# Reference for Reichenbach synchronisation and non-standard special relativity

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?

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• You may want to read en.wikipedia.org/wiki/Einstein_synchronisation – CuriousOne May 24 '16 at 7:12
• Thanks, but I already know the standard synchronisation and what this implies. This new synchronisation leads to a total different theory, in which we may not have simmetric velocities and also the generalized transformation may not form a group, and in which Einstein special relativity is only a particular case. – Nunzio Damino May 24 '16 at 7:15
• Did you look at the page? Now, if we believe this historian/philosopher philsci-archive.pitt.edu/674/2/epsilon_sim.pdf (and if I understand the piece correctly), then Reichenbach himself did not try to reach non-standard conclusions about simultaneity. Nor do I see any particular hint that redefining the synchronization procedure leads to different physics. It may lead to different clock readings (after all, you are diddling with the baseline of your main instrument here!), but why would nature care about what your screwdriver does to your atomic clock? – CuriousOne May 24 '16 at 7:30
• In general I agree with you, but as I saw in lessons this effectively leads to a new theory. For this reason I am looking for references on this, because everyone says that is refuted, but my professor published some articles on this (that I can't find online), and he says that we can found this in literature – Nunzio Damino May 24 '16 at 7:40
• If the theory is actually different, then it has to make new physical predictions that differ from those of the old theory. I have a feeling that what you are looking here is a statement of the form "If events are simultaneous in one observer system, then one can find a (special) clock synchronization that makes them simultaneous by clock time in other observer systems.". That, of course, doesn't change physics, it just changes labels on events. – CuriousOne May 24 '16 at 8:17

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.

• I agree with your analysis. In some cases Einstein synchronization cannot be employed if referring to non-Minkoswskian extended reference frames. The most elementary, though physically relevant, case is the rotating reference frame. In this case there is a topological obstruction (trying to synchronize circle or clocks at rest with the rotating frame turns out to be impossible because some integrability conditions are violated). Here a different, non isotropic synchronization procedure (due to Born I think) is however possible. – Valter Moretti May 24 '16 at 20:32
• An important issue is how to define the metric of a rest frame defined with a synchronization procedure different from Einstein's one. The answer is a bit technical but physically sound and relies only upon observable facts (the constant value of $c$ measured in closed paths). – Valter Moretti May 24 '16 at 20:34
• Thanks. Also for pointing out the rotating frame, completely forgot about it. Perhaps it would be worthwhile to add your observations, with refs, as an answer. – udrv May 25 '16 at 2:04