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If we cannot define a proper time (or synchronize clocks in different positions) in an inertial frame (independent with the theory of relativity), there seems to be no direct way to confirm the 2 postulates of Einstein. Is that true?

Consider an inertial frame, which is associated with a proper coordinate $(t,x,y,z)$. It seems like there is no way for observers in different positions of this frame to synchronize their clocks. If they move to 1 position to do so, they must accelerate, and they have completely destroyed their inertial frame.

If there is no way one can measure the time in different positions of an inertial frame, how real is the $t$ coordinate of the frame?

Is there any convention to measure such $t$? If there is, how true it is compared with the "real" inertial time?

However, in the end I feel like there is no way we can measure $t$ in different positions without destroying the inertial frame. Therefore it seems like we cannot truly measure the velocity of anything.

I ask this question because there may be a request for proving the constancy of the speed of light, and to measure the speed of light (from A to B) we have to synchronize 2 clocks, which is a very subtle process.

Nick Stauner
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anonymous67
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    As pedantic as it sounds the answer to the title questions is "With a clock". As to the rest, a central fact of relativity is that there is no common, universal time standard. There just isn't. Absolute time is not one of the things that people can agree on in the world that we live in. At low relative velocity we can come very very close to such agreement---good enough for almost all practical purposes---which is why you expect to be able to do that. – dmckee --- ex-moderator kitten Jul 09 '14 at 17:34
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    Well, the question really seems to be not about measuring time, but about synchronizing clocks between different locations. I think there's room for a good answer describing Einstein's procedure. – David Z Jul 09 '14 at 17:36
  • dmckee's comment is as good an answer as you will get, I think, but you might be interested in the discussion here as to what exactly it is that clocks measure – ACuriousMind Jul 09 '14 at 17:36
  • Of course there is no universal time standard. But there IS a Proper Time associated with each inertial frame. And if there is no way to synchronize time between different position, how can we measure the speed of light to prove that it's, indeed, doesn't depend on particular inertial frame – anonymous67 Jul 09 '14 at 17:37
  • I think @DavidZ is right. I addressed the wrong question. There are several different ways to synchronize clocks between separated points at rest with respect to one another. They rely on speed of light signals. – dmckee --- ex-moderator kitten Jul 09 '14 at 17:45
  • Related: http://physics.stackexchange.com/q/52739/2451 – Qmechanic Jul 10 '14 at 20:52

2 Answers2

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Comment to the question (v2): Globally within an inertial frame $I$ in Special Relativity, there is a theoretical (as well as practical) procedure using light rays, known as Einstein synchronization, to synchronize clocks in each space point of the inertial frame $I$, so that at least theoretically, it makes sense to assign a common global time $t$ within an entire inertial frame $I$.

Qmechanic
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    Disclaimer: This answer assumes that Special Relativity (SR) holds (and in particular that the speed of light in vacuum $c$ is a universal constant). – Qmechanic Jul 09 '14 at 18:11
  • Comments: 1. By repeating the synchronization procedure many times, we can test SR. Any inconsistency (that can't be explained by faulty equipment etc) would be groundbreaking. 2. Moreover, if we replace SR with an another (presumably more complicated) theory, a (presumably more elaborate) synchronization procedure might still be possible, depending on the details of that alternative theory. – Qmechanic Jul 10 '14 at 14:24
  • Qmechanic: "By repeating the synchronization procedure many times, we can test SR. Any inconsistency (that can't be explained by faulty equipment etc)" -- This parenthetical remark has profound implications: we always only test hypotheses concerning our models/expectations/prejudices about the "equipment etc" involved having been and remained "not faulty"; we cannot experimentally test our definitions of what we mean by "inconsistent" or "faulty" in the first place. Any theory serving this purpose, such as (S)RT, must be selected beforehand, and stuck to, based on comprehension alone – user12262 Nov 04 '14 at 19:55
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There is an extensive literature on the topic of simultaneity. Most of this literature has been written by philosophers, but despite this it is quite interesting:

http://plato.stanford.edu/entries/spacetime-convensimul/

The upshot is that you can test how long light takes to travel a closed path but you can't test how long it takes to travel from one point to another without further assumptions, which may or may not be reasonable.

The standard convention adopted by Einstein for getting around this is to synchronise two clocks in one place and then move one or both of them very slowly to different positions. This is equivalent to assuming that the speed of light is the same in every direction. There are questions about whether this convention is reasonable. For example, is there any objective criterion for how slowly do you have to move the clocks for them still to count as synchronised at the end of the transport process? And since any clock that fit the criterion for moving slowly in one frame would violate it in many other frames doesn't this imply that regarding the same clock readings on such clocks as simultaneous is purely conventional? I am not taking a particular position on this, just pointing out that there are interesting issues to discuss.

alanf
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