Brent on Parking Paradox

[Alan Grayson]

Clark posted, and I agree, that the paradox is rooted in the assumption that fitting and not fitting of car in garage, from frame of garage and frame of car do not happen at the same time. AG

But you posted "They do happen at the same time as clearly shown on my diagrams.  In the garage frame the entrance door closes before the exit door has to open.  The car is in the garage for about 2.5 nano-seconds. In the car frame the doors are open at the same time so the car extends thru both."

Please explain this apparent discrepancy. AG

[Alan Grayson]

Gentleman's C. Grade as a teacher of SR. AG 

[Jesse Mazer]

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

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[Alan Grayson]

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

I go by what he writes, not how someone interprets his words.  AG

[Jesse Mazer]

On Wed, Jan 22, 2025 at 4:08 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

I go by what he writes, not how someone interprets his words.  AG

So are you just asking an open-ended question about what he means by "at the same time" without imposing your own *interpretation* that this necessarily must conflict with the idea you stated at the beginning, "the assumption that fitting and not fitting of car in garage, from frame of garage and frame of car do not happen at the same time"? You allow for the possibility that his statement and your statement may just be using the informal phrase "at the same time" in different ways, without an actual substantive conflict in ideas?

Jesse

[Alan Grayson]

Whille I am open to any possibility, it's invariably alleged that the disagreement about simultaneity means the contrary events don't occur at the same time, and this allegedly solves the problem. So a good teacher would try to resolve his words without resorting to the "Heavyside" cop out. It's ironic that you, a stickler for precision in words, let this slide so easily. AG 

[Jesse Mazer]

I'm a stickler about words only when I think unclear phrases lead to ambiguity about meaning, but since Brent knows his SR and emphasized many times that the two frames have different definitions of simultaneity I don't think there's any real possibility he was going back on that with these words, although I might criticize his choice of words insofar as they can be potentially misleading to someone who isn't already clear on this stuff.

Jesse

[Alan Grayson]

Brent wrote the car fits and doesn't fit "at the same time". How does this affirm the disagreement about simultaneity? AG 

[Jesse Mazer]

His statement is ambiguous on its own which is why I said I would criticize his word choice, but I did give you a plausible reading of what he could have meant that wouldn't conflict with the relativity of simultaneity (in the garage frame it fits at the same time as some event A, in the car frame it doesn't fit at the same time as the same event A, so a person might use the shorthand 'it fits and doesn't fit at the same time' for this). You criticized this as an interpretation, but your own notion that his words *do* conflict with relativity of simultaneity is also just an interpretation, and I think a much less plausible one given that he affirms the relativity of simultaneity over and over in his posts (presumably you agree that context is relevant when interpreting someone's words).

Jesse

[Brent Meeker]

And F for you as a student of SR.

Brent.

[Alan Grayson]

He may mean this; he may be that; who knows what he actually means and he aint' talking = gentleman's grade of C as a teacher of relativity. AG

[Alan Grayson]

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

[Jesse Mazer]

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

 

On Wed, Jan 22, 2025 at 3:00 PM Alan Grayson <agrays...@gmail.com> wrote:

On Monday, January 20, 2025 at 8:56:01 AM UTC-7 Alan Grayson wrote:

Clark posted, and I agree, that the paradox is rooted in the assumption that fitting and not fitting of car in garage, from frame of garage and frame of car do not happen at the same time. AG

But you posted "They do happen at the same time as clearly shown on my diagrams.  In the garage frame the entrance door closes before the exit door has to open.  The car is in the garage for about 2.5 nano-seconds. In the car frame the doors are open at the same time so the car extends thru both."

