Over the last two years, I have devoted a fair amount of time to studying the issue of convention in special relativity, in particular the role played by convention in the principle of the constancy of the speed of light for every observer, and it is now time to pull my findings together. The summary below contains links to other posts in which I expand on the points made - readers who want to consult those posts may want to right-click on the links to open them in separate tabs.
Fundamentally, the concept of one-way speed relies on the notion of simultaneity in different points and thus on our ability to adjust clocks in different points in a manner which synchronizes them.
I have argued that the concept of simultaneity in different points, or of clock synchronization, is linked to the concept of symmetry as follows:
Two distant clocks in a spatial inertial coordinate system can be synchronized by emitting identical signals in opposite directions from the mid-point between the clocks and adjusting the clocks to the same time when the signals arrive there, provided the conditions in which the two signals are emitted and propagate are symmetrical.
This is not just a concept of simultaneity I have dreamt up. It is the standard concept of simultaneity to which physicists and others have subscribed for hundreds of years and which, through its links with other concepts such as causality, one-way speed and simultaneous existence, is firmly anchored in the English language. Yet physicists and philosophers have paid surprisingly little attention to the requirement of symmetry in the conditions of signal transmission.
Albert Einstein is a notable exception. In one of his articles, he insisted that, for a clock adjustment procedure using signals to qualify as a synchronization procedure, the means of sending signals "must be such that we have no reason to believe that the phenomena of signal transmission in the direction AB differ in any way from the phenomena of signal transmission in the direction BA".
As I have shown in detail here and here, ignoring this requirement may lead to conceptual mayhem.
But establishing whether or not that requirement is fulfilled in any particular spatial inertial frame of reference for any particular type of signal can be more difficult than meets the eye.
Suppose we follow Einstein in using light signals to adjust clocks in accordance with the synchronization procedure set out above. Suppose that to the best of our knowledge light signals propagate in symmetrical conditions in opposite directions in a first frame of reference. Suppose that, for example, all electric and other measurable fields surrounding stationary particles are found to be spherically symmetrical and all macroscopic conditions of signal emission and transmission are found to be symmetrical, too. Then it would appear that those signals can be used to synchronize clocks in that frame of reference.
But those very same signals can then not be used to synchronize clocks by an observer who is moving relative to that frame of reference, since her movement in one particular direction inevitably breaks the symmetry of the conditions of signal emission and/or propagation.
We might think the problem could be overcome by the observer in the second frame sending out her own light signals. But that wouldn't help because empirically they would be found to travel in tandem with the signals sent out in the first frame of reference and are therefore not suitable, either.
So we might be tempted to conclude that Einstein's clock adjustment procedure does not synchronize clocks in the moving frame of reference.
But what if, as physicists assure us, the conditions of signal transmission in the second frame of reference appear to be symmetrical, too? What if all electric and other measurable fields surrounding stationary particles are found to be spherically symmetrical and all macroscopic conditions of signal transmission are found to be symmetrical in that frame, too?
Then it would appear that observers in both frames of reference would be equally entitled, or rather equally ill-placed, to claim that Einstein's procedure synchronizes clocks in their frame of reference.
All we can then say is that if the procedure synchronizes clocks in the first frame, then it does not synchronize clocks in the second, and vice versa, because the requirement of symmetry can only be met in at best one of the frames. But we do not know in which, if in any.
Max Born concluded from this that we might as well use Einstein's procedure to adjust clocks in any inertial frame of reference. And this may well be justified on pragmatic grounds.
But - and this is my key finding - it leaves us with a theory in which in general clocks are not synchronized.
Could we perhaps, as suggested by Einstein, resolve the problem by declaring clocks adjusted in this manner to be synchronized by definition or by convention? The answer is "no" because what is conventional is our choice of clock adjustment procedure and not our choice of synchronization procedure. Even if we agree on a technical definition of "simultaneity (physics)" = "equal time coordinates as measured by Einstein-adjusted clocks", this does not resolve the conceptual problems caused by using a clock adjustment procedure which ignores the requirement of symmetry.
