the front of the garage).

Jesse

 

so it's just the same physical scenario described in different coordinate systems; in the version on the website you need to consider simultaneity for a very different reason, because it's specified that the car's back end can stop simultaneously with the front end in either the car frame and the garage frame, resulting in genuinely different physical scenarios. 

Jesse

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[Alan Grayson]

On Saturday, December 21, 2024 at 12:41:56 AM UTC-7 Jesse Mazer wrote:

On Sat, Dec 21, 2024 at 1:41 AM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 11:20:30 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 11:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 8:03:38 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 7:47:47 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:53 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <agrays...@gmail.com> wrote:

Please define what you mean by local events, with some examples.

I did that in my last two comments on the other thread, the first of which you had said you were going to respond to in more detail. In my second-to-last post see the two paragraphs beginning with the sentence 'But are you asking a different question about what is the motive for demanding that any claims about how things work in different frames needs to pass the test of giving identical local predictions, in order to qualify as good physics?' with the example of the mini bomb and the glass of water, and in my last post see the paragraphs beginning with '"The car fits" or "the car fits" are not statements about local events, i.e. statements about things that happen at a single spacetime point in one of Brent's diagrams'--in that comment I then went on to give examples involving endpoints of the car and garage crossing paths with clock readings and ruler markings given at those specific crossing points in spacetime. Can you re-read those carefully, and if you're still unclear ask follow-up questions to either of those comments?

Note that in these kinds of problems we idealize things like clocks and endpoints of the car as being like point particles that only have a single position coordinate at a single time coordinate (likewise the bomb and the glass of water), which I assume you won't have a problem with if you are willing to similarly idealize the car and garage as 1-dimensional. But if you were to treat clocks etc. as having an extension in space that was tiny compared to the lengths of the car/garage, and passing by the ends of the car garage at a similarly tiny distance, this would differ only negligibly from the idealized calculation of treating them as points.

Jesse

I don't have a problem with idealizations and it's clear that we're using them in this issue. I didn't want to reply on the other thread in order not to mess up your long post which I will eventually respond to. And I realize that the simultaneous endpoints of a perfectly fitting car are not local events but why does the fact that they're not simultaneous in the car frame solve this apparent paradox? And you'll notice the author I quoted doesn't state exactly what the paradox is. AG 

What I'm saying is that "solving the paradox" requires understanding that despite the disagreement over fit, there is no actual disagreement about local events like the ones I mentioned with rulers and clocks at different positions. But to understand conceptually how it can be possible that they can disagree on fitting but still agree on all details about local events, you really need to look at the way the frames have differing definitions of simultaneity. As I pointed out on the other thread, if you imagine a hypothetical world where there is *no* disagreement over simultaneity but each frame still predicts that objects moving in that frame are Lorentz-contracted, then two frames that make different claims about whether the car fit would automatically *also* be disagreeing over clock readings at some local events.

As for the other author you quoted, that person is dealing with a different version of the car/garage paradox where the car is supposed to instantaneously accelerate to come to rest relative to the garage when the front end reaches the back of the garage, and they're saying that this would lead to different physical scenarios depending on whether all points in the car accelerate simultaneously in the car frame, or if they accelerate simultaneously in the garage frame. In the first scenario the back end of the car will come to rest relative to the garage when it's outside the garage (so the car never fit in either frame) and in the second scenario the back end of the car will come to rest when it's inside the garage (so the car did fit in both frames). This wouldn't be a mere difference between frames as in Brent's scenario where there's no acceleration, these would be two physically different options for how to accelerate the car.

There's nothing in that scenario which models it as accelerating (actually decelerating) to get a perfect fit. In fact, the author states that the car fits in the garage from the garage frame, but not in the garage in the car frame. He then states that simultaneity fails in car frame and this is the alleged solution. At least he seems to agree with my concept of what constitutes a paradox. AG

Wrong. The author does have the car stopping to get a perfect fit, but I don't think this matters. We can assume the car is in constant motion and get the same result re; differerence in simultaneity between frames. AG 

There are different ways of formulating the paradox, and as you seem to acknowledge, the author you linked at http://insti.physics.sunysb.edu/~siegel/sr.html does talk about the car stopping, and notes there are different possible physical scenarios for when the back of the car stops if the front stops when it reaches the back wall (i.e. whether the back of the car stops simultaneously with the front according to the car frame's definition of simultaneity or the garage frame's definition of simultaneity). Of course you can also formulate the paradox in terms of different frames' perspective on a car moving inertially through the garage without stopping as Brent did (that's the way the paradox is usually formulated), but then why did you specifically ask about a page that has a completely different version of the problem? 

That scenario was posted, IIRC, by Quentin, in part his demonstration of how simple the solution, and how stupid I am. I prefer the scenario where the car doesn't cease its motion, and IIUC, the alleged solution is the same, which I don't understand; disagreement about simultaneity. AG 

I also prefer to talk about an inertial scenario with no stopping, so let's drop the discussion of that webpage.

OK. You've stated several times that events are invariant under the LT, and you've defined "event" as a point in spacetime. So, if the moving car fits exactly, what basis you do have for claiming the two events in the garage frame, front and back of car with same time, fail to transform simultaneously under the LT, to the car frame? AND, supposing they do NOT transform simultaneously, what exactly is the apparent paradox you think you are trying to solve, and how is the alleged failure of simultaneity in the car frame, the solution? AG 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

Did you read the comment before the one you are responding to here? I don't understand why you think agreement on local events would have anything to do with simultaneity, I explained why it doesn't there.

I don't understand it, because you keep saying events are invariant using the LT, so if you're transforming two events with the same time labels, I would assume the two events, which are simultaneous in the garage frame, will remain simultaneous in the car frame. Are you claiming that if the car doesn't stop, Brent's model, then there is no failure of simultaneity? I've always thought failue of simultanaeity is alleged to be the solution. If not, then what's the problem we're trying to solve, and its solution? Sorry; I feel totally confused. AG

 

Do you think you can define simultaneity in a way that only refers to facts about what's happening at a single point in space time, with no reference to any relation between that point and any other point in spacetime?

No. Of course not. AG

[Jesse Mazer]

On Sat, Dec 21, 2024 at 4:12 AM Alan Grayson <agrays...@gmail.com> wrote:

On Saturday, December 21, 2024 at 12:41:56 AM UTC-7 Jesse Mazer wrote:

On Sat, Dec 21, 2024 at 1:41 AM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 11:20:30 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 11:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 8:03:38 PM UTC-7 Alan Grayson wrote:

On Friday, December 20, 2024 at 7:47:47 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:53 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote:

On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <agrays...@gmail.com> wrote:

Please define what you mean by local events, with some examples.

I did that in my last two comments on the other thread, the first of which you had said you were going to respond to in more detail. In my second-to-last post see the two paragraphs beginning with the sentence 'But are you asking a different question about what is the motive for demanding that any claims about how things work in different frames needs to pass the test of giving identical local predictions, in order to qualify as good physics?' with the example of the mini bomb and the glass of water, and in my last post see the paragraphs beginning with '"The car fits" or "the car fits" are not statements about local events, i.e. statements about things that happen at a single spacetime point in one of Brent's diagrams'--in that comment I then went on to give examples involving endpoints of the car and garage crossing paths with clock readings and ruler markings given at those specific crossing points in spacetime. Can you re-read those carefully, and if you're still unclear ask follow-up questions to either of those comments?

Note that in these kinds of problems we idealize things like clocks and endpoints of the car as being like point particles that only have a single position coordinate at a single time coordinate (likewise the bomb and the glass of water), which I assume you won't have a problem with if you are willing to similarly idealize the car and garage as 1-dimensional. But if you were to treat clocks etc. as having an extension in space that was tiny compared to the lengths of the car/garage, and passing by the ends of the car garage at a similarly tiny distance, this would differ only negligibly from the idealized calculation of treating them as points.

Jesse

I don't have a problem with idealizations and it's clear that we're using them in this issue. I didn't want to reply on the other thread in order not to mess up your long post which I will eventually respond to. And I realize that the simultaneous endpoints of a perfectly fitting car are not local events but why does the fact that they're not simultaneous in the car frame solve this apparent paradox? And you'll notice the author I quoted doesn't state exactly what the paradox is. AG 

What I'm saying is that "solving the paradox" requires understanding that despite the disagreement over fit, there is no actual disagreement about local events like the ones I mentioned with rulers and clocks at different positions. But to understand conceptually how it can be possible that they can disagree on fitting but still agree on all details about local events, you really need to look at the way the frames have differing definitions of simultaneity. As I pointed out on the other thread, if you imagine a hypothetical world where there is *no* disagreement over simultaneity but each frame still predicts that objects moving in that frame are Lorentz-contracted, then two frames that make different claims about whether the car fit would automatically *also* be disagreeing over clock readings at some local events.

As for the other author you quoted, that person is dealing with a different version of the car/garage paradox where the car is supposed to instantaneously accelerate to come to rest relative to the garage when the front end reaches the back of the garage, and they're saying that this would lead to different physical scenarios depending on whether all points in the car accelerate simultaneously in the car frame, or if they accelerate simultaneously in the garage frame. In the first scenario the back end of the car will come to rest relative to the garage when it's outside the garage (so the car never fit in either frame) and in the second scenario the back end of the car will come to rest when it's inside the garage (so the car did fit in both frames). This wouldn't be a mere difference between frames as in Brent's scenario where there's no acceleration, these would be two physically different options for how to accelerate the car.

There's nothing in that scenario which models it as accelerating (actually decelerating) to get a perfect fit. In fact, the author states that the car fits in the garage from the garage frame, but not in the garage in the car frame. He then states that simultaneity fails in car frame and this is the alleged solution. At least he seems to agree with my concept of what constitutes a paradox. AG

Wrong. The author does have the car stopping to get a perfect fit, but I don't think this matters. We can assume the car is in constant motion and get the same result re; differerence in simultaneity between frames. AG 

There are different ways of formulating the paradox, and as you seem to acknowledge, the author you linked at http://insti.physics.sunysb.edu/~siegel/sr.html does talk about the car stopping, and notes there are different possible physical scenarios for when the back of the car stops if the front stops when it reaches the back wall (i.e. whether the back of the car stops simultaneously with the front according to the car frame's definition of simultaneity or the garage frame's definition of simultaneity). Of course you can also formulate the paradox in terms of different frames' perspective on a car moving inertially through the garage without stopping as Brent did (that's the way the paradox is usually formulated), but then why did you specifically ask about a page that has a completely different version of the problem? 

That scenario was posted, IIRC, by Quentin, in part his demonstration of how simple the solution, and how stupid I am. I prefer the scenario where the car doesn't cease its motion, and IIUC, the alleged solution is the same, which I don't understand; disagreement about simultaneity. AG 

I also prefer to talk about an inertial scenario with no stopping, so let's drop the discussion of that webpage.

OK. You've stated several times that events are invariant under the LT, and you've defined "event" as a point in spacetime.

No, what I've said is invariant are the local physical facts i.e. *things that are physically happening" at a single point in spacetime, like the reading on a physical clock there, or the crossing point of the worldlines of two physical objects like the back of the car and the front of the garage. (In relativity the word 'event' can either be used to refer to a physical point in spacetime and all the physical things that occur there, or it can be used to refer to some specific physical thing happening there like a clock reading) Since you were OK with the idea of "point in spacetime" as a sort of idealized limit of very small finite regions of spacetime, just think of coordinate-invariant statements about the arrangement of particles (like the atoms making up a clock or a ruler or the end of a car, or the photons making up a light ray) that are inside a very small volume in space if you looked at the particles in that region for a very brief moment of time (we could think of this as an 'infinitesimal' region of spacetime). Things like the hand of an analog clock pointing at a particular mark on the clock within that infinitesimal spacetime region, or a set of photons passing through the region that carry an image of some other event that's on the past light cone of that region.

The *coordinates* associated with a point in spacetime in some frame are not part of what I mean by physical events at that point in spacetime, although there may be some physical clock readings and ruler markings that match up with those coordinates, but not all frames will take those clock/ruler readings as "canonical" in terms of defining coordinates.

 

So, if the moving car fits exactly, what basis you do have for claiming the two events in the garage frame, front and back of car with same time, fail to transform simultaneously under the LT, to the car frame?

By "fail to transform simultaneously" do you just mean the idea that two different points in spacetime which are assigned the same time coordinate in one frame are assigned different time coordinates in another frame? If so, see above, time coordinates are not part of what I mean by "physical events".

 

AND, supposing they do NOT transform simultaneously, what exactly is the apparent paradox you think you are trying to solve, and how is the alleged failure of simultaneity in the car frame, the solution? AG 

The paradox is how the two frames can disagree (in coordinate terms) about whether the car fits, and in particular whether the event A="back of car passes front of garage" happens before or after event B="front of car reaches back of garage", and yet they can agree about *all* local physical facts at the point in spacetime where A occurs and at the point in spacetime where B occurs. 

 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

Did you read the comment before the one you are responding to here? I don't understand why you think agreement on local events would have anything to do with simultaneity, I explained why it doesn't there.

I don't understand it, because you keep saying events are invariant using the LT, so if you're transforming two events with the same time labels,

I don't think I used the phrase "events are invariant using the LT". Physical events don't transform at all, only their coordinate labels do. Also, if you don't *already know* what physical events occurred at a particular point in spacetime (for example you don't know what a clock reads there), but you are given a set of initial conditions in each frame (including initial reading on that same clock at time coordinate 0 in the frame), then you can can *derive* a prediction about the physical event in different ways in different frames, using formulas derived from the LT like the time dilation equation (which tells you how fast the physical clock ticks relative to the time coordinate). In that case both frames will end up with the same prediction about the local physical event, but arrived at with different calculations. If you'd like a numerical example of this using initial conditions from Brent's example, just ask and I can provide one.

 

I would assume the two events, which are simultaneous in the garage frame, will remain simultaneous in the car frame.

No, time labels are just that, labels, they are not actual physical events at each point, or in my above alternative formulation, they are not necessary consequences of any specific arrangement of particles that occurs in a tiny region of spacetime. Please look again at what I posted at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/hYkasRQOAgAJ for some of the other physical events that happen at the same point as the event "front of car reaches back of garage" in Brent's example, and then look at my followup question after the quote:

"In Brent's scenario, assume clocks #1 and #3 at the back and front of the car were synchronized in the car's rest frame by the Einstein synchronization procedure, and clocks #2 and #4 at front and back of the garage were synchronized in the garage's rest frame using the synchronization procedure. Also assume the localized event of the back of the car passing the front of the garage coincided with both clock #1 and clock #2 there reading t=0 and t'=0 respectively, and that this happened right next to the x=0 mark on ruler Rc and the x'=0 mark on ruler Rg. All frames agree on these facts, which are exclusively about what happened at a single point in spacetime, namely the point where the back of the car passed the front of the garage. 

Given these assumptions, according to relativity they will *also* agree in all their predictions about a second event, the event of the front of the car reaching the back of the garage. Specifically they will agree that at the same point in spacetime as this second event, all the following are true:

--Clock #3 at the front of the car read t = -7.5
--Clock #4 at the back of the garage read t' = 3.5
--this event of the front of the car reaching the back of the garage coincided with the x=12 mark on ruler Rc
--this event of the front of the car reaching the back of the garage coincided with the x'=10 mark on ruler Rg

There is no disagreement on any of these local facts. The only disagreement is that each observer adopts a different *convention* about which ruler and clocks to treat as canonical for the sake of assigning coordinates--the car rest frame defines time-coordinates by the clocks at rest in the car frame (clocks #1 and #3) and the ruler at rest in the car frame (Rc), while the the garage frame defines time-coordinates by the clocks at rest in the garage frame (clocks #2 and #4) and the ruler at rest in the garage frame (Rg). Based on these conventions, the car observer says the event of the back of the car passing the front of the garage happened AFTER the event of the front of the car reaching the back of the garage, therefore the car never "fit", while the garage observer says the event of the back of the car passing the front of the garage happened BEFORE the event of the front of the car reaching the back of the garage, therefore the car "did" fit. But this is not a disagreement about any of the local facts I mentioned."

In the above example, do you understand that "Clock #3 at the front of the car read t = -7.5" would be a statement not about coordinates but about the actual configuration of particles in the infinitesimal region of the front of the car reaching the back of the garage, i.e. there is a specific collection of atoms we call "Clock #3" and its physical hand is pointing at a physical painted-on marking that reads -7.5? Likewise that "Clock #4 at the back of the garage read t' = 3.5" is a statement not about coordinates but about a second physical clock in this region and which marking its hand is pointing to? If so you can see why looking at these clock readings (and at the readings in the neighborhood of the different event 'back of car passes front of garage', where both clocks read 0) is not sufficient to settle definitively whether this event happens BEFORE or AFTER the event of the back of the car passing the front of the garage. As a matter of coordinate convention, the car frame takes clock #3 as "canonical" for defining time coordinates, while the garage frame takes clock #4 as canonical for defining time coordinates, so they get different answers in spite of agreeing about the physical readings of both clocks in this region.