Please explain this apparent discrepancy. AG

Gentleman's C. Grade as a teacher of SR. AG 

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[Alan Grayson]

The difference between our grading results is that whereas I am generous, you are not. Further, many of my questions are way above much better grades. For example, when you write that the car fitting and not fitting "happen at the same time", this is obviously a very imprecise, or shall we say sloppy statement which doesn't give good credit to someone who claims to be a teacher of SR. Specifically, in the not fitting case, there are several DIFFERENT times that could be "the same time" in your statement, whereas, for example, in the case where the car fits perfectly, you are referring to a single time. It's quite possible, even likely I would say, that most of those who read your statement wouldn't have notice this distinction. Many of my questions fall into this type of category. I rest my case. AG 

[Alan Grayson]

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

[Alan Grayson]

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

[Jesse Mazer]

On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

The paradox is the seeming danger that the disagreement about fitting could lead to differing predictions local physical facts, and the relativity of simultaneity shows how this danger is avoided. 

In particular, if we have a version of the problem where in the garage frame both garage doors shut simultaneously and then re-open, if both frames *did* agree about simultaneity this would clearly lead to a conflict. In the garage frame, since the car fits entirely within the garage for a short time, that means both doors can close simultaneously without hitting the car; but in the car frame, since the car never fits entirely within the garage, if both doors also closed simultaneously in this frame, one of the doors would have to smash into some part of the car that was blocking the door frame at that moment (whether or not the door collides with the car is a local physical fact). But with the relativity of simultaneity you can show that if the doors shut simultaneously in the garage frame, in the car frame the right door closes first before the front of the car has reached its location so there is no collision, and then the left door closes later after the back of the car has passed it, so a collision is avoided there too.

Jesse

[Alan Grayson]

On Thursday, January 23, 2025 at 2:51:50 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

The paradox is the seeming danger that the disagreement about fitting could lead to differing predictions local physical facts, and the relativity of simultaneity shows how this danger is avoided. 

How do you define the local physical facts that both frames must agree to? AG 

In particular, if we have a version of the problem where in the garage frame both garage doors shut simultaneously and then re-open, if both frames *did* agree about simultaneity this would clearly lead to a conflict. In the garage frame, since the car fits entirely within the garage for a short time, that means both doors can close simultaneously without hitting the car; but in the car frame, since the car never fits entirely within the garage, if both doors also closed simultaneously in this frame, one of the doors would have to smash into some part of the car that was blocking the door frame at that moment (whether or not the door collides with the car is a local physical fact). But with the relativity of simultaneity you can show that if the doors shut simultaneously in the garage frame, in the car frame the right door closes first before the front of the car has reached its location so there is no collision, and then the left door closes later after the back of the car has passed it, so a collision is avoided there too.

Does the resolution of the paradox require the existence of garage doors? If you imagine a garage with no doors, does the paradox continue to exist? AG 

Jesse

[Jesse Mazer]

On Thu, Jan 23, 2025 at 5:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 2:51:50 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

The paradox is the seeming danger that the disagreement about fitting could lead to differing predictions local physical facts, and the relativity of simultaneity shows how this danger is avoided. 

How do you define the local physical facts that both frames must agree to? AG 

I explained the concept in a number of posts on the "ATTN: Jesse" thread you started earlier, like https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/xCpbnK-AAgAJ and https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/IENKOmsaAwAJ

 

In particular, if we have a version of the problem where in the garage frame both garage doors shut simultaneously and then re-open, if both frames *did* agree about simultaneity this would clearly lead to a conflict. In the garage frame, since the car fits entirely within the garage for a short time, that means both doors can close simultaneously without hitting the car; but in the car frame, since the car never fits entirely within the garage, if both doors also closed simultaneously in this frame, one of the doors would have to smash into some part of the car that was blocking the door frame at that moment (whether or not the door collides with the car is a local physical fact). But with the relativity of simultaneity you can show that if the doors shut simultaneously in the garage frame, in the car frame the right door closes first before the front of the car has reached its location so there is no collision, and then the left door closes later after the back of the car has passed it, so a collision is avoided there too.

