The limits of convention in relativity

The article "A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization" by Reza Mansouri and Roman U. Sexl, published in 1977, contains at least two statements that are pertinent to my current investigation into the role of convention in Einstein's light speed principle.

The first is that "one of the most debated problems in special relativity is the role of convention in the definition of simultaneity of distant events and the related question of first-order experiments (first order in v/c)" (p. 498).

"One of the most debated problems in special relativity"! As is clear from my last few posts, that's not exactly reflected in some recent textbooks on special relativity purportedly focusing on conceptual issues.

Mansouri and Sexl quickly make it clear that they believe convention plays an important role in clock synchronization and thus in the definition of simultaneity. They state, for example, that "Einstein's procedure to synchronize clocks at different space points is but one of several possible alternative conventions".

Mansouri and Sexl are thus effectively saying that the synchronization of clocks is a matter of convention. They do not give any particular reason for this statement beyond listing a number of clock adjustment procedures which they all label synchronization procedures.

And that's the crux of the matter. I think it's important to be absolutely clear about what exactly is conventional in Einstein's theory: it's the choice of clock adjustment procedure. Anybody is free to adjust distant clocks any way they like, and some such procedure may be adopted by a whole community or even the whole world as the one to be applied by convention. But, and this is a big but, not every clock adjustment procedure is a synchronization procedure.

To prove that point, it is sufficient to give examples of clock adjustment procedures which are not synchronization procedures, and I have done this in, for example, this and this post. Drawing on those examples, I have argued that in general terms an Einstein-like clock adjustment procedure using signals is a synchronization procedure if and only if the signals used are emitted and propagate in symmetrical conditions in all directions. And I have concluded that on that basis Einstein's clock adjustment procedure is not and cannot be a synchronization procedure.in all uniformly moving frames of reference.

All that may seem straightforward enough. But there is a possible objection to my line of reasoning which I think I need to address in greater detail than I have done.

The objection broadly goes like this: "True, there may have been a time when the idea of simultaneity was based on that of sending out signals in symmetrical conditions, but that concept of simultaneity has become untenable because it's emerged that it's impossible to distinguish between frames of reference in which such symmetry pertains and frames in which it doesn't. Therefore physicists have redefined the concept and have agreed to call distant events with the same time stamp according to Einstein-adjusted clocks "simultaneous". Even if that definition hasn't filtered through into general usage, it's a technical definition of the kind scientists use all the time to ensure their concepts are precise and can be applied operationally. For example, mathematicians talk about "groups" and "rings" in algebra in a very precise technical sense, and they're perfectly free to do so even though the concepts of a "group" or "ring" are used in very different ways in non-mathematical contexts."

Indeed. Absolutely. Physicists are free to do this. But then they shouldn't be using the concept of "simultaneity (physics)" in contexts in which only the symmetry-based concept of simultaneity makes sense. Just like mathematicians shouldn't - and to the best of my knowledge generally don't - use their concept of a "group (algebra)" to talk about group dynamics in social situations, for example.

To be more specific: I think the concept of simultaneity is closely linked to concepts such as synchronization, symmetry, existence, signal, speed, and cause and effect. This link is established in the way people generally think, talk and write about these various concepts. It is thus ingrained in the English language as currently constituted. Similar considerations probably apply to many other languages in which similar concepts exist.

I think the following statements exemplify some of the relationships between those concepts as currently constituted:

1) Events in two places A and B are simultaneous if and only if synchronized clocks located at A and B show the same time when the events occur.

2) Clocks in A and B can be synchronized by setting them to the same time when identical signals emitted in opposite directions from the mid-point M between A and B arrive at the clocks, provided the signals propagate in symmetrical conditions.

3) Signals sent from A to B cannot arrive in B at an earlier time than when they were emitted as measured by synchronized clocks in A and B.

4) If a signal emitted from A arrives in B at an earlier time than when it was emitted, according to clocks positioned in A and B, then those clocks aren't synchronized.

5) A cause in a location A always precedes its effect at a distant location B provided the clocks used to measure time in A and B are synchronized.

6) The one-way speed of a signal between A and B is the distance between A and B divided by the time the signal needs to travel from A to B as measured by synchronized clocks in A and B.

Some of the meaning of "simultaneity", "synchronization", "symmetry", "signal", "speed" and "cause and effect" is established in these relationships.

It is thus not possible to "redefine" one such concept and expect its relationship with other, related concepts to be unaffected. For example, I would hold that the concept of cause and effect relies on a symmetry-based concept of simultaneity and becomes inapplicable in some circumstances if the requirement of symmetry is given up.

And this is exactly what happens if Einstein's clock adjustment procedure is adopted: while we may not know whether light signals propagate symmetrically in any particular uniformly moving frame of reference, we do know that if they propagate symmetrically in a first frame then they do not propagate symmetrically in other frames that move relative to the first, at least not locally. The result is that the concept of cause and effect, for example, becomes inapplicable in the context of special relativity if superluminal speeds are involved.

Suggestions that superluminal speeds lead to cause and effect or the flow of time being "reversed", as they keep being made in relation to recent neutrino experiments at CERN, are thus misguided: they are the result of uncritically and unwittingly applying concepts that rely on a symmetry-based concept of simultaneity to a theory in which that concept has been abandoned.

After this little digression, it's time to mention the second statement made by Mansouri and Sexl that is pertinent to my investigations. This is the "remarkable result", as the authors describe it, that "a theory maintaining absolute simultaneity is equivalent to special relativity" (Mansouri/Sexl's emphasis, p. 503).

My discussion of this statement will, however, have to wait until my next post.