The principle of relativity as annunciated by Galileo, Newton, Einstein and many others states that:

♦ There is no mechanical experiment that can be done to detect absolute motion.

A form of this statement is the first postulate of the STR by Einstein. This principle can be rephrased in many formulations, which I will show are all violated by my proposed thought experiment (statement formulations are from Einstein’s Special Theory of Relativity by Max Born).

1.) The laws of mechanics have exactly the same expression as when referred to a coordinate system at rest in space.

2.) According to classical mechanics, the velocity of any motion has different values for two observers moving relative to each other.

3.) There are an infinite number of systems of reference moving uniformly and rectilinearly with respect to each other, in which all physical laws assume the simplest form (originally derived for absolute space or the stationary Aether).

4.) The laws of mechanics are invariant with respect to Galilean transformations.

♦ My caboose experiment is a mechanical experiment using sound waves passing through air molecules. It does not find the absolute motion but an intermediary motion that arises from somewhere between absolute motion and relative motion.

According to STR, L will always be L , never allowing any indication of motion by ± vt. The only communication about any motion between reference frames is by the Lorentz and Galilean transformations; behind the Greek mask of time dilation and length contraction of units, a difference is seen from the perspective of the other reference frame.

1a.) The usual mechanics law that is presumed is the simple form v = [d / t], not t = L ± vt as I have shown by this experiment. And it is t = L ± vt in an infinity of other reference frames moving rectilinearly and uniformly relative to the initial reference frame, considered at rest.

2a.) Any and all observers, in motion and at rest, measure the same value for the velocity of the train. It is not a different value for different observers

3a.) There are an infinite number - at rest and in motion - but they do not assume the simplest form of physical laws in each frame. They take on the more complicated form I have shown above. That mimics the MM experiment.

4a) Physicists have long known that sound waves and light waves violate invariance, and I think I have found an experiment that utilize this scientific knowledge. That is, waves are a fount of mechanical information about Nature. Thus they each violate the principle of relativity, with considerable controversy attached. The Lorentz transformation is an overcoming approach for light waves; and my caboose thought experiment overcomes this invariance for with sound waves.

The violation of invariance results mostly from the consideration that the wave does not increase or decrease its velocity based on the velocity of the source or receiver; the motion of material objects do pick up a momentum from a force, which as a consequence, masks its true velocity across reference frames. In other words the wave does not pick up momentum from its source, so the wave might appear to go slower or faster; or the path length might seem to shorten or lengthen, depending upon the direction and magnitude of the source’s velocity.

For sound waves the wave crests grow closer together, or farther apart as the wave travels through the medium, but does not change velocity. For light waves, the STR proposes that alterations in space-time account for the differences arising from the point of view of separate observers in separate reference frames.

Both observers will say that the wave has the same single velocity in her and his own and the other’s references frame, either v = [L / t] - c, or, v = c - [L / t]; but a material object will have a different velocity as measured by each observer looking at the other‘s reference frame. In addition, each observer will use the same simple formula, v = [d / t], of motion for the same object within his or her own reference frame (moving or at rest), but use the velocity addition from the transformation equations in looking at the other’s reference frame. This, I think is the crux of invariance.

I think the use of sound waves in this thought experiment violate the principle of relativity and the first postulate of the Special Theory of Relativity. This experiment thus contradicts the assertions of the definitions of motion as expressed by Galileo, Newton, and Einstein.