Newton's idea of simultaneity

If, as Kevin Brown says in his book on relativity, Einstein's clock adjustment procedure using light signals leads to the same clock adjustment as Newton's clock adjustment procedure using objects, it is worth investigating whether or not Newton's procedure is a synchronization procedure, in other words whether or not it ensures that events with equal time coordinates are simultaneous.

From a purely logical point of view, it is clear that in general Newton's procedure cannot be a synchronization procedure because I have already shown, here and in subsequent posts, that in general Einstein's procedure is not a synchronization procedure.

But it would be nice to be able to see that directly, by examining Newton's procedure more closely.

In Newton's procedure - or more precisely the procedure which is implicit in his laws of mechanics - two clocks A and B in a first spatial inertial system S1 are adjusted to show the same time when identical objects projected in opposite directions from the mid-point between A and B using identical acceleration mechanisms arrive at those clocks, provided the conditions in which the objects are accelerated and in which they travel are symmetrical in both directions. Events with equal time coordinates in S1 are then simultaneous by virtue of the very meaning of simultaneity.

The crucial question is how we can then adjust clocks in a second spatial inertial system S2 that moves relative to the first. According to Newton, we can do that by accelerating the clocks, the objects and the accelerating mechanisms used in S1 so that they come to rest in S2 and performing the same procedure in S2 to adjust distant clocks in that system.

Let's assume that in both frames the procedure is performed in "empty space", notably in the absence of any medium such as air which might disturb the symmetry of the conditions in which the objects are accelerated or travel.

But even in the absence of any medium such as air, after the clocks, the acceleration mechanisms and the objects have been accelerated in one particular direction, are the conditions in which the procedure is then performed in S2 still symmetrical in opposite directions?

Newton evidently thought they were. And it's easy to see why. Newton didn't know that "empty space" is in fact filled with all manner of fields which surround any object. To him, the objects used in S2 would be just the same objects as they were in S1 and the symmetry of the conditions of any further acceleration and movement in opposite directions would not have been disturbed by their acceleration from S1.

That is why he thought that, as measured by Newton-adjusted clocks in S1, two identical objects at rest in S2 would undergo the same acceleration if they were projected in opposite directions using identical acceleration mechanisms. Today we know that this is not the case.

And that does not come as a surprise given that today we know that all objects are surrounded by, for example, electromagnetic fields. We also know that disturbances in such fields need some time to travel over any closed path.

Let's take the example of a simple electron whose field is spherically symmetrical in S1 and let's see how that field is affected if the electron is accelerated locally, for example as the result of a collision.

Qualitatively, and without adjusting any clocks, any field disturbance can be expected to propagate symmetrically around the electron's original position of rest, but the movement of the electron in one particular direction then creates asymmetrical conditions in the field surrounding it.

Quantitatively, let's assume that at a time t1 in S1 an electron at rest in S1 and surrounded by a spherically symmetrical field undergoes such a sudden acceleration to a speed v.

The field is represented here by a series of concentric spheres surrounding the electron. At the time t2 > t1 in S1, the electron moves at v and information about its acceleration is spreading outwards through the electron's field. Each of the spheres surrounding the electron starts to move at v when the information about the acceleration reaches it, leading to the following situation at the time t2:

As the information spreads further, the area around the electron in which the sphere density is asymmetrical grows:

At the boundary between areas of different density, shown in red, an electromagnetic signal propagates away from the electron (for details on how this happens, see Lesson 4 in this document by Daniel V. Schroeder). Any further sudden acceleration of the electron would give rise to a new electromagnetic signal. And the light speed law appears to be that any acceleration information always traverses the same number of spheres in the same amount of time. This means that locally in S1 the speed of an electromagnetic wave is independent of the speed of the light-emitting body.

The sphere model illustrates the fact that if the field around an electron, and thus around any object containing electrons, is symmetrical, then the field around the same electron accelerated locally to a speed v is no longer symmetrical. And for that reason Newton's clock adjustment procedure applied in a second frame S2 moving at a speed v relative to S1 is not a synchronization procedure.

At least not locally. Over cosmic distances, Newton's or Einstein's procedure may well be applicable to sets of clocks that move at a speed v relative to one another. The reason for that is that clocks that are very distant from each other may be moving relative to each other as a result of certain kinds of acceleration which disturb the local fields around them only negligibly. As far as I understand it, cosmic expansion and gravity are examples of such locally non-perturbative accelerations:

Locally, however, all particles or objects are subjected to the same gravitational or cosmic expansion influences. Therefore, if they move relative to each other locally then that must be the result of previous local accelerations which have disturbed the electric fields surrounding them.

My investigation into whether or not Newton's clock adjustment procedure is a synchronization procedure has led me to develop my sphere model of electricity and light propagation a bit further in this post.

After these flights of fancy, it is time to test my thoughts against the best of the literature on simultaneity in Newton's and Einstein's theories. And that leads me straight back to Kevin Brown's book Reflections on Relativity. In my next post.