Aurora Effect in case of free rotation

A round-trip experiment shows a constant value of its duration regardless of the orientation of the measuring instrument. What does it mean physically if an observer conducts that experiment? The following picture shows the answer to that question.

Aurora Effect in case of measuring instrument casual rotation

In that case, the observer uses a measuring instrument (a rod) with a length of Z-C1. The measuring signal covers the distance Z-C1-Z in case the instrument is located statically in the medium. The situation changes dramatically in case of motion.

Suppose now this. The measuring instrument has some speed relative to the medium. In that case, the measuring signal leaves the first point of the instrument at point A of the continuum. Suppose also this. The measuring instrument keeps a perpendicular orientation regarding its motion. In that case, the measuring signal reaches the other end of the rod at point C1, which is associated with the medium at rest. At that very moment, the first point of the rod reaches point Z of the medium at rest.

The rod's last point reflects the measuring signal as soon as it reaches it. Therefore, it comes back and meets the first point of the rod at point B of the continuum at rest. In that case, the duration of forward and backward propagation of the measuring signal becomes equal to each other. Therefore, distance A-C1 becomes equal to B-C1, and point Z keeps its location in the middle of the distance AB. Obcerver-to-medium relative motion happens in the direction AB.

Suppose now that the observer rotates the rod but keeps its orthogonal orientation regarding the direction of absolute motion.

In that case, the experiment maintains physical symmetry in signal propagation, and the duration of forward and backward propagation remains the same. Therefore, the other end of the rod changes consequently to points C3, C2, and C4 without any change in measurements (A-C3 = B-C3, and so on). The rod reaches its initial orientation at the end of the experiment.

Suppose now this. The observer rotates the rod in the plain of motion. In other words, the vector of absolute velocity ever lies in that plain. In that case, the measurement becomes asymmetric. As explained above, the duration of forward propagation becomes unequal to the duration of backward propagation.

As a result, at some rod orientations, the measuring signal covers distance AD in forward propagation and distance DB in backward orientation. Distance AD is unequal to BD. However, their sum equals the distance of the round-trip experiment A-CN-B (A-C1-B, A-C3-B, and so on), as explained above.

The observer rotates the rod further. At some moment, it coincides with the direction of absolute velocity. In that case, the measuring signal covers distance A-F1 in forward propagation and F1-B in backward propagation. Those are minimal and maximal distances that the signal covers during the experiment in any orientation of the measuring instrument. However, their sum remains constant regarding any other orientation of the measuring instrument.

In further rotation, the measuring instrument reaches point C2. In that case, the duration of forward and backward propagation remains equal again because the measuring signal covers distances A-C2 in forward propagation and C2-B in backward propagation.

With further rotation, the rod reaches the opposite orientation that it had when the signal reaches point D. In that case, the signal covers distance AE in forward propagation and distance EB in backward propagation. Moreover, those distances are equal to each other by elements, i.e., AE = DB and AD = EB. In other words,

In further rotation, the rod reaches the opposite orientation regarding absolute velocity. In that case, the signal covers distance A-F2 in forward propagation and F2-B in backward propagation. The statement given above becomes evident in that case because the signal covers paths A-F1 in forward propagation and F1-B in backward propagation in case of propagation in the opposite direction.

In further rotation, the rod reaches its initial orientation, and the measuring signal propagates again by the optical path A-C1-B.

That experiment shows some fundamental aspects of measurements:

All the aspects mentioned above look fine if the measuring instrument can freely rotate in space. However, it seems physically impossible if an observer uses a measuring instrument mounted on the Earth.

In that case, the instrument comprises (at least) two atomic clocks located a few kilometers from each other and a communication channel that connects them. The “free rotation” of such a measuring instrument becomes physically impossible. What does happen in such cases of measurements?

The following article gives you the answer to that question.