Can we really ever accurately test SR time dilation?

[PAllen]

While I agree no one in their right mind would really use any inertial coordinates other than the standard ones, the motivation for pointing out the conventionality is twofold:

1) Recognizing that you cannot empirically rule out interpretations like LET which explain that the operational results are consistent with anisotropic lightspeed of a certain type combined with length contraction. That is, even the standard inertial coordinates have an interpretation in which one way speed of light is anisotropic.

2) The strong preference for standard inertial coordinates is unique to inertial observers in SR. If you consider non-inertial observers in SR, or any observers in GR, there is no such preferred simultaneity. For each feature of inertial coordinates you might want to carry over to one of these cases, you are led to pick a different simultaneity convention. From this point, especially since the actual universe is not remotely compatible with global inertial coordinates (on cosmological scales), I think it is useful to emphasize there is an element of convention even in the inertial SR case. And making arguments about objective intergalactic simultaneity in the actual universe is basically nonsense.

 

[pervect]

The important point to convey to students is that the invariance of the one-way speed of light in terms of coordinates in which the Newtonian equations of motion are valid (roughly speaking) is not conventional, it is an empirical fact.

Personally, I agree totally.

My argument goes something like this. Suppose we collide two equal masses moving in opposite directions, and they come to a complete stop. Then there is one, and only one, clock synchronization in which we measure their velocities to be equal (using the usual two-clock definition of velocity). This is variously called the Einstein clock synchronization, or an isotropic clock synchronization.

It's also the one that makes angular momentum an even function of velocity, one that's independent of direction.

I've made the argument a lot of times, but I'm not sure I've convinced anyone, though it seems extremely obvious to me.

I was wondering if you had any quotes from the literature that made this point. At the moment, I don't have any :-(.

Another route to the same idea is actually writing down a Lagrangian for a free particle in terms of the particular coordinates using a particular clock synchronization (something else I've never seen done in print, though it turns out to be not terribly hard).

 

[PAllen]

My argument goes something like this. Suppose we collide two equal masses moving in opposite directions, and they come to a complete stop. Then there is one, and only one, clock synchronization in which we measure their velocities to be equal (using the usual two-clock definition of velocity). This is variously called the Einstein clock synchronization, or an isotropic clock synchronization.
...

Note that this, and what follows, argue for the preference for a particular clock synch (or simultaneity convention) for inertial coordinates in SR. They do not actually address the one way speed of light, given the LET type interpretation.

Anyway, as I noted above, the real value of emphasizing conventionality of simultaneity is when you consider non-inertial observers or GR situations.

 

[TrickyDicky]

Totally agree with Russell E and Pervect on this. Fortunately for this thread they are much more articulate than I am explaining this.

Anyway, as I noted above, the real value of emphasizing conventionality of simultaneity is when you consider non-inertial observers or GR situations.

Fine but this thread is about SR so having that in mind the logical thing is to suppose we are all referring to conventional (no pun intended) SR, is hard to see why the other guy would rudely insist so much that I was wrong (well LOS made clear there were personal motives rather than scientific).

As for "non-inertial observers" in SR, maybe some precissions are in order. Given the fact that SR is considered to apply to flat spacetime the "standard observer" is inertial and covers the whole spacetime (observers are inherently nonlocal). Of course this doesn't mean that in SR we can't use non-inertial frames (like Rindler) but even though they are usually called also observers, they are not exactly the same in the sense that proper observers in SR since they are in flat spacetime are extended to the whole spacetime. But in any case one can always transform back from the Rindler chart to the inertial chart and the inertial frame is always preferred in SR.

The thing is that as soon as one deals with a curved spacetime one can never have the kind of extended to all spacetime observers one had in SR, but one should not confuse this situation with the non-inertial "observers" of SR. The latter can always be transformed to the extended inertial observers.