Does the resolution of the paradox require the existence of garage doors? If you imagine a garage with no doors, does the paradox continue to exist? AG 

You can define it in any other way that allows you to physically identify specific events on the worldlines of different parts of the garage (like the front and back openings) and different parts of the car (like front and back end of the car), like if you imagine clocks attached to them so you can identify points an a worldline by the readings on the attached clock. And the paradox is about a theoretical situation anyway (we don't have the practical ability to shoot a car through a garage fast enough that there would be measurable disagreements about fit), it would be a fatal flaw for the theory of relativity if any situation whatsoever led to conflicting predictions about local events, regardless of whether it was realized.

Jesse

[Alan Grayson]

On Thursday, January 23, 2025 at 6:03:17 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 5:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 2:51:50 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

The paradox is the seeming danger that the disagreement about fitting could lead to differing predictions local physical facts, and the relativity of simultaneity shows how this danger is avoided. 

How do you define the local physical facts that both frames must agree to? AG 

I explained the concept in a number of posts on the "ATTN: Jesse" thread you started earlier, like https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/xCpbnK-AAgAJ and https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/IENKOmsaAwAJ

 

In particular, if we have a version of the problem where in the garage frame both garage doors shut simultaneously and then re-open, if both frames *did* agree about simultaneity this would clearly lead to a conflict. In the garage frame, since the car fits entirely within the garage for a short time, that means both doors can close simultaneously without hitting the car; but in the car frame, since the car never fits entirely within the garage, if both doors also closed simultaneously in this frame, one of the doors would have to smash into some part of the car that was blocking the door frame at that moment (whether or not the door collides with the car is a local physical fact). But with the relativity of simultaneity you can show that if the doors shut simultaneously in the garage frame, in the car frame the right door closes first before the front of the car has reached its location so there is no collision, and then the left door closes later after the back of the car has passed it, so a collision is avoided there too.

Can the above result be obtained by simply using the LT time translation t --> t' applied to the endpoints of the car fitting in garage from the pov of the garage frame, or is more required? TY, AG

[Brent Meeker]

Having the doors close and then open seems like a confusing complication to me.  That's why I start with the exit door closed and the entrance door open.  Then there are only two "door" events.  The exit door opens and the entrance door closes.  If that's the time order, there's a period when both doors are open.  If, in a different reference frame, the order is reversed, there's a period when both doors are closed.  Talk of simultaneity is slightly misleading, what we're talking about is reversal of time order between the car's reference frame and the garage's reference frame.  Of course that implies that there is some intermediate reference frame in which the exit door opens and the entrance door closes simultaneously, but that's not the essence of the seeming paradox.

Brent

[Alan Grayson]

So, what IS the essence of the seeming paradox? AG

[Brent Meeker]

That's exactly what my diagram shows.  Didn't you look at it?

Brent

[Brent Meeker]

Apparently it's that some people cannot understand that changing reference frames can change the order of events.

Brent

[Alan Grayson]

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

[Jesse Mazer]

On Fri, Jan 24, 2025 at 12:06 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 6:03:17 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 5:55 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 2:51:50 PM UTC-7 Jesse Mazer wrote:

On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:

On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer wrote:

On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7 Jesse Mazer wrote:

Brent hasn't chosen to answer your question, but my guess would be he just means if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A). He obviously isn't disputing the notion that the two frames have different definitions of simultaneity since he made this point many times in his comments.

Jesse

If that's what Brent means, how is this related to the breakdown of simultaneity? AG 

Are you asking about where to find a breakdown of simultaneity in my statement 'if you pick some specific event where part of the car is inside the garage, like the event A of the back of the car passing the garage entry door, in the garage frame the car is fully inside the garage "at the same time" as event A (using the garage frame definition of other events simultaneous with A), while in the car frame the front of the car is already well past the exit of the garage "at the same time" as event A (using the car frame definition of other events simultaneous with A)'? 