 

Are you claiming that if the car doesn't stop, Brent's model, then there is no failure of simultaneity? I've always thought failue of simultanaeity is alleged to be the solution. If not, then what's the problem we're trying to solve, and its solution? Sorry; I feel totally confused. AG

No, in terms of the time-coordinates they assign to physical events, the two frames always disagree about simultaneity and in some cases about the order of pairs of events which aren't simultaneous in either frame, like the events A and B above.

 

 

Do you think you can define simultaneity in a way that only refers to facts about what's happening at a single point in space time, with no reference to any relation between that point and any other point in spacetime?

No. Of course not. AG

OK, that's why statements about simultaneity are not statements about local physical events.

Jesse

 

 

If you think you can, tell me what specific local facts you are referring to, given a particular choice of point in spacetime (say, the point where the worldline of the back of the car crosses the worldline of the front of the garage).

Jesse 

so it's just the same physical scenario described in different coordinate systems; in the version on the website you need to consider simultaneity for a very different reason, because it's specified that the car's back end can stop simultaneously with the front end in either the car frame and the garage frame, resulting in genuinely different physical scenarios.

      

            Jesse 

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[Alan Grayson]

You seem to offer ambiguous definitions of "events" which are frame independent, like the reading of a clock. I am not claiming time labels as such are frame independent. I plan to spend some time reading your long statement below. In the meantime, since you affirm disagreement about simultaneity is the solution to the apparent paradox, please define exactly what paradox you are trying to solve. In my analysis using length contraction, we have the car fitting in garage frame, but not in car frame. Anything wrong with just accepting this result? If not, why not? How exactly does disagreement about simultaneity solve the paradox, whatever it is? TY, AG

 

or the crossing point of the worldlines of two physical objects like the back of the car and the front of the garage. (In relativity the word 'event' can either be used to refer to a physical point in spacetime and all the physical things that occur there, or it can be used to refer to some specific physical thing happening there like a clock reading) Since you were OK with the idea of "point in spacetime" as a sort of idealized limit of very small finite regions of spacetime, just think of coordinate-invariant statements about the arrangement of particles (like the atoms making up a clock or a ruler or the end of a car, or the photons making up a light ray) that are inside a very small volume in space if you looked at the particles in that region for a very brief moment of time (we could think of this as an 'infinitesimal' region of spacetime). Things like the hand of an analog clock pointing at a particular mark on the clock within that infinitesimal spacetime region, or a set of photons passing through the region that carry an image of some other event that's on the past light cone of that region.

The *coordinates* associated with a point in spacetime in some frame are not part of what I mean by physical events at that point in spacetime, although there may be some physical clock readings and ruler markings that match up with those coordinates, but not all frames will take those clock/ruler readings as "canonical" in terms of defining coordinates.

 

So, if the moving car fits exactly, what basis you do have for claiming the two events in the garage frame, front and back of car with same time, fail to transform simultaneously under the LT, to the car frame?

By "fail to transform simultaneously" do you just mean the idea that two different points in spacetime which are assigned the same time coordinate in one frame are assigned different time coordinates in another frame?

Not exactly. I'm thinking of measurable time, such as the same time the front of car reaches end of garage, and back of car reach the front of garage. (from pov of garage frame). These events seem to satisfy your definition of simultaneous events, and your claim that they are frame independent under the LT. If so, since they must transform frame-independent using the LT, I don't see how they could yield any disagreement in simultaneity, which seems to be required to solve the paradox, whatever it might be. AG

 

If so, see above, time coordinates are not part of what I mean by "physical events".

 

AND, supposing they do NOT transform simultaneously, what exactly is the apparent paradox you think you are trying to solve, and how is the alleged failure of simultaneity in the car frame, the solution? AG 

The paradox is how the two frames can disagree (in coordinate terms) about whether the car fits, and in particular whether the event A="back of car passes front of garage" happens before or after event B="front of car reaches back of garage", and yet they can agree about *all* local physical facts at the point in spacetime where A occurs and at the point in spacetime where B occurs. 

 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

Did you read the comment before the one you are responding to here? I don't understand why you think agreement on local events would have anything to do with simultaneity, I explained why it doesn't there.

I don't understand it, because you keep saying events are invariant using the LT, so if you're transforming two events with the same time labels,

I don't think I used the phrase "events are invariant using the LT". Physical events don't transform at all, only their coordinate labels do.

OK, so if the time labels represent the measured time of physical events, they will transform simultaneously under the LT. But then how can you use failure of simultaneity to solve the paradox? Did Brent affirm or deny failure of simultaneity to "solve" the paradox? AG 

Also, if you don't *already know* what physical events occurred at a particular point in spacetime (for example you don't know what a clock reads there), but you are given a set of initial conditions in each frame (including initial reading on that same clock at time coordinate 0 in the frame), then you can can *derive* a prediction about the physical event in different ways in different frames, using formulas derived from the LT like the time dilation equation (which tells you how fast the physical clock ticks relative to the time coordinate). In that case both frames will end up with the same prediction about the local physical event, but arrived at with different calculations. If you'd like a numerical example of this using initial conditions from Brent's example, just ask and I can provide one.

 

I would assume the two events, which are simultaneous in the garage frame, will remain simultaneous in the car frame.

No, time labels are just that, labels, they are not actual physical events at each point, or in my above alternative formulation, they are not necessary consequences of any specific arrangement of particles that occurs in a tiny region of spacetime. Please look again at what I posted at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/hYkasRQOAgAJ for some of the other physical events that happen at the same point as the event "front of car reaches back of garage" in Brent's example, and then look at my followup question after the quote:

"In Brent's scenario, assume clocks #1 and #3 at the back and front of the car were synchronized in the car's rest frame by the Einstein synchronization procedure, and clocks #2 and #4 at front and back of the garage were synchronized in the garage's rest frame using the synchronization procedure. Also assume the localized event of the back of the car passing the front of the garage coincided with both clock #1 and clock #2 there reading t=0 and t'=0 respectively, and that this happened right next to the x=0 mark on ruler Rc and the x'=0 mark on ruler Rg. All frames agree on these facts, which are exclusively about what happened at a single point in spacetime, namely the point where the back of the car passed the front of the garage. 

Given these assumptions, according to relativity they will *also* agree in all their predictions about a second event, the event of the front of the car reaching the back of the garage. Specifically they will agree that at the same point in spacetime as this second event, all the following are true:

So we have front and back of car satisfying simultaneity, as real events, and using the LT the transformed event to the car frame, are not simultaneous? AG

 

--Clock #3 at the front of the car read t = -7.5
--Clock #4 at the back of the garage read t' = 3.5
--this event of the front of the car reaching the back of the garage coincided with the x=12 mark on ruler Rc
--this event of the front of the car reaching the back of the garage coincided with the x'=10 mark on ruler Rg

There is no disagreement on any of these local facts. The only disagreement is that each observer adopts a different *convention* about which ruler and clocks to treat as canonical for the sake of assigning coordinates--the car rest frame defines time-coordinates by the clocks at rest in the car frame (clocks #1 and #3) and the ruler at rest in the car frame (Rc), while the the garage frame defines time-coordinates by the clocks at rest in the garage frame (clocks #2 and #4) and the ruler at rest in the garage frame (Rg). Based on these conventions, the car observer says the event of the back of the car passing the front of the garage happened AFTER the event of the front of the car reaching the back of the garage, therefore the car never "fit", while the garage observer says the event of the back of the car passing the front of the garage happened BEFORE the event of the front of the car reaching the back of the garage, therefore the car "did" fit. But this is not a disagreement about any of the local facts I mentioned."

In the above example, do you understand that "Clock #3 at the front of the car read t = -7.5" would be a statement not about coordinates but about the actual configuration of particles in the infinitesimal region of the front of the car reaching the back of the garage, i.e. there is a specific collection of atoms we call "Clock #3" and its physical hand is pointing at a physical painted-on marking that reads -7.5? Likewise that "Clock #4 at the back of the garage read t' = 3.5" is a statement not about coordinates but about a second physical clock in this region and which marking its hand is pointing to? If so you can see why looking at these clock readings (and at the readings in the neighborhood of the different event 'back of car passes front of garage', where both clocks read 0) is not sufficient to settle definitively whether this event happens BEFORE or AFTER the event of the back of the car passing the front of the garage. As a matter of coordinate convention, the car frame takes clock #3 as "canonical" for defining time coordinates, while the garage frame takes clock #4 as canonical for defining time coordinates, so they get different answers in spite of agreeing about the physical readings of both clocks in this region.

 

Are you claiming that if the car doesn't stop, Brent's model, then there is no failure of simultaneity? I've always thought failue of simultanaeity is alleged to be the solution. If not, then what's the problem we're trying to solve, and its solution? Sorry; I feel totally confused. AG

No, in terms of the time-coordinates they assign to physical events, the two frames always disagree about simultaneity and in some cases about the order of pairs of events which aren't simultaneous in either frame, like the events A and B above. 

Do you see how this can be confusing? You now claim the two events, with time measured in garage frame when car fits perfectly in garage, don't transform simultaneously, when previously you asserted they DO, under the LT? AG

[Jesse Mazer]

Just calling it ambiguous without explaining why you find it ambiguous isn't helpful. What is ambiguous about the notion of local physical facts that are about configurations of particles in a small local region of spacetime? 

 

I am not claiming time labels as such are frame independent. I plan to spend some time reading your long statement below. In the meantime, since you affirm disagreement about simultaneity is the solution to the apparent paradox, please define exactly what paradox you are trying to solve. In my analysis using length contraction, we have the car fitting in garage frame, but not in car frame. Anything wrong with just accepting this result? If not, why not? How exactly does disagreement about simultaneity solve the paradox, whatever it is? TY, AG

You have already asked this question about why we need to go beyond length contraction a bunch of times and I've answered a bunch of times: the paradox lies in the idea that a disagreement in predictions about whether the car fits would naively *seem* to imply genuine physical contradiciton i.e. different predictions about local physical facts as defined above, but an analysis involving simultaneity can show this isn't the case. I'll copy and paste my answer from https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/p5wwz5C5AQAJ (an answer you didn't really address in your response), and which was itself copying and pasting from some earlier posts:

I have already explained the point here is pedagogical (in several other posts that you never responded to--I think it would help the discussion if you would respond to every post where I ask you a question, instead of taking a sporadic approach). Here was what I said in the first post where I made this point:

'The reason physicists bother to talk about a hypothetical scenario like this is pedagogical, they want to get students to think about situations where the perspective of different frames might *seem* to lead to real physical contradictions, and then looking at it more closely they'll understand how the "real" physical predictions in relativity are always about local events, and that by considering different definitions of simultaneity we can show the two frames do agree about all local events on rulers and clocks.
Do you disagree with my point that if different frames *didn't* have differing definitions of simultaneity, it would be impossible for the two frames to disagree about whether the car or garage was shorter without this leading to conflicting predictions about local events, like what the clocks mounted to front and back of the car will read at the instant they pass clocks attached to the front and back of the garage?'

And in a later post, I elaborated on why differences in simultaneity are critical to avoiding contradictory predictions about localized physical events:

'In an imaginary alternative physics where different frames had no disagreement about simultaneity but different observers still all believed the length contraction equation should apply in their frame, then this would be a genuine paradox/physical contradiction, because different frames would end up making different predictions about local events. Think about it this way--if there were no disagreement about simultaneity, there could be no disagreement about the *order* of any two events (this would be the case even if observers predicted moving clocks run slow like in relativity). But if observer #1 thinks the car is shorter than the garage, he will predict the event A (the back of the car passing the front of the garage) happens before event B (the front of the car reaches the back of the garage), and if observer #2 thinks the car is longer than the garage, he will predict B happens before A. If there were no disagreement about simultaneity this would lead them to different predictions about readings on synchronized clocks at the front and back of the car/garage at the moment of those events, specifically whether the clock at A would show a greater or lesser time than the clock at B.'

 

 

or the crossing point of the worldlines of two physical objects like the back of the car and the front of the garage. (In relativity the word 'event' can either be used to refer to a physical point in spacetime and all the physical things that occur there, or it can be used to refer to some specific physical thing happening there like a clock reading) Since you were OK with the idea of "point in spacetime" as a sort of idealized limit of very small finite regions of spacetime, just think of coordinate-invariant statements about the arrangement of particles (like the atoms making up a clock or a ruler or the end of a car, or the photons making up a light ray) that are inside a very small volume in space if you looked at the particles in that region for a very brief moment of time (we could think of this as an 'infinitesimal' region of spacetime). Things like the hand of an analog clock pointing at a particular mark on the clock within that infinitesimal spacetime region, or a set of photons passing through the region that carry an image of some other event that's on the past light cone of that region.

The *coordinates* associated with a point in spacetime in some frame are not part of what I mean by physical events at that point in spacetime, although there may be some physical clock readings and ruler markings that match up with those coordinates, but not all frames will take those clock/ruler readings as "canonical" in terms of defining coordinates.

 

So, if the moving car fits exactly, what basis you do have for claiming the two events in the garage frame, front and back of car with same time, fail to transform simultaneously under the LT, to the car frame?

By "fail to transform simultaneously" do you just mean the idea that two different points in spacetime which are assigned the same time coordinate in one frame are assigned different time coordinates in another frame?

Not exactly. I'm thinking of measurable time, such as the same time the front of car reaches end of garage, and back of car reach the front of garage. (from pov of garage frame). These events seem to satisfy your definition of simultaneous events, and your claim that they are frame independent under the LT. If so, since they must transform frame-independent using the LT, I don't see how they could yield any disagreement in simultaneity, which seems to be required to solve the paradox, whatever it might be. AG

As I illustrate in my longer numerical example of local events which you say you're going to address in a future post, in the same local region of spacetime where the front of the car reaches the back of the garage you have two *different* clock readings, on clock #3 at the front of the car and clock #4 at the back of the garage, each of which had previously been synchronized with the clocks at the back of the car and the front of the garage using the Einstein synchronization procedure, used in the car rest frame to synchronize the two car clocks and used in the garage rest frame to synchronize the two garage clocks. Both the clocks at the back of the car and the front of the garage read 0 when they passed each other, but when the clock at the front of the car reaches the back of the garage, the car clock in that local region read -7.5 and the garage clock in the same local region read 3.5. So, without arbitrarily picking one set of clocks as canonical and discarding the other readings (i.e. picking which to use to define a frame-dependent notion of time), how are you supposed to get any definite statement about the "measurable time" between the local event of the back of the car passing the front of the garage and the local event of the front of the car reaching the back of the garage? Do you think the "measurable time" here would be -7.5 or 3.5 or neither?

 

 

If so, see above, time coordinates are not part of what I mean by "physical events".

 

AND, supposing they do NOT transform simultaneously, what exactly is the apparent paradox you think you are trying to solve, and how is the alleged failure of simultaneity in the car frame, the solution? AG 

The paradox is how the two frames can disagree (in coordinate terms) about whether the car fits, and in particular whether the event A="back of car passes front of garage" happens before or after event B="front of car reaches back of garage", and yet they can agree about *all* local physical facts at the point in spacetime where A occurs and at the point in spacetime where B occurs. 

 

In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events,

But if frames agree on local events, an event being defined as a position and time in spacetime, there can be no violation of simultaneity. AG

Did you read the comment before the one you are responding to here? I don't understand why you think agreement on local events would have anything to do with simultaneity, I explained why it doesn't there.

I don't understand it, because you keep saying events are invariant using the LT, so if you're transforming two events with the same time labels,

I don't think I used the phrase "events are invariant using the LT". Physical events don't transform at all, only their coordinate labels do.

OK, so if the time labels represent the measured time of physical events, they will transform simultaneously under the LT.

See above, there are no local physical facts which represent "measured time" in some way that's independent of a convention about which set of physical clocks to treat as canonical. The only local physical facts are the clock readings themselves, which can differ in the same local region of spacetime, if you're looking at clocks in motion to each other which are part of sets that have been previously synchronized by the Einstein convention in their rest frames.

 

But then how can you use failure of simultaneity to solve the paradox? Did Brent affirm or deny failure of simultaneity to "solve" the paradox? AG 

Also, if you don't *already know* what physical events occurred at a particular point in spacetime (for example you don't know what a clock reads there), but you are given a set of initial conditions in each frame (including initial reading on that same clock at time coordinate 0 in the frame), then you can can *derive* a prediction about the physical event in different ways in different frames, using formulas derived from the LT like the time dilation equation (which tells you how fast the physical clock ticks relative to the time coordinate). In that case both frames will end up with the same prediction about the local physical event, but arrived at with different calculations. If you'd like a numerical example of this using initial conditions from Brent's example, just ask and I can provide one.

 

I would assume the two events, which are simultaneous in the garage frame, will remain simultaneous in the car frame.

No, time labels are just that, labels, they are not actual physical events at each point, or in my above alternative formulation, they are not necessary consequences of any specific arrangement of particles that occurs in a tiny region of spacetime. Please look again at what I posted at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/hYkasRQOAgAJ for some of the other physical events that happen at the same point as the event "front of car reaches back of garage" in Brent's example, and then look at my followup question after the quote:

"In Brent's scenario, assume clocks #1 and #3 at the back and front of the car were synchronized in the car's rest frame by the Einstein synchronization procedure, and clocks #2 and #4 at front and back of the garage were synchronized in the garage's rest frame using the synchronization procedure. Also assume the localized event of the back of the car passing the front of the garage coincided with both clock #1 and clock #2 there reading t=0 and t'=0 respectively, and that this happened right next to the x=0 mark on ruler Rc and the x'=0 mark on ruler Rg. All frames agree on these facts, which are exclusively about what happened at a single point in spacetime, namely the point where the back of the car passed the front of the garage. 

