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I apologize if my question turns out to be just a matter of aesthetic preference, but I think it has some scientific content.

Any help would be greatly appreciated.

Thank You in Advance.

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- Thread starter lugita15
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- #1

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I apologize if my question turns out to be just a matter of aesthetic preference, but I think it has some scientific content.

Any help would be greatly appreciated.

Thank You in Advance.

- #2

ghwellsjr

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- #3

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Yes, I understand all that. I am perfectly aware of the fact that you can never measure the one-way speed of light, and that clocks which have been synchronized according to the Einstein convention in one frame won't be synchronized in any other frame, etc.

But I don't see the relevance to my basic question, which is: what does it say about Einstein synchronization that it is equivalent to the slow transport of clocks? It seems to me that slow transport singles out Einstein sychronization as somehow special or unique.

- #4

ghwellsjr

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At the time Einstein came out with SR, virtually everyone continued to believed in the existence of an absolute ether rest frame, the only one in which it was true that clocks were synchronized because they believed in a concept of an absolute, universal time. They believed they were not at rest with respect to the ether and so when they got null results to detect that motion (including slow transport of clocks), they explained it by saying their own rods and clocks were modified to make it appear that they were stationary in the ether. LET was a perfectly viable theory in which the concept of absolute time and space could be maintained and in which the slow transport of clocks would be explained away, just like all the other "null" results.

So when Einstein arbitrarily defined the one-way speed of light to be a constant in all directions for any inertial observer, he was making the audacious claim that that observer was identical to being at rest in the absolute ether rest frame, thus setting aside any need to identify or be concerned with any actual ether rest frame.

- #5

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Well, SR is mostly about the relation between the rigidity of objects and an isotropic speed associated with the measurement of motion. If we were to accelerate perpendicular rods to travel at a relative speed to the rest frame, then the rest frame would then measure a rod that lies along the direction of motion to be length contracted while a perpendicular rod is not, although they were measured the same when at rest. Observers in the new frame, however, would still consider the rods to be the same length as each other because they will line up when one of the rods is rotated to the orientation of the other. This is also true according to the rest frame, but the rest frame uses its own stationary rods by which to compare the lengths of the other frame. Massless particles will travel the lengths of perpendicular rods in either frame and meet back at the intersection of the rods simultaneously according to any frame, so they can always be measured to have travelled the same distances in the same times as measured by the frame where the rods are stationary, and the simultaneity convention can be set accordingly, with massless particles travelling the same distance in the same time in any direction, although the universal speed c being measured the same by every frame is assumed.

This being said, the slower we transport a clock from the rest frame, the closer it remains to the simultaneity of the rest frame, but not that of the new frame. That is to say, if we quickly accelerate an object to a relative speed of v, then let it coast at that relative speed for some distance according to the rest frame, then quickly bring it to rest, the slower it coasts for the same distance, the closer it will be to the reading upon the rest frame's clock that coincides in the same place when it comes back to rest, the difference between the reading upon that clock and that of the rest frame being (d / v) (1 - sqrt(1 - (v/c)^2)). However, let's say we compare clocks at either end of a rod that continues to travel inertially at v. If the rod is accelerated with Born rigid motion to a relative speed v, then the difference in readings between the clocks at each end of the rod will be (l / v) arctanh(v / c) according to the rod's frame. This is independent of how quickly the rod is accelerated to v or how long it travels after becoming inertial again, it is always the same. So if one were to compare clocks within the new frame at either end of a rigid rod rather than comparing to clocks of the rest frame, then slow transport, or slow acceleration to v rather, makes no difference between the readings of the clocks in the new frame.

This being said, the slower we transport a clock from the rest frame, the closer it remains to the simultaneity of the rest frame, but not that of the new frame. That is to say, if we quickly accelerate an object to a relative speed of v, then let it coast at that relative speed for some distance according to the rest frame, then quickly bring it to rest, the slower it coasts for the same distance, the closer it will be to the reading upon the rest frame's clock that coincides in the same place when it comes back to rest, the difference between the reading upon that clock and that of the rest frame being (d / v) (1 - sqrt(1 - (v/c)^2)). However, let's say we compare clocks at either end of a rod that continues to travel inertially at v. If the rod is accelerated with Born rigid motion to a relative speed v, then the difference in readings between the clocks at each end of the rod will be (l / v) arctanh(v / c) according to the rod's frame. This is independent of how quickly the rod is accelerated to v or how long it travels after becoming inertial again, it is always the same. So if one were to compare clocks within the new frame at either end of a rigid rod rather than comparing to clocks of the rest frame, then slow transport, or slow acceleration to v rather, makes no difference between the readings of the clocks in the new frame.

