One of the few attempts to justify Einstein's clock adjustment procedure that I have seen in the literature is contained in a book by Max Born, Einstein's Theory of Relativity, first published in German in 1920. New editions were published in English in 1962 and in German in 1964.
In the 1964 edition, Born describes a clock adjustment procedure which is essentially equivalent to that presented by Einstein in his 1905 article: clocks in A and B in a uniformly moving frame of reference are adjusted to show the same time when a flash of light emanating from the midpoint C of a straight line between A and B reaches the clocks. Born notes that, if sound signals rather than light signals are used, this procedure results in disagreements between different frames of reference over which events are simultaneous. He adds that, in the case of sound, only the frame of reference that is at rest relative to the body of air in which the sound propagates has the right time, but no such distinction can be made if light signals are used 'because absolute movement relative to the light ether is a concept which, according to all our experience, has no physical reality'.
Born concludes that the procedure can be applied in any frame of reference using light signals. But since light signals observe the same no-overtaking rule as sound signals, the same kinds of disagreement arise, in other words 'if two such frames moving uniformly and in a straight line relative to each other meet and, for example, the clocks A and A' show the same time, then the hands of clocks B and B' will be in different positions. Both frames are equally entitled to claim that they have the right time, for each can maintain that it is at rest because all laws of nature are the same in both frames. But if two are equally entitled to make the same claim, which by its very nature can only be granted to one, then we must conclude that the claim is in fact meaningless: There is no absolute simultaneity. Once this has been grasped, it is difficult to understand that many centuries of exact research had to pass before this simple fact was recognized.' (pp. 197-98)
Born is right to say that, if a light ether existed, Einstein's clock adjustment procedure would not constitute a synchronization procedure in all frames of reference. However, the absence of an ether does not mean that Einstein's clock adjustment constitutes a synchronization procedure. This is because the real test for the usability of Einstein's clock adjustment procedure as a synchronization procedure is not whether or not there is a universal medium in which the signals propagate but, much more generally, whether or not the conditions in which the signals are emitted or propagate are symmetrical in opposite directions.
Whatever those signals are - waves in a universal medium; particles that are ejected without the need for a medium; or something else - it is clear that if the conditions of emission and propagation are symmetrical in opposite directions in one frame of reference, then they cannot also be symmetrical for the very same signals from the point of view of an observer who is moving relative to that frame of reference.
It is true that, if we don't know whether those conditions are symmetrical in two given frames of reference, then those two frames are equally entitled, or rather equally ill-placed, to claim that they have the right time if their clocks are Einstein-adjusted. But it does not follow that 'having the right time' is meaningless, it just means that we do not have sufficient information to decide which, if any, of the frames really does have the right time.
Perhaps Born's argument is that such information is unobtainable in principle because the laws of nature do not contain any parameter expressing any lack of symmetry in the propagation of light. This is an important point which requires further analysis.
First, it should be emphasized that in this context the "laws of nature" can only refer to laws that do not rely on the concept of distant simultaneity, since this is the very concept Born is seeking to define. In particular, the constancy of the one-way speed of light is not included in those laws.
Second, the relevant laws of nature are to a large extent based on observations and experiments in terrestrial laboratories, in which the conditions in which light is emitted and propagates may well be constant, and this may be the reason why those laws do not contain any parameter determining the presence or absence of symmetry.
For example, according to a more modern theory of light propagation than the ether model, electromagnetic radiation can be regarded as outwardly propagating disturbances in the electric fields of charged particles. Such disturbances may, for example, be caused by sudden, local accelerations of those particles - see for example Lesson 4 in this document by Daniel V. Schroeder. In this model, any light source carries the field in which the light propagates around with itself. Light emitted by a source that is stationary on Earth thus propagates in constant and quite possibly broadly symmetrical conditions in different directions, regardless of, for example, the position of the Earth in its orbit around the sun.
The "local acceleration history" of a source of light could thus 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.
Nevertheless, it may well be that from the point of view of a charge that has undergone local acceleration, for example as a result of a collision, everything still looks symmetrical in its new frame of reference and that thus "local acceleration history" is not directly observable. Worse, it may be difficult or impossible to reconstruct such acceleration histories if we do not already have a frame of reference which we know to be symmetrical and which we can thus use to define simultaneity.
If that is so - and I will have to look into these issues in much greater detail in subsequent posts on alternative definitions and theories that are compatible with observation and experiment - then Einstein's clock adjustment procedure may be justified on pragmatic grounds as a procedure that yields simple laws and enables accurate predictions, as long as it is made clear that it is not a synchronization procedure.
In summary, Born raises an important issue, which is the detectability of asymmetrical conditions in the emission or propagation of light, although he only does so in relation to the outmoded ether theory of light. His point that there may be no practical alternative to Einstein's clock adjustment procedure if there is no such detectability deserves careful consideration. On the other hand, Born fails to make a convincing case for the claim that Einstein's clock adjustment procedure is a synchronization procedure in all uniformly moving frames of reference.
So, what led Born to believe that Einstein's clock adjustment procedure can function as a synchronization procedure? I think the main reason is that he took it for granted that the one-way speed of light is constant for all observers. As he puts it at the start of his chapter on simultaneity, 'experience teaches us that the speed of light always has the same value c, regardless of the state of motion of the observer', and this fact requires us to drop 'the principles of defining space and time as they have always been applied until now'. (p. 194) In reality, of course, defining space and time, and in particular distant simultaneity, is a step that comes before experience can tell us anything about the constancy of c for all observers.
Born's approach of using the constancy of c as his starting point is reminiscent of Einstein's desire to adjust clocks in such a way that Maxwell's laws, and thus the constancy of c, are valid in all frames of reference. Neither of these physicists seems to have been interested primarily in exploring how clocks need to be adjusted in order to arrive at a meaningful definition of simultaneity. The result, I fear, is a theory in which clocks are not synchronized and consequently concepts that rely on synchronization, such as distant simultaneity, one-way speed and causality, break down.
Einstein's and Born's writings thus raise an intriguing possibility: 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.
For now, however, this is merely a hypothesis which requires further testing against some of the more recent specialized literature on time and simultaneity in physics, starting with writings on these issues by Max Jammer and Allen Janis - in my next post.