In fact, the apparently widespread belief that Einstein's 1905 clock adjustment procedure is a synchronization procedure, or can be declared to be one "by definition", has led some physicists to draw spectacular but misguided conclusions on issues such as causality and existence. These conclusions are the result of what I have called the "simultaneity syndrome" in modern physics: the continued and uncritical application of concepts depending on synchronization, such as one-way speed, causality and distant simultaneous existence, in the framework of a theory in which clocks have not in fact been synchronized.
Some of the more lucid writers on special relativity seem to have sensed that Einstein's clock adjustment procedure may not be the most obvious choice to qualify as a synchronization procedure. They have therefore come up with a number of alternative and supposedly more intuitive clock adjustment procedures, such as slow clock transport or the requirement that observers in different frames of reference agree on their speed relative to each other. The most persuasive alternative is perhaps to go back to the procedure implicit in Newton's laws, using objects as signals rather than light.
The problem with all of these procedures is that they are perfectly equivalent with Einstein's procedure and therefore they are not synchronization procedures, either.
That is not to say that they are useless. As a number of writers from Henri Poincaré and Albert Einstein to Kevin Brown and Helmut Günther have pointed out, we may want to choose a clock adjustment procedure which makes the laws of physics particularly simple, and that's what all the procedures mentioned above do: they lead to the familiar symmetrical laws of mechanics and they ensure that Maxwell's equations of electromagnetism are valid in any inertial frame of reference.
We just need to bear in mind that, in the framework of a theory based on such a clock adjustment procedure, clocks are not necessarily synchronized. As a result, in such a theory events with equal time coordinates are not necessarily simultaneous; one-way "speeds" are potentially meaningless "coordinate speeds measured with clocks which are not necessarily synchronized"; and the concept of causality may not be applicable when "superluminal speeds" are involved.
Then everything falls into place: the principle of the constancy of the "speed of light" for every observer, for example, since it becomes clear that the "speed" it refers to is a purely formal "coordinate speed" obtained from clocks which are not necessarily synchronized; or the "time quakes" which occur in special relativity when distant observers begin to move relative to each other, since, again, the only "time" that is subjected to such swings is a purely formal "coordinate time" shown by clocks which are not synchronized.
Ultimately it may thus seem that the strangeness of special relativity does not correspond to anything in the observed phenomena but is purely the result of a clock adjustment procedure which is not a synchronization procedure. In other words, the world may not actually be half as weird as a superficial reading of some physics books might suggest. And it may seem that I could therefore stop right here and close this blog, job done.
But I can't. Special relativity includes a number of fairly strange statements which are independent of any clock adjustment procedure. These include the empirical facts that the two-way speed of light is found to be the same in every spatial inertial frame of reference if clocks of identical construction are used, and that a twin who makes a round-trip will be younger on her return than her sibling who stayed at home all the while.
These are facts which are not necessarily entirely expected and which therefore call for an explanation. So there remains some work to be done for me.
A lot of work. Because I believe that in order to arrive at such an explanation I will first have to gain a much better understanding of some areas of physics than I currently possess. I mention only classical electrodynamics, quantum electrodynamics and general relativity. At least that's what I imagine.
And there is more. I have complained the length and breadth of this blog that Einstein's clock adjustment procedure is not a synchronization procedure, but have I been able to offer a meaningful alternative? I have not.
I have talked about the possibility that the "acceleration history" of a source of light could be a parameter which is missing from the laws of nature as currently formulated and which may help to determine whether or not the conditions in which light propagates in opposite directions from that source are symmetrical.
In that context I have developed a rudimentary "sphere model" of electricity which would seem to explain the fact that the speed of light is locally independent of the uniform movement of the source of the light in a spatial inertial frame of reference.
But these are feeble attempts compared to the magnitude of the task.
I think a good starting point to take my inquiries further is the constancy of the two-way speed of light for all inertial observers. How have physicists explained it? How would I explain it? Is it even a phenomenon that can be explained or must it be accepted as a fundamental fact of nature? I think it would be reasonable to expect a relatively long wait before my next post.
