Kevin Brown on convention in relativity

In his book Reflections on Relativity (2010), Kevin Brown talks about the light speed principle in special relativity in great detail. He makes careful distinctions between what is empirical fact and what is conventional or a matter of decision-making. He acknowledges that different choices are possible and that there are and always have been debates among physicists on which of these are preferable. And he engages with those debates.

All of this makes his book a pleasure to read for somebody who has long felt that there is much more to relativity than what most textbooks tell their readers. Somebody who, as a student, despaired of an approach to the teaching of physics which allowed no room for debate or questions. Somebody who, years later, by writing this blog, is trying to gain a deeper understanding of special relativity than he could ever have hoped to gain as an undergraduate.

And there is more. Kevin Brown, with his knowledge of the historical background, his awareness of conceptual issues and his grasp of technical details, clearly comes down on the side of Newton and Einstein on the issue of simultaneity, and thus on the side of Einstein's light speed principle. Which makes his writings an ideal test for a sceptic like myself.

Brown makes it clear early on in his book that there is a choice regarding time coordinates. He says one possibility is to choose them so that inertia is isotropic, in other words "the force required to accelerate an object from rest to a given speed is the same in all directions". This "effectively establishes the planes of simultaneity of inertial coordinate systems".

Brown's main argument in favour of time coordinates which ensure inertial isotropy is that they lead to "the usual symmetrical laws of mechanics" and are therefore "the most intuitive, convenient, and readily accessible systems" (pp. 24-27).

Elaborating on these ideas, he approvingly quotes Henri Poincaré as saying in 1898 that we naturally choose our coordinate systems "in such a way that the statements of the natural laws are as simple as possible", and according to Brown that "almost invariably means inertial coordinates". "We simply choose, of our own free will, to use inertial coordinates - with the corresponding inertial definition of simultaneity - because this renders the statement of physical laws and the descriptions of physical phenomena as simple and perspicuous as possible, by taking advantage of the maximum possible symmetry," Brown insists. The constancy of the speed of light in terms of such coordinates is then "an empirical fact" (pp. 290-291).

Brown acknowledges, however, that "it could be argued that a total unique temporal ordering of events is a more useful organizing principle than the isotropy of inertia". This is true "especially if we regard the total temporal ordering of events as a requirement of intelligibility". But, Brown goes on, that approach "suffers from a certain inherent lack of conviction, because while asserting the ontological reality of anisotropy in all but one (unknown) frame of reference, it unavoidably requires us to disregard that assertion and arbitrarily assume one particular frame as being 'the' rest frame" (pp. 292-293).

Brown's account adds up to a very detailed, clear and persuasive argument for choosing time coordinates in accordance with Einstein's or Newton's clock adjustment procedures, which turn out to be equivalent.

But there is a question which Brown does not address directly. Like all the other authors discussed in this blog, Brown says events with equal time coordinates as measured by Einstein- or Newton-adjusted clocks are "simultaneous" without exploring or explaining why that should be the case. However, unlike any of the authors discussed before, Brown drops a number of hints suggesting that there may in fact be a problem with "simultaneity" in special relativity.

One of these hints is his acknowledgment that choosing time coordinates in accordance with Einstein's or Newton's clock adjustment procedure may lead to a problem of "intelligibility". Sadly, Brown does not explore what this problem consists in and how it comes about.

My own view is, of course, that Einstein's and Newton's clock adjustment procedures - for all their benefits in terms of simplicity and symmetry - lead to a situation in which equal time coordinates do not invariably imply a relationship of simultaneity. And that this fact renders the resulting theory unintelligible unless it is made explicit and its repercussions on the applicability of concepts that rely on the concept of simultaneity are explored and explained.

Brown indirectly addresses some of these repercussions in a chapter on "The Breakdown of Simultaneity". He points out that, if Einstein's or Newton's clock adjustment procedure are used, an accelerated observer may find that one and the same distant event "is assigned multiple times of occurrence" (p. 313). I'd suggest that this would only pose a problem if we took the meaning of "simultaneity" in relativity seriously, because we'd then have to conclude that for such an observer certain events do not just appear to occur but really do occur several times over, which is nonsense. The problem resolves itself if we realise that, in general, equal time coordinates in relativity do not imply a relationship of simultaneity in the first place.