Given these assumptions, according to relativity they will *also* agree in all their predictions about a second event, the event of the front of the car reaching the back of the garage. Specifically they will agree that at the same point in spacetime as this second event, all the following are true:

So we have front and back of car satisfying simultaneity, as real events, and using the LT the transformed event to the car frame, are not simultaneous? AG

I don't understand what "So we have front and back of the car satisfying simultaneity, as real events" means. Front and back of the car describe worldlines that pass through many different events/points in spacetime, if you are talking about two specific events on the wordlines of front and back, which ones do you mean? And the statement of mine you are responding to said nothing about simultaneity so I don't know why you wrote "So" in response to what I wrote. Were you referring to the part where I talked about clocks and front and back of car and garage being synchronized by the Einstein synchronization procedure? If so, the Einstein procedure itself only "synchronizes" clocks in a frame-dependent way, you synchronize two clocks at rest relative to each other by assuming the time for light to travel from clock A to clock B must be the same as the time for the light to travel from B to A, that's true in the clocks' rest frame but other frames where the clocks are in motion say these two light travel times are *not* equal, so setting the time on the two clocks with this assumption leads them to be synchronized in the time coordinates of their rest frame but out-of-synch in the time coordinates of other frames.

 

 

--Clock #3 at the front of the car read t = -7.5
--Clock #4 at the back of the garage read t' = 3.5
--this event of the front of the car reaching the back of the garage coincided with the x=12 mark on ruler Rc
--this event of the front of the car reaching the back of the garage coincided with the x'=10 mark on ruler Rg

There is no disagreement on any of these local facts. The only disagreement is that each observer adopts a different *convention* about which ruler and clocks to treat as canonical for the sake of assigning coordinates--the car rest frame defines time-coordinates by the clocks at rest in the car frame (clocks #1 and #3) and the ruler at rest in the car frame (Rc), while the the garage frame defines time-coordinates by the clocks at rest in the garage frame (clocks #2 and #4) and the ruler at rest in the garage frame (Rg). Based on these conventions, the car observer says the event of the back of the car passing the front of the garage happened AFTER the event of the front of the car reaching the back of the garage, therefore the car never "fit", while the garage observer says the event of the back of the car passing the front of the garage happened BEFORE the event of the front of the car reaching the back of the garage, therefore the car "did" fit. But this is not a disagreement about any of the local facts I mentioned."

In the above example, do you understand that "Clock #3 at the front of the car read t = -7.5" would be a statement not about coordinates but about the actual configuration of particles in the infinitesimal region of the front of the car reaching the back of the garage, i.e. there is a specific collection of atoms we call "Clock #3" and its physical hand is pointing at a physical painted-on marking that reads -7.5? Likewise that "Clock #4 at the back of the garage read t' = 3.5" is a statement not about coordinates but about a second physical clock in this region and which marking its hand is pointing to? If so you can see why looking at these clock readings (and at the readings in the neighborhood of the different event 'back of car passes front of garage', where both clocks read 0) is not sufficient to settle definitively whether this event happens BEFORE or AFTER the event of the back of the car passing the front of the garage. As a matter of coordinate convention, the car frame takes clock #3 as "canonical" for defining time coordinates, while the garage frame takes clock #4 as canonical for defining time coordinates, so they get different answers in spite of agreeing about the physical readings of both clocks in this region.

 

Are you claiming that if the car doesn't stop, Brent's model, then there is no failure of simultaneity? I've always thought failue of simultanaeity is alleged to be the solution. If not, then what's the problem we're trying to solve, and its solution? Sorry; I feel totally confused. AG

No, in terms of the time-coordinates they assign to physical events, the two frames always disagree about simultaneity and in some cases about the order of pairs of events which aren't simultaneous in either frame, like the events A and B above. 

Do you see how this can be confusing? You now claim the two events, with time measured in garage frame when car fits perfectly in garage, don't transform simultaneously, when previously you asserted they DO, under the LT? AG

I never asserted that they do "transform simultaneously" in terms of time coordinates (and simultaneity is a purely coordinate-dependent notion), I just said that readings on each clock in the local neighborhood of a given event are agreed by all observers. But different observers disagree on which local clocks to treat as canonical for the sake of defining a time coordinate, and since they pick different local clocks they get different conclusions about the time coordinate (like -7.5 vs. 3.5 above).

Jesse

 

 

Do you think you can define simultaneity in a way that only refers to facts about what's happening at a single point in space time, with no reference to any relation between that point and any other point in spacetime?

No. Of course not. AG

OK, that's why statements about simultaneity are not statements about local physical events.

Jesse 

 

If you think you can, tell me what specific local facts you are referring to, given a particular choice of point in spacetime (say, the point where the worldline of the back of the car crosses the worldline of the front of the garage).

Jesse 

so it's just the same physical scenario described in different coordinate systems; in the version on the website you need to consider simultaneity for a very different reason, because it's specified that the car's back end can stop simultaneously with the front end in either the car frame and the garage frame, resulting in genuinely different physical scenarios.

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[Alan Grayson]

To be perfectly candid, I don't understand most of your comments above, but I will study them much more, hopefully to change this situation. So it's not necessary to repeat them again. But what can enlighten me is if you would directly answer a few questions I have about the problem at hand.  Firstly, using Einstein's synchronization method, if we assume the car perfectly fits in the garage, and clocks in the garage frame are synchronized, can we assume the front and back end of car are synchronized in the garage frame? If so, is the proposed solution of the paradox the fact that these events are NOT synchronized in the car frame? Yes or No? If this is how the solution is modeled, what EXACTLY is the problem this lack of synchronization in the car frame is supposed to resolve? That is, what EXACTLY is the paradox that you think you're resolving by relying on lack of synchronization in the car frame, when the front and rear end events of the car are synchronized in the garage frame? TY, AG 

[Jesse Mazer]

I don't understand what it means to say "front and back end of car are synchronized". Are you referring to a scenario like what I described where there are clocks attached to the front and back of the car (at rest relative to the car), which have been synchronized in the car's rest frame using the Einstein synchronization method? If so, the answer is no, these two clocks will *not* be synchronized in the garage frame. On the other hand, if you are considering a scenario where the car fits exactly from the perspective of the garage frame, are you just asking whether the event A="back of car passes front of garage" and the event B="front of car passes back of garage" are these events A and B simultaneous in the garage frame (ignoring the issue of what the car's own clocks read in the local neighborhood A and B)? If so, yes, this would be the definition of what it means for the car to fit exactly in the garage frame. Or did you mean something different than either of these?

 

If so, is the proposed solution of the paradox the fact that these events are NOT synchronized in the car frame? Yes or No?

If you meant the latter, i.e. the events A and B are simultaneous in the garage frame, then yes, it's essential to the resolution of the paradox to notice these events are non-simultaneous in the car frame.

 

If this is how the solution is modeled, what EXACTLY is the problem this lack of synchronization in the car frame is supposed to resolve? That is, what EXACTLY is the paradox that you think you're resolving by relying on lack of synchronization in the car frame, when the front and rear end events of the car are synchronized in the garage frame? TY, AG 

Why do you keep asking the exact same question? See the section of my previous post on this thread starting with "You have already asked this question about why we need to go beyond length contraction a bunch of times and I've answered a bunch of times: the paradox lies in the idea that a disagreement in predictions about whether the car fits would naively *seem* to imply genuine physical contradiction i.e. different predictions about local physical facts as defined above, but an analysis involving simultaneity can show this isn't the case." I also copy and pasted a more detailed argument from a previous post where I explained why, in a hypothetical world where different observers did *not* disagree about simultaneity but still had different predictions to the question of whether the car fits, this would *necessarily* lead them to different predictions about local physical facts like clock readings. If you have questions/criticisms you can follow up by responding to that, but asking me the same question over and over and then never addressing the answer I give you isn't going to get us anywhere.

Jesse

[Alan Grayson]

OK. I now have a clearer understanding of your position in this matter. Fundamentally, there are two contrary views; whether length contraction OR disagreement about simultaneity should inform us about reality. In your view, in effect, the analysis leading to a paradox, length contraction, even though it depends on the LT, should be regarded as "naive", because, presumably, it establishes that relativity is a flawed theory. What principle, if any, determines your choice? AG  

[Jesse Mazer]

Where are you getting that? Obviously relativity involves both without contradiction, they are both directly derivable from the LT. My point is that if someone understands that each frame predicts length contraction but they do *not* also understand the relativity of simultaneity, they may naively be led to the view that the two frames predict contradictory things about local physical facts. Go back and read the post I referenced above if you don't understand why.

 

In your view, in effect, the analysis leading to a paradox, length contraction, even though it depends on the LT, should be regarded as "naive", because, presumably, it establishes that relativity is a flawed theory.

What I referred to as naive is the assumption of length contraction without relativity of simultaneity, which would *not* be what you'd get from the LT. There is no similar flaw (or genuine as opposed to apparent paradox) when you assume both together, which is how special relativity works.

Are you in fact confident that relativity leads to contradictory predictions about local physical facts? Or is it that you're not sure, or maybe even inclined to trust the judgment of generations of physicists and physics students who have studied such scenarios and think no such contradictions about local facts are possible in SR, but your position is that "relativity is a flawed theory" *even if* all frames make consistent predictions about local physical facts?

Jesse

[Jesse Mazer]

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

--In both frames, set the origin of our coordinate system to be the point where the back of the car passes the front of the garage--then that point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and t' = 0 in the car frame.

--In the garage frame, at t = 0 the front of the car is at the same position as the back of the garage, at position x = 20, so that's the position and time of the event of the front of the car passing the back of the garage in the garage frame.

--In the car frame, at t' = 0 the back of the garage must be at x' = 16 (since we know the front of the garage is at position x' = 0 at time t'=0, and using Lorentz contraction in the car frame we know the garage has length 16 in this frame), and the front of the car is at rest at x' = 25, so a distance of 25-16 = 9 from the back of the garage, which in this frame has already passed the front of the car at that moment.

--If the back of the garage is moving at 0.6c in the -x' direction and at t' = 0 is now a distance 9 away from the front of the car, we can conclude that in this frame it must have passed the front of the car at 9/0.6 = 15 nanoseconds earlier. So at t' = -15 in the car frame, the back of the garage was at the same position as the front of the car, which has a fixed position of x' = 25 in the car frame. 

--Since all the car clocks are synched to coordinate time t' in the car frame, this tells us that when the front of the car was passing the back of the garage, the clock at the front of the car showed a reading of -15 nanoseconds.

--And this prediction about the reading on the clock at the front of car when it passes the back of the garage, which was calculated above just using the garage's contracted length and velocity combined with the idea that the front of the garage was at position x' = 0 at time t' = 0 in the car frame, matches up with what you'd get if you instead used the LT to calculate the answer, using the knowledge that in the garage frame, the front of the car was at position x = 20 at time t = 0. If you apply the LT equation t' = gamma*(t - vx/c^2) here, you get t' = 1.25*(0 - 0.6*20) = -15. So, it all works out consistently.

Jesse

[Alan Grayson]

The apparent paradox starts in the rest frame where the car has greater length than the garage. No one doubts the car will NOT fit in the garage given these initial conditions. Now, with the car moving, using the LT, in the garage frame the car's length can go arbitrarily close to zero as the car's velocity approaches c, while the length of the garage remains unchanged. So, at this point in the analysis, everyone is in agreement that the car can, and will easily fit in the garage for large enough velocity. This, in effect, absent other considerations, shows a flaw in SR. However, disagreement about simultaneity appears to come to the rescue. But why does it supercede the results of length contraction? Is it because we're modeling the situation that requires the car to perfectly fit in the garage from the garage frame at the same time as viewed from the car frame? I can't claim to be sure of what's going on here, but I don't think a flaw in relativity can be absolutely ruled out. AG

[Alan Grayson]

Note: I was writing the above while you posted your prior comment, which I will study carefully. AG

[Jesse Mazer]

Why? What's the flaw is saying that if the car's length as seen in the garage frame is different depending on its velocity in that frame, the question of whether it fits in a garage can change depending on its velocity too? Even people who naively think there's a flaw in relativity usually argue this based on considering that *both* observers are supposed to see things moving relative to themselves contracted, so they disagree about which of the two objects is experiencing contraction. Are you suggesting above that even if we don't consider the perspective of the car observer at all, the mere fact that the answer to "does the car fit" changes in the garage frame depending on whether the car is at rest or moving in the garage frame would indicate a flaw?

 

However, disagreement about simultaneity appears to come to the rescue. But why does it supercede the results of length contraction?

It doesn't supercede it at all, as I said above they both work together.

 

Is it because we're modeling the situation that requires the car to perfectly fit in the garage from the garage frame at the same time as viewed from the car frame? I can't claim to be sure of what's going on here, but I don't think a flaw in relativity can be absolutely ruled out. AG

OK, does this mean your answer to my question "Are you in fact confident that relativity leads to contradictory predictions about local physical facts?" would be something like "no, I'm not confident, but I'm not confident such a contradiction can be absolutely ruled out"? Or when you say "I don't think a flaw in relativity can be absolutely ruled out", are you talking about some kind of flaw distinct from a disagreement about local physical facts like clock readings?

Jesse

[Alan Grayson]

I can't answer your questions until I fully understand your numerical example in your last post. I have always been agnostic on whether SR is flawed. Ostensibly, it seems inconsistent, but I can't rule out the opposite, that it is consistent. AG 

[Alan Grayson]

Sorry, that was VERY wrong.  I mis-stated. I meant that the easy fit in the garage from the pov of the garage frame, ostensibly contradicts the view from the car frame, that the car cannot fit in the garage since the garage length contracts. AG 

Even people who naively think there's a flaw in relativity usually argue this based on considering that *both* observers are supposed to see things moving relative to themselves contracted, so they disagree about which of the two objects is experiencing contraction. Are you suggesting above that even if we don't consider the perspective of the car observer at all, the mere fact that the answer to "does the car fit" changes in the garage frame depending on whether the car is at rest or moving in the garage frame would indicate a flaw?

 

However, disagreement about simultaneity appears to come to the rescue. But why does it supercede the results of length contraction?

It doesn't supercede it at all, as I said above they both work together.

 

Is it because we're modeling the situation that requires the car to perfectly fit in the garage from the garage frame at the same time as viewed from the car frame? I can't claim to be sure of what's going on here, but I don't think a flaw in relativity can be absolutely ruled out. AG

OK, does this mean your answer to my question "Are you in fact confident that relativity leads to contradictory predictions about local physical facts?" would be something like "no, I'm not confident, but I'm not confident such a contradiction can be absolutely ruled out"? Or when you say "I don't think a flaw in relativity can be absolutely ruled out", are you talking about some kind of flaw distinct from a disagreement about local physical facts like clock readings?

I'm still not absolutely clear what you mean by "local physical facts". I think SR suggests contrary predictions about local physical facts, that is, the two frames disagree about whether the car fits or not. AG

Jesse

[Alan Grayson]

I am not confident that such a contradiction can be categorically denied. It's unlikely, given the history of experts studying this problem, but neither can I absolutely rely on their judgements. I hope to resolve this issue for myself, in our discussions. AG 

Jesse

[Jesse Mazer]

Earlier you said you found my definition "ambiguous" but didn't elaborate on what you found ambiguous about it, now you're doing the same thing by saying you're "still not absolutely clear" but saying nothing about what you find unclear. What is unclear about the notion of facts which just concern configurations of matter/energy in a tiny neighborhood of space and time around a single point in spacetime? (We can also just refer to physical facts about that exact point, if you allow idealizations like clocks and ruler markings which are point particles and can occupy exactly the same point in spacetime as some other point event like the crossing-point of the worldlines of back of car and front of garage...you said you were OK with such idealizations, but if we wish to speak less ideally we can just say that disagreement between frames about what's happening in the neighborhood of a point approaches zero in the limit as the size of the neighborhood in spacetime approaches zero.) If you want to continue to assert this is unclear/ambiguous you have to at least ask some followup questions, and give examples of facts where you think it's not straightforward to give a yes/no answer about whether it would be a "local physical fact" in this sense.

Earlier on this thread I asked "Do you think you can define simultaneity in a way that only refers to facts about what's happening at a single point in space time, with no reference to any relation between that point and any other point in spacetime?" And you answered "No. Of course not." So in that case it seems like you did understand my notion of "facts about what's happening at a single point in space time" well enough to answer, what has changed for you?

Jesse

[Alan Grayson]

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

  |  - In both frames, set the origin of our coordinate system to be the point where the back of the car passes the front of the garage--then that point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and t' = 0 in the car frame. 

OK.

--In the garage frame, at t = 0 the front of the car is at the same position as the back of the garage, at position x = 20, so that's the position and time of the event of the front of the car passing the back of the garage in the garage frame. 

OK. 