If so, in that statement I'm saying that the two frames disagree about which event at the front of the car is simultaneous with A, the garage frame picks an event B on front of the car's worldline where the front of the car is inside the garage and hasn't yet reached the exit, the car frame picks a different event C on the front of the car's worldline where the front of the car is outside the garage, having already passed through the exit. In the garage frame A is simultaneous with B, in the car frame A is simultaneous with C.

Jesse

OK, let's suppose you've identified events which aren't simultaneous in both frames, you still have a car, the same car, which fits in one frame and never in the other. For me this still seems paradoxical even though I agree that relativity allows different frames to make different measurements of the same phenomena such as the B and E fields in E&M.  AG

Here's what I want to know; how exactly do you define the paradox (what it is), and how does the disagreement about simultaneity solve it for you? AG 

The paradox is the seeming danger that the disagreement about fitting could lead to differing predictions local physical facts, and the relativity of simultaneity shows how this danger is avoided. 

How do you define the local physical facts that both frames must agree to? AG 

I explained the concept in a number of posts on the "ATTN: Jesse" thread you started earlier, like https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/xCpbnK-AAgAJ and https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/IENKOmsaAwAJ

 

In particular, if we have a version of the problem where in the garage frame both garage doors shut simultaneously and then re-open, if both frames *did* agree about simultaneity this would clearly lead to a conflict. In the garage frame, since the car fits entirely within the garage for a short time, that means both doors can close simultaneously without hitting the car; but in the car frame, since the car never fits entirely within the garage, if both doors also closed simultaneously in this frame, one of the doors would have to smash into some part of the car that was blocking the door frame at that moment (whether or not the door collides with the car is a local physical fact). But with the relativity of simultaneity you can show that if the doors shut simultaneously in the garage frame, in the car frame the right door closes first before the front of the car has reached its location so there is no collision, and then the left door closes later after the back of the car has passed it, so a collision is avoided there too.

Can the above result be obtained by simply using the LT time translation t --> t' applied to the endpoints of the car fitting in garage from the pov of the garage frame, or is more required? TY, AG

You would want to first apply the LT to the garage door closing events in the garage frame, in order to find the coordinates of the closing events (both position and time) in the car frame. No *single* pair of events on the endpoints of the car would be sufficient to get an understanding of fitting vs. not fitting, since checking if the car fits at some time coordinate in a given frame requires knowing the *simultaneous* position of the front and back of the car in that frame, but a pair of events at the front and back of the car which are simultaneous in one frame will be non-simultaneous in the other. But you could take the x(t) functions for front and back of the car in one frame and substitute them into the LT and solve the resulting equations to find the x'(t') functions for front and back of the car in the other frame. 

You can also figure out x(t) and x'(t') for the back and front of the car with less algebra just by using the length contraction equation. For example if in the car frame the back end of the car has fixed position x'=0 and the front end has fixed position x'=10, this tells you the car has length 10 in its own frame, so if the car has velocity 0.6c in the garage frame it should have a contracted length of 10*(1/sqrt(1 - 0.6^2)) = 8 in the garage frame. That tells you that in garage frame the back of the car should have x(t)=0.6c*t and the front of the car will have x(t)=8 + 0.6c*t (these equations ensure that the distance between front and back is always 8 at any value of t, and that both have a velocity of 0.6c in this frame; the equation for the back of the car also ensures that at t=0 it has position x=0, which has to be true if it had position x'=0 at t'=0 in the garage frame, since the LT maps x=0,t=0 to x'=0,t'=0). And then if you want, you can double check these equations by taking a particular value of x,t for any event along the worldline of the back of the car (say, t=5 seconds and x=3 light-seconds, which is along the line x(t)=0.6c*t) and applying the LT position translation equation x' = gamma*(x - vt) to verify it gives a value of x'=0 in the garage frame (in this example gamma = 1.25 and v=0.6, so you get x' = 1.25*(3 - 0.6*5) = 1.25*(3 - 3) = 0), likewise with applying the LT position translation equation to any event on the worldline of the front of the car and verifying it gives a value of x'=10.