Another hint in Brown's book that the concept of simultaneity in relativity may be flawed is his acknowledgment that Einstein's clock adjustment procedure relies on the assumption of "memorylessness", in other words the idea that an elementary particle does not "somehow 'remember' its entire history of accelerations and thereby 'know' its present absolute velocity relative to a common fixed reference" (p. 53). The potential importance of a particle's acceleration history is of course something I have emphasized in previous blog posts (for example here), although I have not used expressions such as "memory" or "remembering".

Again, sadly, Brown does not develop this point beyond mentioning that "Weyl's unified field theory" was apparently built on the premise that particles can remember their acceleration history. Unfortunately I have not been able to find any documentation on that theory to see how it relates to my own ideas.

The possibility that a particle's acceleration history may determine whether or not light emitted by that particle propagates in symmetrical conditions in all directions is also relevant to Brown's assertion that a total temporal ordering would require us to "arbitrarily" choose one frame of reference in which light is deemed to propagate isotropically. If the assumption of "memorylessness" were wrong and if we knew something about the acceleration history of a system of particles we want to study, then perhaps our choice of reference frame in which light is deemed to propagate in symmetrical conditions would not have to be entirely arbitrary. And we might find that there is not just one but many frames of reference in which light locally propagates in symmetrical or at least broadly symmetrical conditions.

Brown's book thus contains a number of pointers regarding the issue of convention in the light speed principle which I intend to follow up in this blog over the years and decades to come.

Before I conclude this post, I would like to mention another book which I have come across recently and which is just as clear as Brown's on the element of convention in the light speed principle, but which has similar limitations regarding the meaning of "simultaneity" in relativity.

This is the textbook "Special Relativity - A new way into Einstein's world" by Helmut Günther (2007). The author says he wants to break with traditional introductions to special relativity which "start by confronting unsuspecting readers with the incredible postulate of the universal constancy of the speed of light - Einstein's principle of relativity - and then leave them to lose themselves in endless musings about the no less incredible consequences concerning the behaviour of moving measuring rods and clocks" (p. 7).

An excellent plan!

Günther proceeds to give due prominence to the role of clock adjustment procedures in the light speed principle and shows how the Lorentz transformations and Einstein's whole theory can be derived very simply by:

a) adjusting clocks in a first frame of reference Σ using Einstein's clock adjustment procedure;

b) requiring clocks in any other frame of reference S moving at v relative to Σ to be adjusted such that Σ is measured to be moving at -v from the point of view of S - Günther calls this the "elementary principle of relativity";

c) finding empirically that the time dilation and length contraction factors in Σ have the values they have in special relativity (pp. 36-60).

All that is very clear and very interesting.

But an important pillar of the whole edifice crumbles in a single sentence on page 36, where Günther asserts that "in principle" we are "free to agree how to synchronize clocks" in the S frames. He adds that we are in fact well-advised to follow Henri Poincaré in choosing a procedure which makes the transformation formulas particularly simple and symmetrical, and that it is therefore sensible to apply b) above.

We are "free to agree how to synchronize clocks"? Really? So, if we agree to "synchronize" two clocks at opposite ends of a table by setting one to 1 o'clock and the other to 2 o'clock, then we have in fact synchronized them? That's plain nonsense because, at the risk of repeating myself, not every clock adjustment procedure is a synchronization procedure! And there is no reason to believe - and Günther does not even try to make that case - that the clock adjustment procedure implicit in b) above actually synchronizes clocks in the S frames.

So, Günther, for all his best intentions, ends up still confronting unsuspecting readers with a rather incredible claim, namely that his "elementary principle of relativity" has anything to do with synchronizing clocks!

And that concludes my review of the literature on the role of convention in the light speed principle.

Of course, if any of my readers think that there are important publications on the issue which I have failed to mention, I'd love to hear about them.

In the meantime, I'd recommend the following to anybody trying to gain a proper understanding of the special theory of relativity:

READ Albert Einstein, read Reza Mansouri/ Roman U. Sexl, read Kevin Brown and read Helmut Günther. Pay particular attention to their explanation of the role of convention in the light speed principle, because convention plays an important role in that principle and all the above-mentioned authors are very clear about that.

BUT replace every mention of "synchronization" in those publications with "clock adjustment", every mention of "simultaneous events" with "events with equal time coordinates" and every mention of "speed" with "coordinate speed using clocks which are not necessarily synchronized".

AND do not fall into the trap of the simultaneity syndrome, in other words be aware that any concepts that rely on synchronization, such as one-way speed, causality and simultaneous existence, have at best limited applicability in special relativity.

THEN you should be well-placed to begin to make sense of it all.

A fuller summary of my findings to date, and a glimpse of which questions I am going to address next, will have to wait until my next post.