A question on proper time in special relativity

[PAllen]

But...if the synchronization method (e.g bullets synchronization method) is isotropic and light propagation process was non isotropic, it did not follow the constancy of one-way speed of light, I believe.

Wrong. There is no logically consistent model in which identically launched bullets can be assumed to have isotropic one way speed while light does not. The epsilon parameter describing the only allowed form of anisotropy applies to all physics. That is, any clock synchronization technique in SR amounts to a choice of epsilon. Any that assumes full isotropy for any synchronization method is choosing epsilon of 1/2.

 

[cianfa72]

Then the one-way-bullet-speed is measured as isotropic.

...only if the process of sending bullets is actually isotropic.

 

[PAllen]

...only if the process of sending bullets is actually isotropic.

is assumed to be isotropic for a fully specified launch method.

 

[cianfa72]

Wrong. There is no logically consistent model in which identically launched bullets can be assumed to have isotropic one way speed while light does not. The epsilon parameter describing the only allowed form of anisotropy applies to all physics. That is, any clock synchronization technique in SR amounts to a choice of epsilon. Any that assumes full isotropy for any synchronization method is choosing epsilon of 1/2.

So in this case at hand the point is that if we assume full isotropy (epsilon of 1/2) it applies to identically launched bullets as well to one-way light speed

 

[PAllen]

So in this case the point is that if we assume full isotropy (epsilon of 1/2) it applies to identically launched bullets as well to one-way light speed

Yes.

 

[Dale]

But...if the synchronization method (e.g bullets synchronization method) was isotropic but light propagation process was not, it did not follow the constancy of one-way speed of light, I believe.

It does follow, actually. That is part of what Reichenbach showed. If the identical bullets are isotropic then the identical lasers are isotropic.

 

[cianfa72]

It does follow, actually. That is part of what Reichenbach showed. If the identical bullets are isotropic then the identical lasers are isotropic.

So choosing epsilon=1/2 two spatially separated events are said simultaneus if and only if they are simultaneous accoring any specific "isotropic" synchronization method chosen.

 

[Dale]

So choosing epsilon=1/2 two events are said simultaneus if and only if they are simultaneous accoring any specific "isotropic" synchronization method chosen.

Yes, that is correct

 

[cianfa72]

Yes, that is correct

Furthermore it follows that whatever "isotropic" method used -- assuming the constancy of two-way speed of light on closed paths equals to c -- then the one-way lightspeed has to be c (or just 1 when normalized).