I had a dream.

[Alan Grayson]

Yes, literally, last night, I had a dream wherein I was describing a physics problem which puzzles me, to three physicists. It went like this. First I postulated three inertial frames positioned on a straight line, with clocks synchronized, and two traveling toward each other at the same constant velocity v, and the third at rest, located midway between the moving frames. I didn't explain how these frames could be constructed, but it's clear that it's possible. Now maybe I am falling into a Newtonian error, but ISTM that the moving frames will pass each other at the location of the rest frame, and all observers will be able to view all three clocks since they're juxtaposed. Consequently, all three clocks will be seen as indicating the same time. Note that the stationary frame represents the stationary train platform in texts which establish the clock rates in moving frames (represented by moving trains) are slower when compared to stationary frames. In the model proposed in my dream, it's hard to claim that the three clocks indicate different times since the moving clocks are synchronized and their motions are symmetric. So, there doesn't appear to be any differential rates for these clocks. Maybe use of the LT will change this situation, since it guarantees the invariance of the SoL, but it's hard to see why the clock readings for the moving frames could be different from each other, given the symmetry of their motion. In the dream, the physicists were baffled and couldn't resolve the issue, which, to repeat, is how the clock rates for the moving frames could indicate that each clock in a moving frame, was ticking slower than its symmetric other. AG

[Brent Meeker]

On 10/18/2024 4:00 AM, Alan Grayson wrote:
> Yes, literally, last night, I had a dream wherein I was describing a
> physics problem which puzzles me, to three physicists. It went like
> this. First I postulated three inertial frames positioned on a
> straight line, with clocks synchronized, and two traveling toward each
> other at the same constant velocity v, and the third at rest, located
> midway between the moving frames. I didn't explain how these frames
> could be constructed, but it's clear that it's possible. Now maybe I
> am falling into a Newtonian error, but ISTM that the moving frames
> will pass each other at the location of the rest frame, and all
> observers will be able to view all three clocks since they're
> juxtaposed. Consequently, all three clocks will be seen as indicating
> the same time. Note that the stationary frame represents the
> stationary train platform in texts which establish the clock rates in
> moving frames (represented by moving trains) are slower when compared
> to stationary frames. In the model proposed in my dream, it's hard to
> claim that the three clocks indicate different times since the moving
> clocks are synchronized and their motions are symmetric. So, there
> doesn't appear to be any differential rates for these clocks. Maybe
> use of the LT will change this situation, since it guarantees the
> invariance of the SoL, but it's hard to see why the clock readings for
> the moving frames could be different from each other, given the
> symmetry of their motion.

It's not the an symmetry of their motion, it's the symmetry of how you
define "now".  When the 3 clocks are together momentarily they can all
be set to the same time and there's no ambiguity about it. But once they
are apart there is no unambiguous way to compare them.  Whether they
read the same value "at the same" is ambiguous because "at the same
time" depends on the state of motion of whoever is judging the times to
be the same.  And this is not just because of the relative motion of the
clocks.  There is the same ambiguity even if the clocks are stationary
relative to one another but are at different locations.

> In the dream, the physicists were baffled and couldn't resolve the
> issue, which, to repeat, is how the clock rates for the moving frames
> could indicate that each clock in a moving frame, was ticking slower

> than its symmetric other. AG --
Which I already explained how to prove to yourself.

Brent

[Alan Grayson]

I am unclear what "now" means. How is it defined? Can't we use the round-trip light time to establish that the frames which will eventually be moving toward each other, are initially at rest with respect to each other, at a known fixed distance, and use it to synchronize their clocks, and to then apply the same impulse at the same time to both, to get the frames moving symmetrically? This doesn't seem ambiguous. Also, using the third clock, we can establish, as is done in relativity texts, that clocks in moving frames have slower rates than clocks in stationary frames. Using this fact, and the fact that when the moving frames meet, no time contraction is noticed (since these clocks will show the same time), we have another contradiction. AG 

[Brent Meeker]

So what?  They won't be synchronized in any reference frame moving relative to them.  You can arbitrarily foliate flat space time to define comparisons as "now", but it has no physical significance.  You're unclear on what "now" means because it doesn't mean anything.

and to then apply the same impulse at the same time to both, to get the frames moving symmetrically? This doesn't seem ambiguous. Also, using the third clock, we can establish, as is done in relativity texts, that clocks in moving frames have slower rates than clocks in stationary frames.