     --In the car frame, at t' = 0 the back of the garage must be at x' = 16 (since we know the front of the garage is at position x' = 0 at time     t'=0, and using Lorentz contraction in the car frame we know the garage has length 16 in this frame), and the front of the car is at rest at x' = 25, so a distance of 25-16 = 9 from the back of the garage, which in this frame has already passed the front of the car at that moment. 

?

--If the back of the garage is moving at 0.6c in the -x' direction and at t' = 0 is now a distance 9 away from the front of the car, we can conclude that in this frame it must have passed the front of the car at 9/0.6 = 15 nanoseconds earlier. So at t' = -15 in the car frame, the back of the garage was at the same position as the front of the car, which has a fixed position of x' = 25 in the car frame.  

 

?

--Since all the car clocks are synched to coordinate time t' in the car frame, this tells us that when the front of the car was passing the back of the garage, the clock at the front of the car showed a reading of -15 nanoseconds. 

 

 ?

--And this prediction about the reading on the clock at the front of car when it passes the back of the garage, which was calculated above just using the garage's contracted length and velocity combined with the idea that the front of the garage was at position x' = 0 at time t' = 0 in the car frame, matches up with what you'd get if you instead used the LT to calculate the answer, using the knowledge that in the garage frame, the front of the car was at position x = 20 at time t = 0. If you apply the LT equation t' = gamma*(t - vx/c^2) here, you get t' = 1.25*(0 - 0.6*20) = -15. So, it all works out consistently.

 ?

Jesse

Perhaps you can rewrite the text on the sections I don't follow. About ambiguities in your defintion of local events, I was referring to the comparison of a spacetime event which is transformed to another frame using the LT.  Is the transformed event also local? AG

[Jesse Mazer]

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

  |  - In both frames, set the origin of our coordinate system to be the point where the back of the car passes the front of the garage--then that point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and t' = 0 in the car frame. 

OK.

--In the garage frame, at t = 0 the front of the car is at the same position as the back of the garage, at position x = 20, so that's the position and time of the event of the front of the car passing the back of the garage in the garage frame. 

OK. 

     --In the car frame, at t' = 0 the back of the garage must be at x' = 16 (since we know the front of the garage is at position x' = 0 at time     t'=0, and using Lorentz contraction in the car frame we know the garage has length 16 in this frame), and the front of the car is at rest at x' = 25, so a distance of 25-16 = 9 from the back of the garage, which in this frame has already passed the front of the car at that moment. 

?

You agreed above that in the car frame, the front of the garage was at position x' = 0 at time t' = 0, yes? And you also agreed that in the car frame, the garage has length 16, yes? So why would you have any doubt that if the front end of the garage is at position x' = 0 at time t' = 0 in the car frame, then the back end must be at position x' = 16 at the same time t' = 0 in the car frame? That's just what "length" in a given frame means, the distance between the two ends of an object at a single moment in time in that frame. To put it another way, if this was just a classical 1D problem and I told you a rod had length 16 and at t' = 0 the front end was at position x' = 0, and it was moving in the -x direction, would you have any doubt the back end would be at x' = 16 at the same moment?

Or do you agree that this is straightforward, but have questions about why the front of the car would be at rest at x' = 25 (this also seems straightforward since you agreed its back end is at x' = 0 and its length is 25)? Or why, granted the back end of the garage is at x' = 16 and the front end of the car is at x' = 25 at this moment, the distance between them at this moment must be 9?

Please clarify your confusion on this sentence, and if we can straighten it out we can move on to your next "?"

 

About ambiguities in your defintion of local events, I was referring to the comparison of a spacetime event which is transformed to another frame using the LT.  Is the transformed event also local? AG

If you already know the local physical facts at a given point in spacetime (like a physical clock reading in the neighborhood of some other physical event like the front of the car reaching the back of the garage), you don't transform them at all when switching to a different frame, you only transform the coordinate labels assigned to these facts.

If you *don't* already know the local physical facts at a given point in spacetime, but are given some boundary conditions in that frame (like a set of 'initial conditions', though you can also work backwards from boundary conditions rather than forward, which is why I think it's better to just call them 'boundary conditions'), then you can use various equations derived from LT (like length contraction and time dilation) to *predict* the local physical facts at a point in spacetime that occurs later or earlier than the boundary conditions. This is the sort of thing I was doing in my example when I calculated that the clock at the front of the car would read -15 at the moment it passed the back of the garage, working backwards from the boundary conditions at t' = 0 in the car frame, and making use of the Lorentz contraction equation to figure out the length of the garage in this frame. If we were given the corresponding boundary conditions in a different frame and used them to predict what the clock at the front of the car would read when it passes the garage, we'd get the exact same answer of -15.

Jesse

 

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[Jesse Mazer]

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

 

BTW I forgot to reply to this line since it was an overall "OK", but just wanted to note that this is the standard meaning of "[object's] rest frame" in physics--it refers to the inertial coordinate system where the object, in this case the car, has position coordinates that don't change with coordinate time, so the car is said to be "at rest" in this coordinate system. It is the garage, not the car, that is moving in the car's rest frame, since the garage's coordinate position does change with time in this frame--this relative perspective on who is "moving" and who is "at rest" is just as true in classical mechanics as in special relativity (though of course there is no length contraction accompanying motion in classical mechanics), see the discussion of Galilean relativity at https://www.physicspace.com.ng/2018/09/galilean-relativity-2.html with Galileo's own discussion of an observer below decks of a windowless ship who has no way of knowing if the ship is at moving smoothly over the water or at rest relative to it. If you don't understand this sort of basic observation about classical mechanics in an inertial coordinate system (along with other basic observations like the classical relation between 'length' and coordinates of endpoints of an object, or classical relation between 'velocity' and the way position coordinates of an object change with coordinate time), that's something you really need to bone up on a little before tackling relativity.

Jesse

[Alan Grayson]

IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage. When the car is moving, we have been calling the other two frames, simply the car frame and the garage frame. About local events, if one measures x, t in one frame, which presumably are local events, and then transform to x', t' in another frame using the LT, are the primed values local event in your definition of local? Finally, if disagreement about simultaneity is alleged to solve the paradox, why did Brent deny my claim that there must be one objective reality; namely, that the car can, or cannot, fit in the garage? Is the paradox we're discussing rooted in this disagreement about local events? TY, AG

[Alan Grayson]

For clarification purposes; when t is measured using the readings on a clock, and transformed to t' via the LT, do you agree that these times have nothing to do with coordinate times in spacetime (which are just labels)? AG 

[Jesse Mazer]

On Mon, Dec 23, 2024 at 8:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, December 23, 2024 at 4:09:38 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

 

BTW I forgot to reply to this line since it was an overall "OK", but just wanted to note that this is the standard meaning of "[object's] rest frame" in physics--it refers to the inertial coordinate system where the object, in this case the car, has position coordinates that don't change with coordinate time, so the car is said to be "at rest" in this coordinate system. It is the garage, not the car, that is moving in the car's rest frame, since the garage's coordinate position does change with time in this frame--this relative perspective on who is "moving" and who is "at rest" is just as true in classical mechanics as in special relativity (though of course there is no length contraction accompanying motion in classical mechanics), see the discussion of Galilean relativity at https://www.physicspace.com.ng/2018/09/galilean-relativity-2.html with Galileo's own discussion of an observer below decks of a windowless ship who has no way of knowing if the ship is at moving smoothly over the water or at rest relative to it. If you don't understand this sort of basic observation about classical mechanics in an inertial coordinate system (along with other basic observations like the classical relation between 'length' and coordinates of endpoints of an object, or classical relation between 'velocity' and the way position coordinates of an object change with coordinate time), that's something you really need to bone up on a little before tackling relativity.

Jesse

IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage.

This isn't really a matter of opinion, just standard terminology; in physics books (in classical mechanics as well as relativity) you will only ever see "rest frame" defined relative to specific objects, and you will never see any reference to "the" rest frame without it being defined relative to such an object, nor is the phrase "isn't moving" understood as meaningful unless you add something like "isn't moving relative to [some other frame or object]". Please don't make up your own terminology, it'll just confuse things unnecessarily. Finally, note that nowhere in either my or Brent's formulations was it stated that the car initially was at rest relative to the garage, for the purposes of the problem you can assume the two have been in relative motion since a time of -infinity in both frames. You're also free to assume the car has been floating in space without accelerating for eternity and the garage accelerated to get close to it before coasting inertially, it should make no difference to the analysis of subsequent events (earlier when we were discussing the twin paradox you agreed that any acceleration prior to the period of time we are analyzing should make no difference).

When the car is moving, we have been calling the other two frames, simply the car frame and the garage frame. About local events, if one measures x, t in one frame, which presumably are local events,

x, t are not configurations of matter and energy in a local region, are they? That is the only definition of local event or physical fact I have been using. If you want to use x to refer to a marking on a specific physical ruler, and t to refer to a reading on a specific physical clock, then you have to specify the details about them in the problem (what they are at rest relative to, how the clock was synchronized, etc.), as I did when I introduced rulers and clocks into the problem. But normally x and t just refer to coordinate labels for events.

 

Finally, if disagreement about simultaneity is alleged to solve the paradox, why did Brent deny my claim that there must be one objective reality; namely, that the car can, or cannot, fit in the garage?

Fitting/not fitting not a local event by the definition I gave you (can you define 'fitting' in a way that refers only to configurations of matter and energy in the neighborhood of individual points in spacetime?), so if one takes the view that only local physical facts are the "objective reality", then this obviously doesn't qualify.

Jesse

[Jesse Mazer]

Time coordinates are always assumed to be *derived* from physical clock readings, but as I've told you several times, if different frames each have their own set of synchronized clocks then there will be *multiple* clocks in the neighborhood of the same local event, and different frames make different choices of which clock to take as "canonical" for the purpose of defining their time coordinates. In the most recent numerical example I gave, in the neighborhood of the event of the front of the car passing the back of the garage there was a clock at rest in the garage frame reading 0, and a clock at rest in the car frame reading -15, and both frames agree on both these local physical facts; but the garage frame takes the clock at rest in that frame as canonical and so assigns this event a coordinate label of t = 0, while the car frame takes the clock at rest in that frame as canonical and so assigns this event a coordinate label of t' = -15.

Jesse

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[Brent Meeker]

All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame.

Brent

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[Alan Grayson]

On Monday, December 23, 2024 at 9:33:36 PM UTC-7 Brent Meeker wrote:

All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame.

Brent

I know that. What I don't know is which question you're allegedly answering. AG

[Alan Grayson]

On Monday, December 23, 2024 at 9:06:31 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 8:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, December 23, 2024 at 4:09:38 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

 

BTW I forgot to reply to this line since it was an overall "OK", but just wanted to note that this is the standard meaning of "[object's] rest frame" in physics--it refers to the inertial coordinate system where the object, in this case the car, has position coordinates that don't change with coordinate time, so the car is said to be "at rest" in this coordinate system. It is the garage, not the car, that is moving in the car's rest frame, since the garage's coordinate position does change with time in this frame--this relative perspective on who is "moving" and who is "at rest" is just as true in classical mechanics as in special relativity (though of course there is no length contraction accompanying motion in classical mechanics), see the discussion of Galilean relativity at https://www.physicspace.com.ng/2018/09/galilean-relativity-2.html with Galileo's own discussion of an observer below decks of a windowless ship who has no way of knowing if the ship is at moving smoothly over the water or at rest relative to it. If you don't understand this sort of basic observation about classical mechanics in an inertial coordinate system (along with other basic observations like the classical relation between 'length' and coordinates of endpoints of an object, or classical relation between 'velocity' and the way position coordinates of an object change with coordinate time), that's something you really need to bone up on a little before tackling relativity.

Jesse

IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage.

This isn't really a matter of opinion, just standard terminology; in physics books (in classical mechanics as well as relativity) you will only ever see "rest frame" defined relative to specific objects, and you will never see any reference to "the" rest frame without it being defined relative to such an object, nor is the phrase "isn't moving" understood as meaningful unless you add something like "isn't moving relative to [some other frame or object]". Please don't make up your own terminology,

I'm definitely NOT doing that. Rather, that's how the frame names have been used throughout this discussion by members of this MB. AG

[Jesse Mazer]

On Mon, Dec 23, 2024 at 11:47 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, December 23, 2024 at 9:06:31 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 8:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, December 23, 2024 at 4:09:38 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

 

BTW I forgot to reply to this line since it was an overall "OK", but just wanted to note that this is the standard meaning of "[object's] rest frame" in physics--it refers to the inertial coordinate system where the object, in this case the car, has position coordinates that don't change with coordinate time, so the car is said to be "at rest" in this coordinate system. It is the garage, not the car, that is moving in the car's rest frame, since the garage's coordinate position does change with time in this frame--this relative perspective on who is "moving" and who is "at rest" is just as true in classical mechanics as in special relativity (though of course there is no length contraction accompanying motion in classical mechanics), see the discussion of Galilean relativity at https://www.physicspace.com.ng/2018/09/galilean-relativity-2.html with Galileo's own discussion of an observer below decks of a windowless ship who has no way of knowing if the ship is at moving smoothly over the water or at rest relative to it. If you don't understand this sort of basic observation about classical mechanics in an inertial coordinate system (along with other basic observations like the classical relation between 'length' and coordinates of endpoints of an object, or classical relation between 'velocity' and the way position coordinates of an object change with coordinate time), that's something you really need to bone up on a little before tackling relativity.

Jesse

IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage.

This isn't really a matter of opinion, just standard terminology; in physics books (in classical mechanics as well as relativity) you will only ever see "rest frame" defined relative to specific objects, and you will never see any reference to "the" rest frame without it being defined relative to such an object, nor is the phrase "isn't moving" understood as meaningful unless you add something like "isn't moving relative to [some other frame or object]". Please don't make up your own terminology,

I'm definitely NOT doing that. Rather, that's how the frame names have been used throughout this discussion by members of this MB. AG

I doubt you are remembering that correctly, especially if you are referring to either Brent or myself who have been most active in talking about the details of specific numerical examples. You can go back through the threads at https://groups.google.com/g/everything-list , just looking at Brent's first few posts on this thread, he seems to consistently talk about what's happening in "the car's reference frame" or "the garage's reference frame", no comments about "the rest frame" or saying anything "isn't moving" except in relation to another object, and I'm sure I wouldn't have done that either. But you are free to re-read the thread and see if you can find any counter-example to prove me wrong.

Jesse

[Alan Grayson]

On Monday, December 23, 2024 at 3:04:58 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

  |  - In both frames, set the origin of our coordinate system to be the point where the back of the car passes the front of the garage--then that point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and t' = 0 in the car frame. 

OK.

--In the garage frame, at t = 0 the front of the car is at the same position as the back of the garage, at position x = 20, so that's the position and time of the event of the front of the car passing the back of the garage in the garage frame. 

OK. 

     --In the car frame, at t' = 0 the back of the garage must be at x' = 16 (since we know the front of the garage is at position x' = 0 at time     t'=0, and using Lorentz contraction in the car frame we know the garage has length 16 in this frame), and the front of the car is at rest at x' = 25, so a distance of 25-16 = 9 from the back of the garage, which in this frame has already passed the front of the car at that moment. 

?

You agreed above that in the car frame, the front of the garage was at position x' = 0 at time t' = 0, yes? And you also agreed that in the car frame, the garage has length 16, yes? So why would you have any doubt that if the front end of the garage is at position x' = 0 at time t' = 0 in the car frame, then the back end must be at position x' = 16 at the same time t' = 0 in the car frame? That's just what "length" in a given frame means, the distance between the two ends of an object at a single moment in time in that frame. To put it another way, if this was just a classical 1D problem and I told you a rod had length 16 and at t' = 0 the front end was at position x' = 0, and it was moving in the -x direction, would you have any doubt the back end would be at x' = 16 at the same moment?

Or do you agree that this is straightforward, but have questions about why the front of the car would be at rest at x' = 25 (this also seems straightforward since you agreed its back end is at x' = 0 and its length is 25)? Or why, granted the back end of the garage is at x' = 16 and the front end of the car is at x' = 25 at this moment, the distance between them at this moment must be 9?

In the car's rest frame, the back end of garage is at x' = 16, but in the garage's rest frame, front of car is x = 25 (not x'), so you can't subtract apples from oranges. AG 

[Alan Grayson]

That's what I've been saying. No one uses "rest frame" when describing the results in either frame when the car is moving. You introduced that terminology recently, claiming it is standard. AG

[Jesse Mazer]

No one uses the words "the rest frame" in isolation as you did (that was what I was calling non-standard terminology), but they certainly use phrases like "the car's rest frame" and "the garage's rest frame" to refer to the inertial frame where the object in question has a fixed position coordinate (so they have exactly the same meaning as 'car's reference frame' or 'garage's reference frame'). It's more common for examples in relativity to involve rockets, so if you do a search on http://books.google.com for the phrase "rocket's rest frame" (putting it in quotation marks so google understands you want the whole phrase), you will find plenty of textbook examples, and it seems there are even more examples if you use the slightly different wording "rest frame of the rocket". Meanwhile your phrase "the car is moving" is also non-standard terminology since it isn't in relation to any particular object or reference frame. In one frame the car is at rest and the garage is moving, in the other frame the garage is at rest and the car is moving, neither is more correct than the other.

