Reference for Reichenbach synchronisation and non-standard special relativity

Question

My professor introduced in the last lesson a new method for clock synchronisation, which he called "Reichenbach synchronisation". In this new method, two clock A and B synchronise themself with the relation

$$ t_B = t_A + \varepsilon(t_A' -t_A) \qquad \varepsilon \in ]0,1[. $$

Where A emits a signal at time $t_A$, it arrives at B at time $t_B$ and then returns in A at time $t_A'$.

So he states that simultaneity is a conventional aspect of relativity, and then he start to develop the theory using these assumptions. My problem is that I can't find any reference for this theory, neither in textbooks neither in publications. Can you list me a bibliography for these arguments, and if possible, download link for research papers?

Answer 1

Reichenbach's original volume, "Axiomatization of the Theory of Relativity", appeared in 1924. It is one of a long string of works that periodically rediscover and/or explore the issue of non-Einstein synchronization in Special Relativity. See for instance this review on "Synchronization Gauges and the Principles of Special Relativity" and refs. therein (arXiv link). It discusses many previous results in a unified framework, while making it clear that none "challenge the SRT, […] but simply lead to a number of formalisms which leave the geometrical structure of Minkowski space-time unchanged."

There are a few things that must always be kept in mind regarding this topic.

• Despite various claims to the contrary, the issue of non-Einstein synchronization is a valid one. In fact we naturally use a non-Einstein synchronization every time we look at the night sky: we automatically assign to each star the same time index as that on our hand watch. We know very well that light has travelled many years to reach us, and what we observe has long passed at the original location. But as far as practical reasons are concerned, we interpret the light that we receive now as a time index of now for each and every star we see. In contrast, Einstein synchronization requires us to assign a different time index to each star, taking into account its distance in light-years. But short of upcoming augmented reality visors, we are biologically ill-equipped to see the world in such terms from the start.

• The important point: Einstein synchronization is not, by any means, the only type of synchronization compatible with Special Relativity. The latter can be consistently formulated for a much wider class of synchronization protocols. But no such protocol will produce a different theory when correctly applied. The result is still Special Relativity, albeit in a somewhat different form.

• What is so interesting about non-Einstein synchronizations? It turns out that the specifics of length contraction and time dilation depend on the synchronization scheme. This does not mean in any way that we can make length contraction and time dilation go away in every frame as mere artifacts. They are always there in some form. But their relationship to synchronization is a subtle one that warrants further exploration.

• How is Einstein synchronization special? It is the only synchronization in which the one-way speed of light is isotropic and homogeneous in any reference frame. Non-Einstein synchronizations have the disadvantage that they necessarily introduce an apparently anisotropic one-way speed of light (the above example of night-sky synchronization does this too!), although the two-way speed always remains isotropic and homogeneous. So if we want a formalism in which the postulate of the speed of light is necessarily manifest in the one-way speed, we are stuck with Einstein synchronization. If we relax this requirement to allow an apparent (but not factual!) "symmetry breaking" in the one-way speed, while keeping the two-way speed manifestly invariant, other classes of compatible synchronizations become available.