I don't know where you get this stuff.  No relativity text I know even recognizes the concept of "stationary".  It's called "relativity" for a reason!

Brent

Using this fact, and the fact that when the moving frames meet, no time contraction is noticed (since these clocks will show the same time), we have another contradiction. AG 

> In the dream, the physicists were baffled and couldn't resolve the
> issue, which, to repeat, is how the clock rates for the moving frames
> could indicate that each clock in a moving frame, was ticking slower
> than its symmetric other. AG --
Which I already explained how to prove to yourself.

Brent

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[Alan Grayson]

Haven't you seen in texts the case of a train (the moving frame) and the station (the fixed or stationary frame) used to develop some of the basic concepts of relativity? Maybe the LT or maybe time dilation. I distinctly recall this. I didn't pull it out of the proverbial hat. Anyway, suppose we have two frames in SR and each frame sees time dilation manifested in the other frame. If they occurred at the same time, this would be a paradox, so the solution must be that the observations are at different times. How can this be established? AG  

[Brent Meeker]

Are these frames moving relative to one another?  Then they will see time dilation in one another as they pass by AT THE SAME TIME AND PLACE.

Brent

so the solution must be that the observations are at different times. How can this be established? AG  

Using this fact, and the fact that when the moving frames meet, no time contraction is noticed (since these clocks will show the same time), we have another contradiction. AG 

> In the dream, the physicists were baffled and couldn't resolve the
> issue, which, to repeat, is how the clock rates for the moving frames
> could indicate that each clock in a moving frame, was ticking slower
> than its symmetric other. AG --
Which I already explained how to prove to yourself.

Brent

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[Alan Grayson]

Well, the station obviously wasn't moving, but there were other examples. It was a good text, but I can't recall its name. If I get the energy, I'll try to find it on Amazon if it's still in print. AG 

Then they will see time dilation in one another as they pass by AT THE SAME TIME AND PLACE.

Then, IMO, we have a paradox. How can an observer see another's observer's clock running slower, and vice-versa, at the same time and place? Years ago when we discussed this, you seemed to take the position that breakdown in simultaneity could resolve the issue. Now you seem to be backing off from this explanation. AG 

[Brent Meeker]

Because years ago it was not assumed they were at the same place, in which case there can be no motion-independent assessment of their relative rates.

Brent

[Alan Grayson]

Maybe this will help. In the text which I recall, it was not assumed that both frames were in motion. Whereas the train was moving, the station was not, and could not be imagined as moving. So maybe,  the idea that time dilation occurs only applies when one frame cannot be assumed to be moving. When both frames are moving, the only way to determine time dilation is to have synched clocks and determine if one falls behind the other. In this situation, due to symmetry, each clock will fall behind the other at the same time and place -- actually at every time and place -- which IMO is impossible and paradoxical. AG 

[Brent Meeker]

Each time you post you introduce more new confusions until I despair of unraveling them.  Go take a class or hire a tutor.

Brent

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[Alan Grayson]

On Friday, October 18, 2024 at 11:05:40 PM UTC-6 Brent Meeker wrote:

Each time you post you introduce more new confusions until I despair of unraveling them.  Go take a class or hire a tutor.

Brent

 

I helped you understand that the observable universe is finite. Goodbye and good luck. AG

[Alan Grayson]

Yes, that's a good suggestion. I'd like to have a tutor, and I'm even willing to pay for it. Unfortunately, and not to be negative, I don't think you qualify. Firstly, the tutor must be really knowledgeable of physics, and you failed that test when your replied ("bullshit") to my statement that the observable universe is finite in spatial extent. Seriously, this is pretty simple and well established, as evidenced by the fact that it's been measured as having a radius of 46 BLY (a unit of distance!). That's 46 BLY in all directions, from any location in the observable universe, applying the Cosmological Principle. You should know that that's as far as we can observe. Beyond that distance is the unobservable universe with space expanding faster than the SoL, c. After I corrected your misstatement, you never gave me a cordial handshake, acknowledging your error. Maybe it was your pride or vanity or laziness which prevented you from doing so. But the kind of tutor I might employ, would a straight-shooter, not reluctant to admit an error.