Jesse

[Jesse Mazer]

On Tue, Dec 24, 2024 at 12:12 AM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, December 23, 2024 at 3:04:58 PM UTC-7 Jesse Mazer wrote:

On Mon, Dec 23, 2024 at 4:10 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, December 22, 2024 at 10:05:54 PM UTC-7 Jesse Mazer wrote:

BTW, since you seem to be interested in a scenario where the car and garage are exactly matched in length in the garage frame, something which isn't true in Brent's scenario, here's a different scenario you could look at, where I'm again using units where c=1, let's say nanoseconds for time and light-nanoseconds (i.e. distance light travels in one nanosecond) for distance.

--Car's rest length is 25, garage's rest length is 20, car and garage have a relative velocity of 0.6c, so gamma factor is 1/sqrt(1 - 0.6^2) = 1.25

OK. 

 

--In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.

OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG 

  |  - In both frames, set the origin of our coordinate system to be the point where the back of the car passes the front of the garage--then that point will have coordinates x = 0 and t = 0 in the garage frame, x' = 0 and t' = 0 in the car frame. 

OK.

--In the garage frame, at t = 0 the front of the car is at the same position as the back of the garage, at position x = 20, so that's the position and time of the event of the front of the car passing the back of the garage in the garage frame. 

OK. 

     --In the car frame, at t' = 0 the back of the garage must be at x' = 16 (since we know the front of the garage is at position x' = 0 at time     t'=0, and using Lorentz contraction in the car frame we know the garage has length 16 in this frame), and the front of the car is at rest at x' = 25, so a distance of 25-16 = 9 from the back of the garage, which in this frame has already passed the front of the car at that moment. 

?

You agreed above that in the car frame, the front of the garage was at position x' = 0 at time t' = 0, yes? And you also agreed that in the car frame, the garage has length 16, yes? So why would you have any doubt that if the front end of the garage is at position x' = 0 at time t' = 0 in the car frame, then the back end must be at position x' = 16 at the same time t' = 0 in the car frame? That's just what "length" in a given frame means, the distance between the two ends of an object at a single moment in time in that frame. To put it another way, if this was just a classical 1D problem and I told you a rod had length 16 and at t' = 0 the front end was at position x' = 0, and it was moving in the -x direction, would you have any doubt the back end would be at x' = 16 at the same moment?

Or do you agree that this is straightforward, but have questions about why the front of the car would be at rest at x' = 25 (this also seems straightforward since you agreed its back end is at x' = 0 and its length is 25)? Or why, granted the back end of the garage is at x' = 16 and the front end of the car is at x' = 25 at this moment, the distance between them at this moment must be 9?

In the car's rest frame, the back end of garage is at x' = 16, but in the garage's rest frame, front of car is x = 25 (not x'), so you can't subtract apples from oranges. AG 

No, the car's rest length is 25, so that's its length in the *car's* rest frame, by definition. Since the back of the car is at rest at x' = 0 in this frame, the front must be at rest at x' = 25 in this frame.

Meanwhile the car is moving at 0.6c in the garage's rest frame so its length is Lorentz-contracted down to 25/1.25 = 20, meaning at t = 0 the front of the car is at x = 20 in the garage's rest frame.

Jesse

[Alan Grayson]

On Monday, December 23, 2024 at 9:38:34 PM UTC-7 Alan Grayson wrote:

On Monday, December 23, 2024 at 9:33:36 PM UTC-7 Brent Meeker wrote:

All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame.

Brent

I know that. What I don't know is which question you're allegedly answering. AG

 

More important question; didn't you deny my claim that for a sufficient velocity the car either fits or doesn't fit, as an objective fact that the paradox seems to deny? AG 

[Brent Meeker]

On 12/23/2024 9:36 PM, Alan Grayson wrote:

On Monday, December 23, 2024 at 9:38:34 PM UTC-7 Alan Grayson wrote:

On Monday, December 23, 2024 at 9:33:36 PM UTC-7 Brent Meeker wrote:

All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame.

Brent

I know that. What I don't know is which question you're allegedly answering. AG

 

More important question; didn't you deny my claim that for a sufficient velocity the car either fits or doesn't fit, as an objective fact that the paradox seems to deny? AG

If I was thinking clearly I did.  An objective fact is not reference frame dependent.

Brent

[Alan Grayson]

Obviously, you guys can only speak in riddles, so I have to assume you can't answer the underlying question; how the car can and cannot fit in the garage, depending on which frame one measures from. Or better yet, let's accept the chief asshole's solution, Quentin, who fallen in love with the model of a car instantaneously stopping inside the garage, while appealing to disagreement of simultaneity as the answer with no further analysis, while accusing me of being a troll as his last resort and final solution. Troll out! 

[Brent Meeker]

On 12/23/2024 11:48 PM, Alan Grayson wrote:

On Monday, December 23, 2024 at 11:03:36 PM UTC-7 Brent Meeker wrote:

On 12/23/2024 9:36 PM, Alan Grayson wrote:

On Monday, December 23, 2024 at 9:38:34 PM UTC-7 Alan Grayson wrote:

On Monday, December 23, 2024 at 9:33:36 PM UTC-7 Brent Meeker wrote:

All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame.

Brent

I know that. What I don't know is which question you're allegedly answering. AG

 

More important question; didn't you deny my claim that for a sufficient velocity the car either fits or doesn't fit, as an objective fact that the paradox seems to deny? AG

If I was thinking clearly I did.  An objective fact is not reference frame dependent.

Brent

Obviously, you guys can only speak in riddles,

If you would ever solve one the riddles you might learn something.  Telling you answer just leads to your saying you're not convinced and around it goes.

so I have to assume you can't answer the underlying question;

Or you might assume you just too dumb or stubborn to learn the answer.

Brent

[Alan Grayson]

You have no answer, just some plots pretending to an answer. Just riddles upon riddles. AG 

[Alan Grayson]

You have no answer, just some plots pretending to be an answer. Just riddles upon riddles. AG 

Why I don't believe the gurus here have the answer; you'll note how easy it is to pose the question, and how easy it is to offer a proposed solution; namely, the disagreement about simultaneity. But that's obviously not enough. As Quentin's behavior exemplifies; the mere statement of the solution is hardly sufficient. One then needs an ARGUMENT connecting the alleged solution, to the construction of the problem; that is, the paradox. But Quentin is totally UNAWARE of this requirement, which his link fails to provide, and then he's perfectly satisfied with accusing me as a troll. You, Brent, allege the solution in your plots, which I admit I fail to see the connecting argument just alluded to. But if you really understood the solution, and pride yourself in your teaching skills of relativity, you could offer a text solution, which should be a relatively short paragraph. But that remains wanting. AG 

[Alan Grayson]

Reviewing how time transforms using the LT, it does appear that for a perfectly fitting car for which its time parameter is identical at its end points, time does NOT transform to identical time parameters of the car's end points in the car frame, since in the garage frame the spatial parameter of the end points differ in the transformation equation. I'm not entirely certain, but I think this establishes the disagreement concerning simultaneity between the frames. Now, to resolve the paradox, requires an ARGUMENT to, in effect, DECONSTRUCT the claim of a paradox depending on this disagreement. AG  

[Jesse Mazer]

The argument is that both frames agree on all the local physical facts at the front of the car as it reaches the back of the garage--in my example they both agree that the physical clock at rest relative to the car there reads -15 and the physical clock at rest relative to the garage there reads 0. Their only disagreement is the *convention* they each use about which physical clock to treat as canonical for the purpose of assigning an abstract time-coordinate to that location in spacetime.

Once one realizes that they agree about all local physical facts at each point in spacetime, and that in relativity local physical facts are the only "objective facts" about what happens in a given problem, the paradox is deconstructed--there is no actual disagreement about any objective facts here, just about conventions for defining abstract coordinate labels.

Jesse

[Alan Grayson]

What convention are you referring to? Einstein uses the same clocks in each frame, which are synchronized at rest, and then go out of synch when motion is initiated. He never refers to different clocks. And the LT has both clocks, whatever they might be, in its transformation equations, namely t and t'. I've never seen of any choice about which physical clock is treated as canonical. Any clock seems satisfactory. But even if your argument holds, it's not obvious how this would DECONSTRUCT the argument that the car fits in the garage in one frame, but not in the other. AG

Once one realizes that they agree about all local physical facts at each point in spacetime,

Is measured time the same in both frames? Of course not. Does this mean measured time is NOT a physical fact which is frame dependent? AG

[Alan Grayson]

If your clocks have different readings when the car reaches the end of the garage, are they not physical facts that disagree? How does a choice of which clock is canonical change this situation? I'm not an expert in SR, but I have read parts of books and articles about it, as well as studying it formally at universities, and I have NEVER heard any discussion of what's canonical for clocks. AG

[Alan Grayson]

Is your analysis consistent with Brent's? Does he also refer in any way to canonical clocks as deconstructing the paradox? Do you know that the word "canonical", as the Canonical Gospels, refers to "lawful" or "accepted" or "authoritative"? When used in relativity, do you mean that clocks in one frame are not to be trusted, so we chose those in another frame which are trustworthy? AG 

[Jesse Mazer]

Are you talking about the 1905 paper? He does in that paper imagine originally creating two rigid measuring systems at rest with each other and then imparting a velocity to one relative to the previous rest state (in section 3 starting at https://einsteinpapers.press.princeton.edu/vol2-trans/160 ), but this notion of them starting at rest relative to one another isn't an essential part of his argument, you could equally well imagine two rigid measuring systems that have been moving relative to each other forever (or at least for the whole duration we are considering in the problem), and he dispenses with this notion in other works where he discusses two measuring systems in relative motion (like the section of his book Relativity: The Special and General Theory at https://philosophie.ens.fr/IMG/EGS%20Einstein%20relativity%208-9.pdf ). And although both systems are equipped with the same *types* of clocks, they are not literally sharing the same individual clocks--there are some clocks at rest relative to the first rigid system, and a different set of clocks at rest relative to the second system. Finally, he doesn't imagine syncing the clocks beforehand and then seeing them "naturally" go out-of-sync when one system is imparted a velocity relative to the first, instead he talks about synchronizing each system's own clocks using his light-signal method *after* he talks about giving them a relative velocity, on the page at https://einsteinpapers.press.princeton.edu/vol2-trans/160 where he writes:

"The origin of one of the two systems (k) shall now be imparted a (constant) velocity v in the direction of increasing x of the other system (K), which is at rest, and this velocity shall also be imparted to the coordinate axes, the corresponding measuring rod, and the clocks. ... Further, by means of the the clocks at rest in the system at rest and using light signals in the manner described in §1, the time t of the system at rest is determined for all its points where there is a clock; likewise, the time tau of the moving system is determined for all the points of the moving system having clocks that are at rest relative to this system, applying the method of light signals described in §1 between the points containing these clocks."

 

And the LT has both clocks, whatever they might be, in its transformation equations, namely t and t'. I've never seen of any choice about which physical clock is treated as canonical.

Yes, but in terms of physical clock readings, all frames agree that *both* of those readings t and t' are seen on clocks from different measuring systems that are passing through the region of the event in question, with the different measuring systems and their clocks having a relative velocity. Each frame simply *defines* the time coordinate of an event by the reading on the single clock at that location that is at rest in that frame, not by any of the other clocks that are in motion in that frame--that's all I mean by treating one clock as canonical. Trust me as someone who studied this stuff that this is the standard understanding of how inertial coordinate systems are defined physically, and that it's understood that the section of Einstein's original 1905 SR paper I quoted above is talking about this idea, whether or not you've ever seen it.

 

Any clock seems satisfactory. But even if your argument holds, it's not obvious how this would DECONSTRUCT the argument that the car fits in the garage in one frame, but not in the other. AG

It doesn't! It deconstructs the idea that this constitutes a paradox in the sense of contrary predictions about objective reality, once you realize that in relativity "objective reality" consists only of local physical facts, and that frames can disagree on the order of events (and thus on whether the car fits) without the slightest disagreement about any local physical facts.

 

Once one realizes that they agree about all local physical facts at each point in spacetime,

Is measured time the same in both frames? Of course not. Does this mean measured time is NOT a physical fact which is frame dependent? AG

I referred not just to a "physical fact" but to an *objective* physical fact, i.e. one that doesn't depend on human conventions (as an analogy, if you choose a position for the origin of a spatial coordinate system and the orientation of your coordinate axes, there may then be a fact about the x-coordinate of some physical object in this system, but it depends on your conventional choice of how to position our coordinate system so it isn't an objective fact in my sense, for example if another physicist wasn't informed about our choice, we'd have no reason to expect them to independently arrive at the same coordinate system, and thus no reason to expect them to assign the same x-coordinate to that physical object). Measured time between events is not an objective fact in this sense (unless you are talking about proper time between two events along a specific timelike worldline that goes through both, but this can only make sense for events with a time-like rather than a space-like separation), it depends on which clocks you *choose* to use to assign coordinate time. 

Jesse

[Jesse Mazer]

You can ask him, but I'm sure he'd agree that:

A) time coordinates of any inertial frame in SR can ideally be defined in terms of local measurements on a system of measuring rods and clocks which are at rest in that frame, the clocks synchronized by the Einstein convention (like the kind illustrated at http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring )

B) If you have two such systems #1 and #2 in relative motion, and each has a clock in the neighborhood of some specific event E, all observers/frames agree on the objective physical fact about what the clock from system #1 reads at E, and what the clock from system #2 reads at E, and these two readings on the different clocks in motion relative to one another need not agree

C) The frame that uses system #1 to define its coordinates will only use the clock from #1 at E to define the time-coordinate of E in that frame; similarly the frame that uses system #2 to define its coordinates will only use the clock from #2 at E to define the time coordinate of E in that frame.

That last part is all I meant by treating one clock as "canonical", don't read anything into the word beyond that (I was actually thinking not of Church history but of fans of fictional stories set in the same 'universe' who make different choices about which stories to treat as ''canon' when mapping out all the facts about a given fictional world, like the world of Star Trek or Lord of the Rings; these fans understand that it's all a made up story rather than an objective reality, so 'canon' is just a matter of choice, which is more like the attitude of physicists choosing which clocks to use to define time coordinates)

Jesse

[Jesse Mazer]

Minor correction, the link for the first page of section 3 where he starts to talk about this should be https://einsteinpapers.press.princeton.edu/vol2-trans/159 

[Alan Grayson]

FWIW, SR preserves causality, so your claim about time order of events not being preserved is incorrect. And I've seen the Einstein quote and it has no impact on my position in these matters. Do you have a quote where he says that only objective facts are preserved at each event in spacetime? And since coordinate systems are arbitrary, as well as what values clocks are sychronized to, what OBJECTIVE facts at events do you think are preserved? There appear to be none. Finally, my argument that a paradox exist is about as straight-forward as one can imagine, based as it is solely on length contraction, yet you dismiss it out of hand, for an ill-defined concept of limited objective local reality at events in spacetime. IOW, you seem to have defined the paradox out of existence by your claim that only local objective facts are preserved. Based on your extensive reading on SR, does Einstein have anything to say about the Lorentz Parking Paradox? Anything? IMO, unless proven otherwise, it indicates a fatal flaw in SR. AG

[Jesse Mazer]

I said frames *can* disagree on the order of events, not that they *always* disagree on the order of events. For events with a time-like separation, they always agree on the order; for events with a space-like separation, you can find frames that disagree (I have said this several times in our previous discussion). Assuming no FTL causal influences, events with a space-like separation don't causally influence one another. 

 

And I've seen the Einstein quote and it has no impact on my position in these matters. Do you have a quote where he says that only objective facts are preserved at each event in spacetime?

Are you asking if he'd agree that all frames agree on local physical facts? Or are you asking if he'd agree that only such local physical facts are considered "objective"? If the former it'd be very obvious to any physicist that all frames must agree on such local facts, because of considerations of local *interactions* that leave permanent effects like my example in the post at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/Fou17sn5AQAJ about the bomb blowing up near the glass of water and shattering it; I could try to look for a quote of him saying this explicitly if you doubt this, I'm sure I could at least find some physicists talking about this.

If the latter, I suppose calling these facts "objective" is a bit philosophical, but the point is that it's not seen as a defect in a theory or contradiction that different frames can disagree about things that are *not* local facts, but it certainly would if they did make different predictions about local facts. BTW, even in classical mechanics two frames can disagree about the *distance* between two events, so why does disagreement about the *time* between events seem so much more problematic to you?

Out of curiosity I went back and looked at what my old SR textbook had to say about these subjects--the text is "Special Relativity" by A. P. French, which I believe is pretty commonly assigned in intro SR classes. Page 90 talks about how measurements should consist of readings which coincide in space and time with the event they are measuring:

"It is very important to realize, as Einstein in essence pointed out, that the role of an observer is simply to record coincidences, i.e., pairs of events which occur at the same space-time point. A clock reading at a particular point in a given frame of reference is an event in this sense; in- deed, our concern in this chapter is overwhelmingly with events of this kind. The things that we more familiarly think of as physical events—e.g., the collision between two objects, or the emission of a photon by an atom—are, for our purposes, to be regarded as happenings that coincide with events describable as readings on clocks. The incessant references to clock readings may well seem artificial and somewhat wearisome, but they do serve to emphasize an absolutely essential feature—that we are dealing with a very explicit problem of measurement."

