Einstein and time - the plot is thickening

How did Einstein justify his clock adjustment procedure using light signals? And how did he justify the idea that it represents a synchronization procedure not just in some frames of reference but in any frame in which the laws of mechanics hold?

These questions are important because some of the strangest claims of special relativity - as detailed in my previous post - are a direct result of Einstein's clock adjustment procedure and the idea that it represents a synchronization procedure in all such frames of reference.

In his 1905 article "On the Electrodynamics of Moving Bodies", Einstein set out a clock adjustment procedure which, according to him, invariably results in synchronized clocks in separate locations.
According to Einstein (p. 894), a time that is common to a location A in a coordinate system in which Newton's laws of mechanics hold and a location B in the same coordinate system can be defined 'by stipulating by definition that the time it takes for light to travel from A to B is the same as the time it takes for it to travel from B to A. For, let a ray of light leave A at "A time" tA in the direction of B, let it be reflected in B at "B time" tB in the direction of A and let it arrive back in A at "A time" t'A. The two clocks are defined to be synchronous if

tB – tA = t'A – tB.     … '

What Einstein describes here is how, given a first clock in location A, a light signal can be used to adjust a second clock in location B such that the signal arrival time in B lies in the middle between the signal departure and arrival times in A. Einstein then effectively says that clocks adjusted in this way can be declared to be synchronous as a matter of definition. He thus suggests that there is no substance to the concept of simultaneity other than the existence of some systematic procedure to adjust distant clocks.

This position is made more explicit in Einstein's 1916 book, in which he approvingly cites a fictitious participant in a dialogue on simultaneity as saying: "There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled."

In these writings, Einstein thus fails to distinguish between clock adjustment procedures, which may indeed be chosen arbitrarily, and synchronization procedures, which must in fact meet additional criteria, as I have previously shown with reference to sound signals in this and this post.

That is not to say that Einstein did not have any reason to opt for his clock adjustment procedure. The chief reason, it seems, is his stated aim "to arrive at a simple and consistent electrodynamics of moving bodies on the basis of Maxwell's theory for bodies at rest" ("On the Electrodynamics of Moving Bodies", p. 892). In Maxwell's theory, light travels at c in all directions, and generalizing this theory to all frames of reference therefore requires a clock adjustment procedure which ensures that the speed of light is always identical in opposite directions.

While this may well explain Einstein's choice of clock adjustment procedure, it doesn't make that procedure a synchronization procedure. Indeed, both of the criteria that I have identified for a clock adjustment procedure using Einstein's signalling method to qualify as a synchronization procedure appear to be violated.

First, as observed before, Einstein's clock adjustment procedure leads to the theoretical possibility of signals arriving at their destination before they were emitted.

Second, I have suggested that Einstein's clock adjustment procedure is a synchronization procedure only if the conditions in which the signals propagate are symmetrical in opposite directions. This needs to be qualified a little bit. Strictly speaking this is a sufficient rather than a necessary condition, since it may turn out that signals that do not propagate in identical conditions in opposite directions nevertheless lead to the same clock adjustment if the effects of various parameters that are different in different directions cancel each other out. Nevertheless, I would suggest that equal conditions of signal emission as well as propagation in opposite directions should be made a requirement of any (primary) Einstein-like synchronization procedure so that we can be sure that the signal used is suitable.

But if this condition is fulfilled for particular light signals in a particular frame of reference, then the same light signals cannot be used to synchronize clocks in a second frame of reference that moves relative to the first. Let me illustrate the situation with a diagram:

In this diagram, in a frame of reference in which the laws of mechanics hold, some kind of signal - objects projected by an explosion, sound, light or any other signal - is emitted. This event, represented by the star, occurs just as an observer A in a second frame of reference passes by. Suppose that the conditions in which the signal is emitted and propagates are completely symmetrical in all directions in the first frame of reference, and that thus Einstein's synchronization procedure is applicable, producing equal speeds of propagation in opposite directions in that frame.

My contention is that, regardless of the kind of signal used, the same signal cannot then be used to synchronize clocks in A's frame of reference, since A's movement in one of the directions in which the signal propagates means that the symmetry of the conditions in which it is emitted or propagates is inevitably broken.

Now suppose that the same kind of signal is sent out from A at the same time as the first signal, and that empirically it is found to travel in all directions at the same one-way speed (as defined in this post) as the first signal:

Then the second signal cannot be used to synchronize clocks in A's frame of reference, either, since we already know that the first signal cannot be used. This kind of reasoning is completely uncontroversial in the case of, for example, objects projected by an explosion or sound. Surely light cannot be an exception.

Or can it? In a book published in 1962 in English and two years later in German, the physicist Max Born argues that the absence of a universal light medium, or ether, which was already noted by Einstein in 1905, means that each frame of reference in which the laws of mechanics hold is equivalent to any other as far as the propagation of light is concerned and that therefore Einstein's clock adjustment procedure can function as a synchronization procedure in every frame of reference.

Born's reasoning as set out in his book is one of the most detailed attempts to justify the idea that Einstein's clock adjustment procedure is a synchronization procedure that I have found in the literature. It therefore requires very careful analysis - in my next post.