Further, about all those "new confusions" you allege which prompted your despair; they are essentially false inference than the reality of my pov, although I acknowledge a lack of clarity on some issues in my latest discussion of the Clock Paradox in SR. It probably appears that I was in denial of the Principle of Relativity when I cited the train station as some special reference frame for determining the slowing clock rates for moving frames/clocks. I am not denying the Principle of Relativity in SR-- that are no preferred frames, that the laws of physics have the same form in all inertial frames, and all inertial frames are equivalent. This was established by the Michelson-Morley experiment of 1881 (repeated several times thereafter) which yielded a null result for an EM ether, presumably at rest, as the medium for the transmission of EM waves. The alleged preferred frame would be at rest with respect to this ether if it existed, but since it does not, there is no preferred frame in SR. In my recent discussion of the alleged preferred frame of the train station, I was thinking out loud, or shall we say, trying to think "out of the box", not seriously affirming that frame as a preferred frame. For that confusion I take full responsibility, although I note that many discussions of the issue of the Clock Paradox in SR usually compare a moving frame with a fixed or stationary one which seems unmovable like the train station. Some treatments, definitely in the minority, compare a moving clock with an abstract stationary frame with no further constraints. 

The thing I was most concerned with in my previous discussion was whether, and if, the role of the possible breakdown of simultaneity played in the slower clock rate for moving frame, and I thought that the clocks in both frames could by synchronized if the frames were treated identically. Right now I am not convinced of this conclusion. In any event, instead of starting with two frames, one moving and one at rest, I wanted to first discuss how those frames could be constructed, starting with two frames initially at rest. So I considered using the round trip light from one fixed location to a second fixed location, to assure that the distance between them was fixed. If you recall, this is the method for determining the moon's recession from its orbit around the Earth. Astronauts left a mirror on the Moon's surface and radar signals were bounced back to Earth, presumably multiple times, and it was determined the Moon is receding from Earth orbit at slightly less the 4 cm annually. So there was nothing inherently wrong with using this method to guarantee the two points in my model were initially fixed, But to get them both moving at a fixed velocity toward each other, I postulated the same short impulse, F*deltaT, applied to both frames. Although this procedure was, strictly speaking, not necessary, it isn't wrong, though it likely contributed to your confusion.

Since my intention is to compare clock readings when the frame clocks are juxtaposed, I am studying a YouTube video by a physicist at Fermilab, entitled, "Relativity: how people get time dilation wrong", https://www.youtube.com/watch?v=svwWKi9sSAA. I plan to view it again, several times, but so far I tend to believe that breakdown of simultaneity is not an issue in calculating the slowing clock rate for a moving frame. In fact, it's never mentioned! Moreover, and mildly shocking, is that while the author initially acknowledges that a time dilation paradox would exist, if each observer viewed the other frame's clock as running slower, he never makes the comparison, AFAICT! You might want to view this video yourself and see if you agree with my conclusion. In effect, after correctly stating what a time dilation paradox would consist of, he never addresses it.

In conclusion, I see no way to resolve this apparent paradox, since the Principle of Relativity allows us to symmetrically switch frames of reference which keeps the apparent paradox alive and well. Also, with regard to worldlines, you stated recently that it demonstrates slowing clock rates for a moving frame, but did not, as I conjectured, apply breakdown of simultaneity as the solution to the apparent paradox.

AG

[Alan Grayson]

I conjecture that the clocks in the two frames used to test for a clock paradox in SR can be synchronized when they are juxtaposed. Then the comparison can be done at any other point in those frames where another pair are juxtaposed. I could be mistaken, but it sure seems that there's real clock paradox in SR. Does anyone see a problem with this method of sychronization? AG

[Alan Grayson]

If the clocks can be sychronized as indicated above, and if they remain synchronized, then the clock comparisons will show same values when they are juxtaposed the second time. Hence, no time dilation indicated in this scenario. So it seems that time dilation only occurs when one frame is considered at rest. Have to admit; this situation seems more peculiar the more I look into it. AG 

[Alan Grayson]

In other words, IF the clocks in both moving frames can be sychronized with each other, and one then compares the time elapsed between the two juxtaposed positions mentioned above, there is no relativistic time dilation. AG