French goes on to make a point similar to my bomb/glass of water example about how when events coincide at the same point in spacetime this can have permanent effects viewable later:

"Although an event is by definition represented by a single point in space-time, it may nevertheless leave an enduring record of itself. A criminal touches a glass, for example, and leaves a fingerprint. The touching of the glass is an event, occurring at a unique place and a unique time in a given frame of reference. A second later, even if the glass has not been moved, the finger- print is at a different point in space-time. But it remains as a record that a certain event took place. A still more pertinent example would be of a watch that falls onto a concrete floor and stops dead. If it is left where it fell, it represents a permanent record of the "watch-strikes-floor" event. And an observer, coming upon the scene long afterward, can note down the space and time coordinates of the event as measured in a reference frame defined by the floor (for space coordinates) and by the hands of the watch (for time coordinate)."

And then he talks about how we should not be misled by the notion of an observer being "in" a given frame, that each observer can certainly observe the local clock readings of clocks used by different frames:

"The last remark above should make it clear that an observer is not necessarily limited to making measurements in a reference frame to which he himself is attached. One can appeal to all kinds of familiar experience that embody this fact. For example, one is a passenger in a train that shoots through a station. On the platform is a sign with an arrow pointing in the train's direction of motion and carrying the words "New York 10 miles." Just above the sign is a station clock that reads 10:53 A.M. As an observer attached to a certain reference frame, defined by the train, one can nevertheless record the space-time coordinates of an event—"train passes through station"—as measured in the relatively moving reference frame of the station

and the ground to which it is attached.  Very often, however, one will see statements such as the following: "An observer A in frame S observes that an event occurs at position x and time t; the same event is observed to occur at position x' and time t' by an observer B in frame S'." What is really being said here is just that the event has space-time coordinates (x, t) in one frame and (x', t') in the other. But there is conjured up a picture of an observer, cloistered in his own particular frame of reference, unable to record anything except the measures of position and time in that frame. Our example of the passenger in a train shows how unnecessarily restrictive this is. The passenger can note not only the reading on the station clock but also the reading on his own watch."

 

And since coordinate systems are arbitrary, as well as what values clocks are sychronized to, what OBJECTIVE facts at events do you think are preserved? There appear to be none.

I am just talking about the facts of the physical clock readings at each event, like my example where the local event of the front of the car reaching the back of the garage coincided with the local clock in the garage system reading 0 and the local clock in the car system reading -15 (are you planning to return to that example to clarify your '?' responses?) While the choice of which inertial coordinate systems to use is arbitrary, once you have specified that the origin of two inertial coordinate systems coincides and their relative velocity (along with the fact that they are each using clocks synchronized in their own frame by the Einstein procedure), it's not arbitrary which pairs of other clock readings in each system coincide locally (these pairings are of course given by the Lorentz transformation equation for the time coordinate).

 

Finally, my argument that a paradox exist is about as straight-forward as one can imagine, based as it is solely on length contraction, yet you dismiss it out of hand, for an ill-defined concept of limited objective local reality at events in spacetime.

Are you saying that what is ill-defined is calling such local facts "objective" (if so see my comment above), or are you saying that the notion of local physical facts is itself ill-defined? If the latter this would be another example of you just throwing adjectives at without offering any substantive criticism or specific points you want to clarify, similarly to how you earlier called it "ambiguous" and later "not absolutely clear".

 

IOW, you seem to have defined the paradox out of existence by your claim that only local objective facts are preserved. Based on your extensive reading on SR, does Einstein have anything to say about the Lorentz Parking Paradox? Anything? IMO, unless proven otherwise, it indicates a fatal flaw in SR. AG

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions. Whereas the argument that it'd be unacceptable to have a theory where frames could disagree about which events locally coincide is much more straightforward, it would lead to different predictions about local interactions which leave permanent records as in my example of the bomb shattering the glass only if the clock attached to the bomb reads a certain time at the moment it passes the glass.

Jesse

 

Once one realizes that they agree about all local physical facts at each point in spacetime,

Is measured time the same in both frames? Of course not. Does this mean measured time is NOT a physical fact which is frame dependent? AG

I referred not just to a "physical fact" but to an *objective* physical fact, i.e. one that doesn't depend on human conventions (as an analogy, if you choose a position for the origin of a spatial coordinate system and the orientation of your coordinate axes, there may then be a fact about the x-coordinate of some physical object in this system, but it depends on your conventional choice of how to position our coordinate system so it isn't an objective fact in my sense, for example if another physicist wasn't informed about our choice, we'd have no reason to expect them to independently arrive at the same coordinate system, and thus no reason to expect them to assign the same x-coordinate to that physical object). Measured time between events is not an objective fact in this sense (unless you are talking about proper time between two events along a specific timelike worldline that goes through both, but this can only make sense for events with a time-like rather than a space-like separation), it depends on which clocks you *choose* to use to assign coordinate time. 

Jesse

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[Alan Grayson]

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions? AG

[Jesse Mazer]

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Jesse

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[Alan Grayson]

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. AG 

Jesse

[Jesse Mazer]

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right? If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense. The question of which photons from which events on the past light cone of that point are arriving there at that moment is a question about the local configuration of particles (photons) in that region, i.e. a question about local physical facts. If the photons from each end of the car arriving at that point were emitted from points where each respective end of the car was in the garage, both observers see it fitting in the visual sense of both ends appearing to be inside the garage. 

But as I pointed out to you earlier, this is not what physicists generally mean by fitting, since even in classical physics with no length contraction and no disagreements over simultaneity, as long as light travels at a finite speed you can have a situation where some observer *sees* both ends of the car inside the garage even though they are never simultaneously inside in any inertial frame’s coordinates.

For example, if the observer is located at the front of the garage, they will see the back end of the car pass the front of the garage as soon as it happens, but they will be getting a delayed image of the front of the car, so they may be seeing an image of when it was still in the garage even though according to the definition of simultaneity that is shared by all classical frames, it has really passed through the back of the garage by that moment (because the car is longer than the garage). It’s likewise possible to construct a classical example where the observer is located closer to the back of the garage and due to light delays they never see the car fit in a visual sense even though it does fit in terms of simultaneity of all classical frames (because the car is shorter than the garage).

Jesse

[Brent Meeker]

On 12/25/2024 1:34 AM, Alan Grayson wrote:

FWIW, SR preserves causality, so your claim about time order of events not being preserved is incorrect.

Causality requires that cause and effect events be time-like.  Space-like events have a time order that is relative to reference frames and so cannot stand in a cause/effect relation.

Brent

[Alan Grayson]

On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime? AG

[Jesse Mazer]

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. 

Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? 

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight.

 

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, 

Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear.

 

and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?

You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there.

Jesse

 

The question of which photons from which events on the past light cone of that point are arriving there at that moment is a question about the local configuration of particles (photons) in that region, i.e. a question about local physical facts. If the photons from each end of the car arriving at that point were emitted from points where each respective end of the car was in the garage, both observers see it fitting in the visual sense of both ends appearing to be inside the garage. 

But as I pointed out to you earlier, this is not what physicists generally mean by fitting, since even in classical physics with no length contraction and no disagreements over simultaneity, as long as light travels at a finite speed you can have a situation where some observer *sees* both ends of the car inside the garage even though they are never simultaneously inside in any inertial frame’s coordinates.

For example, if the observer is located at the front of the garage, they will see the back end of the car pass the front of the garage as soon as it happens, but they will be getting a delayed image of the front of the car, so they may be seeing an image of when it was still in the garage even though according to the definition of simultaneity that is shared by all classical frames, it has really passed through the back of the garage by that moment (because the car is longer than the garage). It’s likewise possible to construct a classical example where the observer is located closer to the back of the garage and due to light delays they never see the car fit in a visual sense even though it does fit in terms of simultaneity of all classical frames (because the car is shorter than the garage).

Jesse

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[Alan Grayson]

On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. 

Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? 

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

 

Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. 

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, 

Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear.

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG   

[Alan Grayson]

On Thursday, December 26, 2024 at 3:26:41 AM UTC-7 Alan Grayson wrote:

On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

       On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. 

Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? 

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

 

Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. 

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, 

Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear.

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison. Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG

[Alan Grayson]

The juxtaposed spacetime events of comparison will have different labels, since they're from different frames. But physically they're co-located with different physical measurements. This result, I claim, defeats your claim that local measurements are frame independent. AG 

[Jesse Mazer]

On Thursday, December 26, 2024, Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. 

Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? 

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

 

Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. 

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, 

Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear.

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG   

As I explained before, talking about the “rest frame of the [object]” is standard terminology in relativity (as well as in classical mechanics), it just refers to the inertial frame where that object is at rest, i.e. the position coordinate of any part of the object (like its front end) is unchanging with the time coordinate in that frame. If you aren’t willing to just take my word for this, please do the experiment I suggested earlier if going to http://books.google.com and searching for the phrase “rest frame of the rocket” (including the quotation marks), you will find plenty of textbook examples involving rockets that use this phrase, and you’ll be able to see from the context they use it the way I mean.

Jesse

 

and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?

You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there.

Jesse

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[Jesse Mazer]

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse

 

Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG

  

and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?

You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there.

Jesse

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[Alan Grayson]

On Thursday, December 26, 2024 at 2:56:04 PM UTC-7 Jesse Mazer wrote:

On Thursday, December 26, 2024, Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, December 26, 2024 at 3:26:41 AM UTC-7 Alan Grayson wrote:

On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

       On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote:

On Wednesday, December 25, 2024, Alan Grayson <agrays...@gmail.com> wrote:

Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. 

No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other.

I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG

Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits.

As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG  

You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. 

Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? 

 

But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG

Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?

I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves?

Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. 

You didn’t quite answer my question—you are just talking about what they see with their eyes, right?

I used the word "see". Is this not clear enough? AG

 

Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. 

 

If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense.

Really? So if the garage is 10' long in rest frame, 

Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear.

I appreciate your thoroughness but here I just left out "its", as in "... 10' long in its rest frame", and I think you should have easily inferred my meaning. AG 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

[Jesse Mazer]

Given that you had recently objected to my use of the phrases “car’s rest frame” and “garage’s rest frame” and hadn’t acknowledged my response about how this is a standard way of speaking in relativity, I didn’t think it was safe to assume that. It would help if you would acknowledge when something I’ve said has led you to revise a view, even on something minor like terminology, otherwise I don’t know when a given point needs to be re-litigated. The recent discussion about how we can talk about events that are spacelike separated without implying any faster than light causal influence is another example; do I need to keep arguing that or does the fact that you dropped that discussion mean you concede the point?

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting. As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back:

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions. Whereas the argument that it'd be unacceptable to have a theory where frames could disagree about which events locally coincide is much more straightforward, it would lead to different predictions about local interactions which leave permanent records as in my example of the bomb shattering the glass only if the clock attached to the bomb reads a certain time at the moment it passes the glass.

 

Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG

  

and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?

You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there.

Jesse

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[Alan Grayson]

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not. This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

[Alan Grayson]

TYPO!   I meant above,  " ... doesn't seem physically possible in either frame." AG

[Jesse Mazer]

Could you please address my comment above so I know if we’re in disagreement on these points?

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree? If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime? But as I pointed out they won’t have a different visual opinion about whether the car fits in this case, and an observer’s non-visual judgments of the time and position events happen in their frame doesn’t depend on their position in that frame.

Jesse

 

Whereas the argument that it'd be unacceptable to have a theory where frames could disagree about which events locally coincide is much more straightforward, it would lead to different predictions about local interactions which leave permanent records as in my example of the bomb shattering the glass only if the clock attached to the bomb reads a certain time at the moment it passes the glass.

 

Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG

  

and car is .00001' long in garage frame when car is moving,  and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?

You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there.

Jesse

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[Alan Grayson]

I don't object to your terminology. As I stated, if I had included "its" in my statement, there would have been no ambiguity about terminology. And as far as I can recall, I never objected to the use of your quoted statements about rest frames. AG 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that. Which frame are you referring to? Presumably the car frame where you claim the car cannot fit. How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG 

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree?

In this problem we can assume the garage isn't moving as an objective fact, but IIUC we can still use the LT to contract the garage's measured length from the pov of the car frame. Do you agree with this use of the LT? And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

[Jesse Mazer]

You objected multiple times in the last few days to my terminology where "car's rest frame" refers to the frame where the car is at rest (i.e. it has position coordinates that don't change with time) and the garage is moving (so the garage is Lorentz-contracted in the car's rest frame), while "garage's rest frame" symmetrically refers to the frame where the garage is at rest and the car is moving (so the car is Lorentz-contracted in the garage's rest frame). For example in the post at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/XZrHB-IdAwAJ I said:

"In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.”

And you responded:

"OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG"

Then at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/mFVsDGUtAwAJ you responded by imagining “the rest frame” referred to some imaginary initial conditions that were never part of the problem I described, conditions where both the car and garage were at rest relative to each other:

“IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage. When the car is moving, we have been calling the other two frames, simply the car frame and the garage frame.”

Then at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/1AWAOHA4AwAJ you again objected to the standard terminology in which “car’s rest frame” just refers to the frame where the car is at rest in the sense of having a fixed position coordinate, even if it is moving relative to the garage:

“No one uses "rest frame" when describing the results in either frame when the car is moving. You introduced that terminology recently, claiming it is standard. AG”

Then just yesterday at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/O12FCXvmAwAJ you again objected to this standard terminology:

“What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary?”

So it would be helpful to know if you're willing to accept that my use of "car's rest frame" and "garage's rest frame" is the standard way of talking among physicists, or if you still object. 

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that.

Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following:

"You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense?

If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?"

Then at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/KmDqElIUAQAJ you quoted my statement above "If you don't see why the ordering of these two events is considered equivalent to the question of fitting," and you responded by saying "It obviously is. Sorry about the confusion. AG"

In another followup comment at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/gi9RERcVAQAJ you quoted more of the classical covered bridge scenario I had written, and then you replied "I think I agree with your criteria for fit and not fit. What bothers me is the disagreement between frames about fitness or not, and why the alledged lack of simultaneity resolves the apparent contradiction. AG"

So, this is why I thought we had already settled the point that the statement "the car doesn't fit" is totally equivalent to the statement "B happens before A", and the statement "the car does fit" is totally equivalent to the statement "A happens either before or simultaneously with B". If you don't recall making these statements, please go back and look carefully at the covered bridge scenario and tell me if you agree or disagree with your past self!

 

Which frame are you referring to? Presumably the car frame where you claim the car cannot fit.

Read the statement about A and B again, it's an if-then conditional that covers any frame. If we're talking about a frame where B happens before A, then the car does not fit in that frame; if we're talking about a frame where A occurs before B, or simultaneously with it, then the car does fit in that frame.

 

How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG

Yes, the garage can be made arbitrarily short in the car's frame by picking a high relative velocity, why do you think this is at odds with the idea that the car won't fit? Obviously if the length of the garage is shorter than the car, the car will not fit, exactly as would be true in a classical scenario with a garage shorter than a car. And in such a frame, the event B="front of car passes back of garage" happens before the event A="back of car passes front of garage", just as you'd expect in the classical covered bridge scenario I wrote about previously.

 

 

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree?

In this problem we can assume the garage isn't moving as an objective fact,

Neither classical mechanics nor relativity would agree "the garage isn't moving" is an objective fact, if by "objective" you mean something different frames can agree on. Are you saying that you think classical mechanics is indeed fatally flawed because it makes movement vs. rest entirely frame-dependent?

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

Jesse

[Alan Grayson]

I was being sarcastic. Not to be taken at face value. AG 

So it would be helpful to know if you're willing to accept that my use of "car's rest frame" and "garage's rest frame" is the standard way of talking among physicists, or if you still object. 

Instead of haggling over this issue, and possibly taking some of my comments out of context, we agree that when using the LT from either frame, the car or garage length in that frame has not changed from its initial condition, 12' or 10', respectively. At that point it was agreed that car cannot fit in garage because of length considerations. Consequently, following that agreement, I calculated using the LT, that the car fits or not -- fits in garage frame, doesn't fit in car frame -- based solely on length considerations. If the car can't fit from its frame when v = 0, it can't fit for any v > 0, since the garage gets even shorter. I think you and Brent believe it can't fit in car frame due to disagreement about simultaneity, whereas I use length contraction to reach the same conclusion. And we agree it can fit from the pov of the garage frame, since the car's length contracts. So what are we arguing about is this; does the disagreement about fit constitute an objective fact and thus a paradox? AG

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that.

Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following:

"You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense?

As I think I posted, I don't understand the argument that disagreement about simultaneity resolves the paradox. This is surely the standard alleged solution, but using the LT and length contraction, I seem to get a paradox if we assume disagreement about fitting is the cause of the paradox. You claim time-ordering shows the car can't fit. This is my conclusion using length contraction, whiich seems simpler. So, our disagreement of the resolution apparently has nothing to do with whether the car fits from its frame, since we're in agreement that it does not. AG 

If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?"