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I will leave my last reply, but I realize now you might be asking about something different, about natural synchronization techniques. There are other ways to synchronize clocks besides using light and slow transport. For instance, we might rotate a disk and set all clocks around the circumference so that a constant rotation speed will be measured. We could also shoot tennis balls by the same mechanism in different directions and set clocks so that they are measured at the same speed in any direction, for examples. Presumedly any of these synchronization techniques will result with the same simultaneity convention, that of Einstein's. There should also be only one possible synchronization where causality is not violated. However, even if all of these methods result with the same synchronization, other conventions can still be allowed, since they are only convention and do not affect the actual physics of what is taking place. That is, one does not expect different physical results to occur by simply changing the simultaneity convention, but only how the timing of events are measured by frames, which might or might not be more convenient than applying the most natural convention.

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atyy

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To be clear, I'm not claiming that the step from LET to SR was natural or trivial. It was sheer brilliance on Einstein's part, to be able to recognize that the symmetry of the Lorentz transformations was not just a coincidence. If Einstein had not come along, we might still believe in aether.

At the time Einstein came out with SR, virtually everyone continued to believed in the existence of an absolute ether rest frame, the only one in which it was true that clocks were synchronized because they believed in a concept of an absolute, universal time. They believed they were not at rest with respect to the ether and so when they got null results to detect that motion (including slow transport of clocks), they explained it by saying their own rods and clocks were modified to make it appear that they were stationary in the ether. LET was a perfectly viable theory in which the concept of absolute time and space could be maintained and in which the slow transport of clocks would be explained away, just like all the other "null" results.

So when Einstein arbitrarily defined the one-way speed of light to be a constant in all directions for any inertial observer, he was making the audacious claim that that observer was identical to being at rest in the absolute ether rest frame, thus setting aside any need to identify or be concerned with any actual ether rest frame.

Maybe I mistitled my post, but my question is essentially this: Suppose that tomorrow someone proposed that all physics books replace Einstein synchronization with one of the nonstandard simultaneity conventions. Would you raise any objections to this move, and why? I would raise the objection that the new convention would not be consistent with the slow transport of clocks. Would my objection have any real basis, or is it just an aesthetic preference?

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This seems to be a really interesting book. More interesting than even Ohanian's idea is Malament's idea on the same page, which proposes that Einstein synchronization is "the only nontrivial equivalence relation definable in terms of the causal connectibility relation". If this claim is correct, that would be an amazing justification of Einstein synchronization.

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Do you have any justification for this statement?There should also be only one possible synchronization where causality is not violated.

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I know there are other simultaneity convention, but how could they be meaningful if they contradict slow transport?

An excellent question.

Mike Fontenot

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The assumption that the one-way speed of light is c is equivalent to the assumption that slowly transported clocks remain synchronized. Without assuming the one-way speed of light why would you assume that slowly transported clocks remain synchronized. Perhaps clocks become desynchronized based on position also, particularly if we are considering non-inertial frames.Einstein synchronization, as it is conventionally defined, depends on subtle issues like the one-way speed of light. But the slow transport of clocks produces the same simultaneity convention.

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I had gone back and editted the post to throw that statement in at the last minute, because I was thinking that if we have a simultaneity convention where events occur in order of cause and effect, and then we change the synchronization along a spatial dimension, then clocks might read that effects which occur along that dimension would happen earlier than the cause, since the timing of the clocks is different. Now that I think about it some more, though, cause and effect is still limited to the speed of information, so we could potentially change the synchronization so that it edges from c toward a limit of infinite speed of information along that dimension as read by the clocks without violating cause and effect, at least not directly. So only in a Galilean universe would there be only one possible synchronization that does not violate cause and effect with an unlimited speed of information, but Relativity would actually allow some leeway due to the finite limiting speed of c.Do you have any justification for this statement?

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