Jesse

 

Does the resolution of the paradox require the existence of garage doors? If you imagine a garage with no doors, does the paradox continue to exist? AG 

You can define it in any other way that allows you to physically identify specific events on the worldlines of different parts of the garage (like the front and back openings) and different parts of the car (like front and back end of the car), like if you imagine clocks attached to them so you can identify points an a worldline by the readings on the attached clock. And the paradox is about a theoretical situation anyway (we don't have the practical ability to shoot a car through a garage fast enough that there would be measurable disagreements about fit), it would be a fatal flaw for the theory of relativity if any situation whatsoever led to conflicting predictions about local events, regardless of whether it was realized.

Jesse

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[Jesse Mazer]

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Jesse

[Alan Grayson]

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Jesse

[Jesse Mazer]

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated. It's pairs of points in spacetime, or equivalently pairs of local physical events occuring at each point (like the event of the back of the car passing the entrance of the garage vs. the event of the front of the car reaching the back of the garage), that can be spacelike separated. If you know the distance x and time interval t between the two points/events in the coordinates of any inertial frame, to say they are spacelike separated just means that x > ct (and an equivalent definition is that neither point is in the past or future light cone of the other one). For any two such points/events A and B with a spacelike separation, you can always find some frames where A occurs before B and other frames where B occurs before A, that's something that can be derived from the Lorentz transformation equations.

Jesse

[Alan Grayson]

On Friday, January 24, 2025 at 2:21:43 PM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 4:04 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 10:41:45 AM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated.

Right. I was skeptical about what I wrote, when I wrote it. OTOH, since EVENTS can be spacelike separated, I don't see any such events in this problem. For example, the ends of the car aren't spacelike separated; neither are the ends of the garage. If Brent weren't a failing teacher of SR, he would specify what he means. I am in no mood to guess his meaning. AG

[Alan Grayson]

On Friday, January 24, 2025 at 6:06:49 PM UTC-7 Alan Grayson wrote:

On Friday, January 24, 2025 at 2:21:43 PM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 4:04 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 10:41:45 AM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated.

Right. I was skeptical about what I wrote, when I wrote it. OTOH, since EVENTS can be spacelike separated, I don't see any such events in this problem. For example, the ends of the car aren't spacelike separated; neither are the ends of the garage. If Brent weren't a failing teacher of SR, he would specify what he means. I am in no mood to guess his meaning. AG

You covered this issue in an earlier post. I need some time to catch up to your explanations, which I appreciate. AG 

[Jesse Mazer]

On Fri, Jan 24, 2025 at 8:06 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 2:21:43 PM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 4:04 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 10:41:45 AM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated.

Right. I was skeptical about what I wrote, when I wrote it. OTOH, since EVENTS can be spacelike separated, I don't see any such events in this problem. For example, the ends of the car aren't spacelike separated; neither are the ends of the garage. If Brent weren't a failing teacher of SR, he would specify what he means. I am in no mood to guess his meaning. AG

The ends of the car are extended worldlines which include multiple events (just as a line contains multiple points in Euclidean geometry), you can pick a particular event A on the worldline of the back of the car and an event B on the worldline of the front of the car (or on the front and back of the garage) such that A and B have a spacelike separation. As I said, spacelike separation just means that if the spatial separation between the points is x and the temporal separation is t (as measured in some inertial frame), then x > ct; for example, this will be automatically true for any pair of events A and B at the front and back of the car that are simultaneous in that frame (because in the case of simultaneous events, the temporal separation t is 0, so the condition x > ct reduces to x > 0).

Jesse

[Brent Meeker]

On 1/24/2025 5:06 PM, Alan Grayson wrote:

On Friday, January 24, 2025 at 2:21:43 PM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 4:04 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 10:41:45 AM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated.