      Then at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/KmDqElIUAQAJ you quoted my statement above "If you don't see why the ordering of these two events is considered equivalent to the question of fitting," and you responded by saying "It obviously is. Sorry about the confusion. AG"

     In another followup comment at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/gi9RERcVAQAJ you quoted more of the classical covered bridge scenario I had written, and then you replied "I think I agree with your criteria for fit and not fit. What bothers me is the disagreement between frames about fitness or not, and why the alledged lack of simultaneity resolves the apparent contradiction. AG"

If time ordering establishes the car cannot fit in the garage from car's frame, won't the reverse also be true; that the car cannot fit in garage from garage frame for the same reason due to symmetric use of the LT, and that the frames are equivalent in SR. This why I haven't considered disagreement about simultaneity the resolution of the paradox. AG

Which frame are you referring to? Presumably the car frame where you claim the car cannot fit.

Read the statement about A and B again, it's an if-then conditional that covers any frame. If we're talking about a frame where B happens before A, then the car does not fit in that frame; if we're talking about a frame where A occurs before B, or simultaneously with it, then the car does fit in that frame.

 

How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG

Yes, the garage can be made arbitrarily short in the car's frame by picking a high relative velocity, why do you think this is at odds with the idea that the car won't fit?

I think that was a typo. Sorry about that! The car couldn't fit initially, so it can't fit when the garage is shorten from the pov of car frame. AG 

Obviously if the length of the garage is shorter than the car, the car will not fit, exactly as would be true in a classical scenario with a garage shorter than a car. And in such a frame, the event B="front of car passes back of garage" happens before the event A="back of car passes front of garage", just as you'd expect in the classical covered bridge scenario I wrote about previously.

As I commented somewhere here in BLUE, won't the reverse also be true due to frame equivalence in SR and permissible symmetric use of LT; namely, that from pov of garage frame, the car won't fit due to disagreement about simultaneity? AG  

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree?

In this problem we can assume the garage isn't moving as an objective fact,

Neither classical mechanics nor relativity would agree "the garage isn't moving" is an objective fact, if by "objective" you mean something different frames can agree on. Are you saying that you think classical mechanics is indeed fatally flawed because it makes movement vs. rest entirely frame-dependent?

Well, in this case everyone with common sense knows the garage isn't moving, and what we have is relative motion, which allows us to calculate AS IF the garage is moving. AG 

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. AG 

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. In this scenario, we might need a second sychronized garage observer at front of garage. In any case, let's focus on length contraction. AG 

Jesse

[Jesse Mazer]

The Webster’s dictionary comment was sarcastic, but ‘What could be the meaning of “rest frame” associated with “garage”?’ didn’t seem to be a sarcastic question, especially since it echoed your confusion in the other comments I quoted.

 

So it would be helpful to know if you're willing to accept that my use of "car's rest frame" and "garage's rest frame" is the standard way of talking among physicists, or if you still object. 

Instead of haggling over this issue, and possibly taking some of my comments out of context, we agree that when using the LT from either frame, the car or garage length in that frame has not changed from its initial condition, 12' or 10', respectively.

I don’t know what you mean by “its initial condition.” Do you just mean its length its own rest frame? Or do you think it’s essential to the problem that we imagine some initial condition where both are at rest relative to each other, and then the car is accelerated? If so I would definitely object to that, the term “car’s rest frame” has no such implications, it would have exactly the same meaning if we assumed the car and garage have had a fixed relative velocity for an infinite time prior to the car passing through the garage.

 

 At that point it was agreed that car cannot fit in garage because of length considerations. Consequently, following that agreement, I calculated using the LT, that the car fits or not -- fits in garage frame, doesn't fit in car frame -- based solely on length considerations. If the car can't fit from its frame when v = 0, it can't fit for any v > 0, since the garage gets even shorter. I think you and Brent believe it can't fit in car frame due to disagreement about simultaneity, whereas I use length contraction to reach the same conclusion. 

I didn’t use any word like “because” or talk about the best conceptual explanation, I just said that the question of whether the car fits in some frame is *equivalent* to the question of the order of the events A and B in that frame. It is of course also equivalent to the question of whether the length of the car is shorter, greater, or equal to the length of the garage in that frame. Equivalent here just means logical equivalence, ie the truth value of the statement “the car doesn’t fit in this frame” is guaranteed to be the same as the truth-value of “B happens before A in this frame” and *also* the same as the truth-value of “the car is longer than the garage in this frame”; it’s impossible in either relativity or classical physics for one of these statements to be true while another one is false, or vice versa. Do you agree they are equivalent in that sense?

 

And we agree it can fit from the pov of the garage frame, since the car's length contracts. So what are we arguing about is this; does the disagreement about fit constitute an objective fact and thus a paradox? AG

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that.

Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following:

"You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense?

As I think I posted, I don't understand the argument that disagreement about simultaneity resolves the paradox. This is surely the standard alleged solution, but using the LT and length contraction, I seem to get a paradox if we assume disagreement about fitting is the cause of the paradox. You claim time-ordering shows the car can't fit. This is my conclusion using length contraction, whiich seems simpler. So, our disagreement of the resolution apparently has nothing to do with whether the car fits from its frame, since we're in agreement that it does not. AG 

No, I wasn’t talking about the best way to understand or explain why the car doesn’t fit, I was just talking about logical equivalence. But as I have said elsewhere, an analysis of relativity of simultaneity is needed conceptually if you want to answer the *separate* question “given that different frames disagree about whether the car fits, how can we avoid the conclusion that they must disagree in their predictions about local physical facts?”

 

If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?"

      Then at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/KmDqElIUAQAJ you quoted my statement above "If you don't see why the ordering of these two events is considered equivalent to the question of fitting," and you responded by saying "It obviously is. Sorry about the confusion. AG"

     In another followup comment at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/gi9RERcVAQAJ you quoted more of the classical covered bridge scenario I had written, and then you replied "I think I agree with your criteria for fit and not fit. What bothers me is the disagreement between frames about fitness or not, and why the alledged lack of simultaneity resolves the apparent contradiction. AG"

If time ordering establishes the car cannot fit in the garage from car's frame, won't the reverse also be true; that the car cannot fit in garage from garage frame for the same reason due to symmetric use of the LT, and that the frames are equivalent in SR. This why I haven't considered disagreement about simultaneity the resolution of the paradox. AG

No, the event B (front of car reaches back of garage) happens before A (back of car passes front of garage) in the car frame in both my and Brent’s examples, but then when you transform the time coordinates of those events into the garage frame, in Brent’s example A happens before B in the garage frame, in my example A and B are simultaneous in the garage frame (in my example, event A in the garage frame was x=0 and t=0, and event B in the garage frame was x=20 and t=0, with velocity of car frame v=0.6 and gamma=1.25). I don’t know why you think “symmetric use of the LT” would contradict that, but you can check yourself that this is true when transforming the coordinates of those events from garage frame to car frame using these equations:

x’ = gamma*(x - vt)

t’ = gamma*(t - vx)

And then you can double check by using the reverse version to transform the coordinates in the car frame back to the garage frame:

x = gamma*(x’ + vt’)

t = gamma*(t’ + vx’)

In your terms would this be “symmetric use of the LT” or would you consider these two pairs of transformation equations “asymmetric” since one pair has - in the middle and the other pair has + in the middle? The reason for that is that the garage frame defines the car frame to be moving at speed v in the +x direction while the car frame defines the garage frame to be moving at speed v in the -x direction.

 

Which frame are you referring to? Presumably the car frame where you claim the car cannot fit.

Read the statement about A and B again, it's an if-then conditional that covers any frame. If we're talking about a frame where B happens before A, then the car does not fit in that frame; if we're talking about a frame where A occurs before B, or simultaneously with it, then the car does fit in that frame.

 

How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG

Yes, the garage can be made arbitrarily short in the car's frame by picking a high relative velocity, why do you think this is at odds with the idea that the car won't fit?

I think that was a typo. Sorry about that! The car couldn't fit initially, so it can't fit when the garage is shorten from the pov of car frame. AG 

Obviously if the length of the garage is shorter than the car, the car will not fit, exactly as would be true in a classical scenario with a garage shorter than a car. And in such a frame, the event B="front of car passes back of garage" happens before the event A="back of car passes front of garage", just as you'd expect in the classical covered bridge scenario I wrote about previously.

As I commented somewhere here in BLUE, won't the reverse also be true due to frame equivalence in SR and permissible symmetric use of LT; namely, that from pov of garage frame, the car won't fit due to disagreement about simultaneity? AG  

No, see my comment immediately above.

 

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree?

In this problem we can assume the garage isn't moving as an objective fact,

Neither classical mechanics nor relativity would agree "the garage isn't moving" is an objective fact, if by "objective" you mean something different frames can agree on. Are you saying that you think classical mechanics is indeed fatally flawed because it makes movement vs. rest entirely frame-dependent?

Well, in this case everyone with common sense knows the garage isn't moving, and what we have is relative motion, which allows us to calculate AS IF the garage is moving. AG 

In neither classical mechanics nor relativity is there any notion of “moving” apart from relative motion—do you think this is in fact a fatal flaw? I don’t think “common sense” is worth anything in science, and of course the same common sense that might lead people to think objects attached to the surface of the Earth “aren’t moving” in some absolute sense would also lead people to think the Earth itself is at rest in an absolute sense, ie geocentrism.

 

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. AG 

Is “actual motion” an untestable metaphysical belief or do you think there is some experiment that can tell us whether an object is actually in motion or actually at rest? If there was, this would contradict not only special relativity but also the principle of Galilean relativity from classical mechanics that I linked earlier.

 

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. 

If you are talking about visual seeing, what they each would see cannot possibly differ if they are at the same point in spacetime, in this case the moment when the front of the car coincides with the end of the garage. Both would agree on whether the back end appears to be inside or outside the garage visually.

Jesse

[Alan Grayson]

The error you're making is over-idealizing a situation without being aware of it.  Sure, it two objects were the only entities in the universe, there would be no experiment which could distinguish which is in motion, if there was motion. But in this situation we know the car is moving and not the garage for the same reason we know the Earth is rotating, and not the stars. That is, we have other reference points to establish which entity is moving, such as the trees surrounding the garage, etc. And this obvious fact in no way suggests some fundamental flaw with the physics of mechanics. Now, on another issue, I told you I don't understand the how lack of simultaneity resolves the paradox, but since we agree that the car cannot fit in the garage from the pov of the car frame, and fits from the pov of the garage frame, we need not discuss the simultaneity issue. As I recall, you dismissed this by claiming that all that mattered was whether the frames agree about local physics at spacetime points. Now, suppose I agree the SR is a local theory, and what you claim is true, how exactly does that defeat my claim that the disagreement of whether the car fits, is an objective fact which leaves the paradox alive and well? I believe it is, although I can't offer a convincing proof, whereas you dismiss it out of hand relying on locality as your argument, which I see an incomplete -- IOW a handwaving argument. AG 

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. AG 

Is “actual motion” an untestable metaphysical belief or do you think there is some experiment that can tell us whether an object is actually in motion or actually at rest? If there was, this would contradict not only special relativity but also the principle of Galilean relativity from classical mechanics that I linked earlier.

See above comment in GREEN. AG  

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. 

If you are talking about visual seeing, what they each would see cannot possibly differ if they are at the same point in spacetime, in this case the moment when the front of the car coincides with the end of the garage. Both would agree on whether the back end appears to be inside or outside the garage visually.

So the frames agree visually, but you still contend the car doesn't fit from pov of car frame due to disagreement about simultaneity? AG 

Jesse

[Alan Grayson]

The error you're making is over-idealizing a situation without being aware of it.  Sure, it two objects were the only entities in the universe, there would be no experiment which could distinguish which is in motion, if there was motion. But in this situation we know the car is moving and not the garage for the same reason we know the Earth is rotating, and not the stars. That is, we have other reference points to establish which entity is moving, such as the trees surrounding the garage, etc. And this obvious fact in no way suggests some fundamental flaw with the physics of mechanics. Now, on another issue, I told you I don't understand the how lack of simultaneity resolves the paradox, but since we agree that the car cannot fit in the garage from the pov of the car frame, and fits from the pov of the garage frame, we need not discuss the simultaneity issue. As I recall, you dismissed this by claiming that all that mattered was whether the frames agree about local physics at spacetime points. Now, suppose I agree the SR is a local theory, and what you claim is true, how exactly does that defeat my claim that the disagreement of whether the car fits, is an objective fact which leaves the paradox alive and well? I believe it is, although I can't offer a convincing proof, whereas you dismiss it out of hand relying on locality as your argument, which I see as incomplete -- IOW a handwaving argument. AG 

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. AG 

Is “actual motion” an untestable metaphysical belief or do you think there is some experiment that can tell us whether an object is actually in motion or actually at rest? If there was, this would contradict not only special relativity but also the principle of Galilean relativity from classical mechanics that I linked earlier.

See above comment in GREEN. AG  

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. 

If you are talking about visual seeing, what they each would see cannot possibly differ if they are at the same point in spacetime, in this case the moment when the front of the car coincides with the end of the garage. Both would agree on whether the back end appears to be inside or outside the garage visually.

So the frames agree visually, but you still contend the car doesn't fit from pov of car frame due to disagreement about simultaneity? AG 

Jesse

Suggest you view my post about this issue on another thread, in response to Quentin's foolishness, title related to the MWI and SuperDeterminism. AG 

[Alan Grayson]

It's puzzling. Maybe my memory is playing tricks on me. But IIRC you and Brent denied my claim of the existence of an objective reality where both frames agreed on fitting or not, and that the paradox is caused by their disagreement of fitting. I found some video links, posted on the MWI thread (in reply to Quentin and Brent) that establishes both of my claims, and proof that the car fits in both frames. I probably misinterpreted Brent's claim about the role of simultaneity, but his denial of an objective reality, where the frames agreed on fitting, turned me off to pursue his solution via plots. AG

[Jesse Mazer]

Could you address my question here about whether you agree that, given the clarification that I am talking about logical equivalence in the sense I discussed above, the question of whether the car fits is completely equivalent to question of the order of the events A="back of car passes front of garage" and B="front of car reaches back of garage"?

To add to my comment above, I realized that even the minor asymmetry in the two sets of equations was because we were using the same "v" in both, standing for the velocity of the primed frame as measured in the unprimed frame--if we introduce a separate variable v' which stands for the velocity of the unprimed frame as measured in the primed frame, then v=0.6 (really 0.6c but I'm using units where c=1) and v'=-0.6, and in this case the two sets of transformation equations do have an identical form:

x' = gamma*(x - vt)

t' = gamma*(t - vx)

and

x = gamma*(x' - v't')

t = gamma*(t' - v'x')

As I said, you can see for yourself that your argument that symmetry in the LT implies both frames must agree on the order of events doesn't make sense, using event A at x=0 and t=0 and B at x=20 and t=0 (so A and B are simultaneous in this frame); using the first set of transformation equations with gamma = 1.25 and v = 0.6 we get that A has coordinates x'=0 and t'=0 in the primed frame, and B has coordinates x'=25 and t'=-15 (so B happens before A in this frame), and if you plug these primed coordinates into the second set of transformation equations with v' = -0.6 you get back the original unprimed coordinates of A and B.

 

 

Which frame are you referring to? Presumably the car frame where you claim the car cannot fit.

Read the statement about A and B again, it's an if-then conditional that covers any frame. If we're talking about a frame where B happens before A, then the car does not fit in that frame; if we're talking about a frame where A occurs before B, or simultaneously with it, then the car does fit in that frame.

 

How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG

Yes, the garage can be made arbitrarily short in the car's frame by picking a high relative velocity, why do you think this is at odds with the idea that the car won't fit?

I think that was a typo. Sorry about that! The car couldn't fit initially, so it can't fit when the garage is shorten from the pov of car frame. AG 

Obviously if the length of the garage is shorter than the car, the car will not fit, exactly as would be true in a classical scenario with a garage shorter than a car. And in such a frame, the event B="front of car passes back of garage" happens before the event A="back of car passes front of garage", just as you'd expect in the classical covered bridge scenario I wrote about previously.

As I commented somewhere here in BLUE, won't the reverse also be true due to frame equivalence in SR and permissible symmetric use of LT; namely, that from pov of garage frame, the car won't fit due to disagreement about simultaneity? AG  

No, see my comment immediately above.

 

 

As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back

Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions.

Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.

That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree?

In this problem we can assume the garage isn't moving as an objective fact,

Neither classical mechanics nor relativity would agree "the garage isn't moving" is an objective fact, if by "objective" you mean something different frames can agree on. Are you saying that you think classical mechanics is indeed fatally flawed because it makes movement vs. rest entirely frame-dependent?

Well, in this case everyone with common sense knows the garage isn't moving, and what we have is relative motion, which allows us to calculate AS IF the garage is moving. AG 

In neither classical mechanics nor relativity is there any notion of “moving” apart from relative motion—do you think this is in fact a fatal flaw? I don’t think “common sense” is worth anything in science, and of course the same common sense that might lead people to think objects attached to the surface of the Earth “aren’t moving” in some absolute sense would also lead people to think the Earth itself is at rest in an absolute sense, ie geocentrism.

The error you're making is over-idealizing a situation without being aware of it.  Sure, it two objects were the only entities in the universe, there would be no experiment which could distinguish which is in motion, if there was motion. But in this situation we know the car is moving and not the garage for the same reason we know the Earth is rotating, and not the stars. That is, we have other reference points to establish which entity is moving, such as the trees surrounding the garage, etc.

OK, so are you understanding "motion" as relative to some sort of cosmic average of everything in the universe, maybe like using the rest frame of the cosmic microwave background radiation to define "true rest"? But this sort of thing wouldn't make sense of your claim that if the car and garage where initially at rest relative to the surface of the Earth that itself was a state of true "rest", since after all relative to all the stars in the universe or to the CMBR the Earth itself is not at rest as it orbits the sun and rotates on its axis. What's more, it could be that the car's velocity once it's moving relative to the garage actually gives it a lower velocity in the "cosmic rest frame" however you wish to define that, so the garage would be moving faster in this frame. And then there is the issue that however you choose to define the cosmic rest frame, it wouldn't be something picked out as a preferred frame by the dynamical laws of physics themselves, only as an invariably somewhat arbitrary function of the distribution of matter/energy in the universe--if someone else came along and gave a different preferred definition that disagreed with yours, it would just be an aesthetic (or metaphysical) disagreement, you wouldn't have any kind of scientific test that could determine which of these definitions was the "correct" one.

But regardless of what aesthetic or metaphysical beliefs you might have about cosmic rest, there is still the basic terminological matter that this is not what *physicists* ever mean when they talk about "rest" and "motion", they are always using it exclusively in the sense of what you called "relative motion", not any sense of absolute rest or motion. So if you try to interpret standard statements in physics, like talk about some object's "rest frame", in terms of your own non-relative notions it's just going to lead to verbal confusion and misunderstanding, as it has in our discussion. If you do ever return to your list of "?"s about my numerical example, try first re-reading the statements of mine you weren't following with the understanding that I only ever use "rest" and "motion" in the relative way as per standard physics terminology, it might clear some things up.

 

And this obvious fact in no way suggests some fundamental flaw with the physics of mechanics. Now, on another issue, I told you I don't understand the how lack of simultaneity resolves the paradox, but since we agree that the car cannot fit in the garage from the pov of the car frame, and fits from the pov of the garage frame, we need not discuss the simultaneity issue. As I recall, you dismissed this by claiming that all that mattered was whether the frames agree about local physics at spacetime points. Now, suppose I agree the SR is a local theory, and what you claim is true, how exactly does that defeat my claim that the disagreement of whether the car fits, is an objective fact which leaves the paradox alive and well? I believe it is, although I can't offer a convincing proof, whereas you dismiss it out of hand relying on locality as your argument, which I see an incomplete -- IOW a handwaving argument. AG 

 And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG

Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest".

That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. AG 

Is “actual motion” an untestable metaphysical belief or do you think there is some experiment that can tell us whether an object is actually in motion or actually at rest? If there was, this would contradict not only special relativity but also the principle of Galilean relativity from classical mechanics that I linked earlier.

See above comment in GREEN. AG  

 

If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not?

 This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG

By juxtaposed do you just mean both observers are at the same point in spacetime?

 

The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG

 

But as I pointed out they won’t have a different visual opinion about whether the car fits in this case,

So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG

If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car.

I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. 

If you are talking about visual seeing, what they each would see cannot possibly differ if they are at the same point in spacetime, in this case the moment when the front of the car coincides with the end of the garage. Both would agree on whether the back end appears to be inside or outside the garage visually.

So the frames agree visually, but you still contend the car doesn't fit from pov of car frame due to disagreement about simultaneity? AG

Yes, for any specific point in spacetime, different frames agree visually about what is seen at that point (some points see the car as visually longer than the garage, others shorter). And yes, in terms of coordinates assigned in the car frame, the car does not fit. I have not said this is "due to disagreement about simultaneity", if you look at the part of my previous reply about logical equivalence, I started by saying 'I didn’t use any word like “because” or talk about the best conceptual explanation, I just said that the question of whether the car fits in some frame is *equivalent* to the question of the order of the events A and B in that frame. It is of course also equivalent to the question of whether the length of the car is shorter, greater, or equal to the length of the garage in that frame.' 

A little later in that reply I also said 'No, I wasn’t talking about the best way to understand or explain why the car doesn’t fit, I was just talking about logical equivalence. But as I have said elsewhere, an analysis of relativity of simultaneity is needed conceptually if you want to answer the *separate* question “given that different frames disagree about whether the car fits, how can we avoid the conclusion that they must disagree in their predictions about local physical facts?”'

Jesse

[Alan Grayson]

I apologize for being so dumb, but whereas I'm comfortable using relative lengths of car and garage to determine fitting or not, I don't really understand that the reversal of time order, of event B preceding event A, is equivalent to car not fitting in garage. Concerning those videos, two which were reviewed on this MB, one by Brent and one by you, they falsely claim to show that from the car frame, the car really does fit in the garage. This is what one expect to show if the disagreement of the frames is the cause of the paradox, but apparently it isn't, and the disagreement about simultaneity alone is sufficient to resolve the paradox. This is what I am trying now to understand. AG

And we agree it can fit from the pov of the garage frame, since the car's length contracts. So what are we arguing about is this; does the disagreement about fit constitute an objective fact and thus a paradox? AG

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that.

Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following:

"You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense?

As I think I posted, I don't understand the argument that disagreement about simultaneity resolves the paradox. This is surely the standard alleged solution, but using the LT and length contraction, I seem to get a paradox if we assume disagreement about fitting is the cause of the paradox. You claim time-ordering shows the car can't fit. This is my conclusion using length contraction, whiich seems simpler. So, our disagreement of the resolution apparently has nothing to do with whether the car fits from its frame, since we're in agreement that it does not. AG 

No, I wasn’t talking about the best way to understand or explain why the car doesn’t fit, I was just talking about logical equivalence. But as I have said elsewhere, an analysis of relativity of simultaneity is needed conceptually if you want to answer the *separate* question “given that different frames disagree about whether the car fits, how can we avoid the conclusion that they must disagree in their predictions about local physical facts?” 

If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?"

I'm not sure. I have to think about this some more. Why can't we just stick to lengths? AG 

[Alan Grayson]

OK, I give up! How is the paradox solved using disagreement of simultaneity? You can assume the car perfectly fits in garage from the pov of garage frame, and that the endpoints of car are simultaneous. TY, AG

[Quentin Anciaux]

Chatgpt:

Please an explanation for a very stupid with an IQ less than 50.

------

Alright, here’s a super simple explanation:

Imagine a car going super fast, almost as fast as light, and a tiny garage. The car is longer than the garage, so you wonder, "How can it fit?"

What happens:

When something moves really fast, it looks shorter to someone watching it.

If you stand outside the garage, the car looks shorter, so it can fit inside for a moment.

But if you're in the car, the garage looks smaller, so it feels like the car can't fit.

Why it’s okay:

For the person at the garage: The car fits because the car looks smaller.

For the person in the car: The garage doesn’t look big enough, but the doors close at different times, so nothing crashes.

Simple Conclusion:

The car and the garage don’t agree on what happens, but both are right in their own way. It’s not magic—it’s just how speed changes what you see. No crashes, no problem!

Le mar. 31 déc. 2024, 10:55, Alan Grayson <agrays...@gmail.com> a écrit :

OK, I give up! How is the paradox solved using disagreement of simultaneity? You can assume the car perfectly fits in garage from the pov of garage frame, and that the endpoints of car are simultaneous. TY, AG

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[Alan Grayson]

On Tuesday, December 31, 2024 at 3:59:54 AM UTC-7 Quentin Anciaux wrote:

Chatgpt:

Please an explanation for a very stupid with an IQ less than 50.

------

Alright, here’s a super simple explanation:

Imagine a car going super fast, almost as fast as light, and a tiny garage. The car is longer than the garage, so you wonder, "How can it fit?"

What happens:

When something moves really fast, it looks shorter to someone watching it.

If you stand outside the garage, the car looks shorter, so it can fit inside for a moment.

But if you're in the car, the garage looks smaller, so it feels like the car can't fit.

Why it’s okay:

For the person at the garage: The car fits because the car looks smaller.

For the person in the car: The garage doesn’t look big enough, but the doors close at different times, so nothing crashes.

Simple Conclusion:

The car and the garage don’t agree on what happens, but both are right in their own way. It’s not magic—it’s just how speed changes what you see. No crashes, no problem!

I could have written exactly what you just posted, but with my IQ it really doesn't answer the question. Sure the frames disagree. We knew that at the get-go, using length contraction. I'll give you more chances to offer a real solution. Try not to embarass yourself. AG 

[Quentin Anciaux]

Le mar. 31 déc. 2024, 11:19, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, December 31, 2024 at 3:59:54 AM UTC-7 Quentin Anciaux wrote:

Chatgpt:

Please an explanation for a very stupid with an IQ less than 50.

------

Alright, here’s a super simple explanation:

Imagine a car going super fast, almost as fast as light, and a tiny garage. The car is longer than the garage, so you wonder, "How can it fit?"

What happens:

When something moves really fast, it looks shorter to someone watching it.

If you stand outside the garage, the car looks shorter, so it can fit inside for a moment.

But if you're in the car, the garage looks smaller, so it feels like the car can't fit.

Why it’s okay:

For the person at the garage: The car fits because the car looks smaller.

For the person in the car: The garage doesn’t look big enough, but the doors close at different times, so nothing crashes.

Simple Conclusion:

The car and the garage don’t agree on what happens, but both are right in their own way. It’s not magic—it’s just how speed changes what you see. No crashes, no problem!

I could have written exactly what you just posted, but with my IQ it really doesn't answer the question. Sure the frames disagree. We knew that at the get-go, using length contraction. I'll give you more chances to offer a real solution. Try not to embarass yourself. AG 

The only embarrassment is on your side, but no one expects you to understand. Your pride is too high with a too low IQ.

Le mar. 31 déc. 2024, 10:55, Alan Grayson <agrays...@gmail.com> a écrit :

OK, I give up! How is the paradox solved using disagreement of simultaneity? You can assume the car perfectly fits in garage from the pov of garage frame, and that the endpoints of car are simultaneous. TY, AG

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[Alan Grayson]

On Tuesday, December 31, 2024 at 5:19:54 AM UTC-7 Quentin Anciaux wrote:

Le mar. 31 déc. 2024, 11:19, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, December 31, 2024 at 3:59:54 AM UTC-7 Quentin Anciaux wrote:

Chatgpt:

Please an explanation for a very stupid with an IQ less than 50.

------

Alright, here’s a super simple explanation:

Imagine a car going super fast, almost as fast as light, and a tiny garage. The car is longer than the garage, so you wonder, "How can it fit?"

What happens:

When something moves really fast, it looks shorter to someone watching it.

If you stand outside the garage, the car looks shorter, so it can fit inside for a moment.

But if you're in the car, the garage looks smaller, so it feels like the car can't fit.

Why it’s okay:

For the person at the garage: The car fits because the car looks smaller.

For the person in the car: The garage doesn’t look big enough, but the doors close at different times, so nothing crashes.

Simple Conclusion:

The car and the garage don’t agree on what happens, but both are right in their own way. It’s not magic—it’s just how speed changes what you see. No crashes, no problem!

I could have written exactly what you just posted, but with my IQ it really doesn't answer the question. Sure the frames disagree. We knew that at the get-go, using length contraction. I'll give you more chances to offer a real solution. Try not to embarass yourself. AG 

The only embarrassment is on your side, but no one expects you to understand. Your pride is too high with a too low IQ.

You just don't get it. A long long time ago, on a galaxy far far away, the LT was applied on this problem, with the result that the frames disagree about fitting. Tell us exactly what your posts today have revealed differently? LOL. AG 

[Alan Grayson]

On Tuesday, December 31, 2024 at 3:55:00 AM UTC-7 Alan Grayson wrote:

OK, I give up! How is the paradox solved using disagreement of simultaneity? You can assume the car perfectly fits in garage from the pov of garage frame, and that the endpoints of car are simultaneous. TY, AG

Jesse; how has Brent's solution with plots differ in its results from mine, where I just used length contraction? I think they're virtually identical in the results, even though he applies disagreement about simultaneity. TY, AG 

[Jesse Mazer]

 OK, but are you making an effort to understand? In general do you actually want to understand what relativity says about these matters, or do you just want to score a rhetorical "win" for your own arguments? If you're interested in understanding rather than winning then you can't just stick by whatever way of thinking is most comfortable for you, or most conducive to your argument.

Concerning those videos, two which were reviewed on this MB, one by Brent and one by you, they falsely claim to show that from the car frame, the car really does fit in the garage.

I watched the video and I never saw him make the false claim that the pole (which takes the place of a car in that video) fits in the garage in the pole's own frame. If you disagree, can you point to a time index in the video where he says this, or a time index in the first video where he says the car fits in the garage in the car's frame?

 

This is what one expect to show if the disagreement of the frames is the cause of the paradox, but apparently it isn't, and the disagreement about simultaneity alone is sufficient to resolve the paradox. This is what I am trying now to understand. AG

And we agree it can fit from the pov of the garage frame, since the car's length contracts. So what are we arguing about is this; does the disagreement about fit constitute an objective fact and thus a paradox? AG

 

 

What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG 

Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.

It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances.

Jesse 

Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG

Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting.

In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG

You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0.

And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame?

This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here.

Your memory is in error. I never agreed to that.

Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following:

"You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense?

As I think I posted, I don't understand the argument that disagreement about simultaneity resolves the paradox. This is surely the standard alleged solution, but using the LT and length contraction, I seem to get a paradox if we assume disagreement about fitting is the cause of the paradox. You claim time-ordering shows the car can't fit. This is my conclusion using length contraction, whiich seems simpler. So, our disagreement of the resolution apparently has nothing to do with whether the car fits from its frame, since we're in agreement that it does not. AG 

No, I wasn’t talking about the best way to understand or explain why the car doesn’t fit, I was just talking about logical equivalence. But as I have said elsewhere, an analysis of relativity of simultaneity is needed conceptually if you want to answer the *separate* question “given that different frames disagree about whether the car fits, how can we avoid the conclusion that they must disagree in their predictions about local physical facts?” 

If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?"

I'm not sure. I have to think about this some more. Why can't we just stick to lengths? AG 

You could at least ask some questions about whatever is puzzling you rather than just avoiding the subject by switching to exclusive talk about length. Remember, this is a purely classical scenario, no tricky issues of length contraction or simultaneity. Classically, if we have an 18-foot long limousine driving through a covered bridge that's only 6 feet wide, and you're watching from the side with the limousine moving left to right, are you genuinely unsure about whether you'll see the front of the limousine poke out of the right side of the covered bridge BEFORE or AFTER the back of the limousine first disappears behind the left side of the covered bridge? If the front didn't poke out from behind the right side of the covered bridge until AFTER the back disappeared behind the left side, that would mean there was some period of time where the 18-foot limousine was wholly obscured from view behind the 6-foot covered bridge, which doesn't make a lot of sense geometrically.

Jesse

[Quentin Anciaux]

It's the new year, and I'm really really sad we have to had more than 200 exchanges for this obvious mf troll.... we are the everything list, a mailing list which exists for almost 30 years, I was 17 years old when I discovered it, and now the only discussion left is alan Grayson and cosmin stupid... what a disgrace it is ? Anyway happy new year to you all, even to the trolls.

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[Alan Grayson]

All I want is to make some rhetorical points. What else could possibly matter? And NO, I am definitely NOT making any effort to understand. Why should I? After all, I am just a troll and this is what trolls do. AG

This problem arose as an apparent paradox because two frames give diametrically opposite conclusions in a particular situation. My result using length contraction showed the same opposite conclusions. So, in an effort to resolve the paradox, I consulted many sources, and it seems they all reached the same conclusion as I did, but though different routes. That's why Brent posted there's no objective result. Moreover, the videos do not prove, despite what some of them claim, that the car fits in the garage from the pov of the car frame. If the foregoing is correct, I don't believe these various path resolve the paradox. Rather, they're just re-stating it under different conditions. Correct me if I am wrong. AG 

[Quentin Anciaux]

What pains me the most, is that this mailing list had I think the most influential and best thinkers of this century and we're left with that... this list had (and still has for those not in the mind bending dead state) hal finney, wei dai, jurgen Schmidhuber, Russell Standish,  Saibal Mitra, Jason Resch, Terren Suydam, Telmo Menezez,  Brent Meeker, Bruno Marchal and all of the nice non troll and truth seeking humans in this reality that I forgot,  happy new year, happy  new day to be alive to you all and happy discovering of this mind bending reality. I really love you all, even the ones who triggers that bad feelings in me.

Quentin 

[Alan Grayson]

This problem arose as an apparent paradox because two frames give diametrically opposite conclusions in a particular situation. My result using length contraction showed the same opposite conclusions. So, in an effort to resolve the paradox, I consulted many sources, and it seems they all reached the same conclusion as I did, but through different routes. That's why Brent posted there's no objective result. Moreover, the videos do not prove, despite what some of them claim, that the car fits in the garage from the pov of the car frame. If the foregoing is correct, I don't believe these various path resolve the paradox. Rather, they're just re-stating it under different conditions. Correct me if I am wrong. AG