Right. I was skeptical about what I wrote, when I wrote it. OTOH, since EVENTS can be spacelike separated, I don't see any such events in this problem. For example, the ends of the car aren't spacelike separated; neither are the ends of the garage. If Brent weren't a failing teacher of SR, he would specify what he means. I am in no mood to guess his meaning. AG

You mean you just want to keep trolling Jesse.

Brent

 

It's pairs of points in spacetime, or equivalently pairs of local physical events occuring at each point (like the event of the back of the car passing the entrance of the garage vs. the event of the front of the car reaching the back of the garage), that can be spacelike separated. If you know the distance x and time interval t between the two points/events in the coordinates of any inertial frame, to say they are spacelike separated just means that x > ct (and an equivalent definition is that neither point is in the past or future light cone of the other one). For any two such points/events A and B with a spacelike separation, you can always find some frames where A occurs before B and other frames where B occurs before A, that's something that can be derived from the Lorentz transformation equations.

Jesse

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[Alan Grayson]

On Friday, January 24, 2025 at 10:29:03 PM UTC-7 Brent Meeker wrote:

On 1/24/2025 5:06 PM, Alan Grayson wrote:

        On Friday, January 24, 2025 at 2:21:43 PM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 4:04 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, January 24, 2025 at 10:41:45 AM UTC-7 Jesse Mazer wrote:

On Fri, Jan 24, 2025 at 8:53 AM Alan Grayson <agrays...@gmail.com> wrote:

On Thursday, January 23, 2025 at 11:46:46 PM UTC-7 Brent Meeker wrote:

That's exactly what my diagram shows.  Didn't you look at it?

Brent

Sure, I looked at it but I prefer text, and I forgot you're a deaf mute. And NO, I didn't know that frame transformations can invert time relations.  Let's forget it. I forgot you prefer your riddles. Grade C- . AG

The point that the LT can change the order of events with a spacelike separation is one I also talked about many times on the previous thread, for example at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/knVuCxHFAwAJ where I wrote: "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." Likewise in https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/MwKDuJM-AQAJ where I wrote: "Do you understand that when people talk about the relativity of simultaneity in the context of the car/garage problem, they are referring not just to events which are actually simultaneous in some frame, but also the fact that different frames can disagree about the time-ordering of events with a spacelike separation (i.e. neither event is in the past or future light cone of the other event)? The events A and B I was talking about earlier are not simultaneous in either the car frame or the garage frame (at least not with the numerical values for rest lengths and relative velocity given by Brent), but they happen in a different order in the two frames, and the relativity of simultaneity is key to understanding how that's possible, in Newtonian physics where all inertial frames agree about simultaneity there could be no disagreement about the order of any events."

Brent has made this point in the past as well, for example at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/WcxkopmjAAAJ where he wrote: "The facts are events in spacetime.  There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage.  If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit.  But if F and  R are spacelike, then there is no fact of the matter about their time order.  The time order will depend on the state of motion."

Did you really not remember any of these discussions, or did you just misunderstand the meaning of "invert time relations" to be something different than the idea that two events A and B with a spacelike separation can have a different time-order in different frames?

Of course I recall, but I haven't had time to research the issue, such as why the frames in the problem are, or might be, spacelike separated. AG 

Frames have no specific location, they are coordinate systems covering all of spacetime, so it doesn't make sense to say *frames* can be spacelike separated.

Right. I was skeptical about what I wrote, when I wrote it. OTOH, since EVENTS can be spacelike separated, I don't see any such events in this problem. For example, the ends of the car aren't spacelike separated; neither are the ends of the garage. If Brent weren't a failing teacher of SR, he would specify what he means. I am in no mood to guess his meaning. AG

You mean you just want to keep trolling Jesse.

Brent

No. Of course not. All your education, but in the final analysis, when it comes to teaching SR, you're a worthless, insulting prick. Jesse uses text, and I find it very useful. Jesse; hold up on your posts while I catch up. AG