In the current paper we present an explanation of several fundamental tests of special relativity from the perspective of the frame co-moving with a rotating observer. The solution is of great interest for real time applications because Earth-bound laboratories are inertial only in approximation. We present the derivation of the Sagnac, Michelson-Morley, Kennedy-Thorndike and the Hammar experiments as viewed from the Earth-bound uniformly rotating frame, that is, the frame of the laboratory where the experiment is taking place. To our best knowledge such an attempt has never been made before, possibly due to its mathematical difficulty, so no precedents exist, this is a first. The current paper brings new information in the following areas:
-new explanation of the Sagnac experiment
-new explanation of the Michelson-Morley experiment
-new explanation of the Hammar experiment
-new explanation of the Kennedy Thorndike experiment
The main thrust of the paper is to give a consistent explanation of various tests of special relativity as judged from the perspective of the rotating frame of the experimental setup. The theoretical results are shown to be consistent with the results derived for inertial frames in the specialty literature. The exact symbolic solutions are nevertheless different from the results obtained for inertial frames. This should not be surprising since the rotation actually “modulates” the proper speeds of the light wave-fronts.
General coordinate transformations; Hammar experiment; Kennedy-Thorndike experiment; Michelson-Morley experiment; Sagnac experiment; Uniform rotation motion
03.30.+p, 52.20.Dq, 52.70.Nc
Real life applications include accelerating and rotating frames more often than the idealized case of inertial frames. Our daily experiments happen in the laboratories attached to the rotating, continuously accelerating Earth. Usually, such experiments are explained from the perspective of an external, inertial frame because special relativity in rotating frames is viewed as more complicated. In the present paper, we will construct a straightforward explanation by applying the formalisms developed in previous work [1-6]. More exactly, we apply the formalisms derived in [1-3] to explaining the results of some of the most important tests of special relativity as viewed from the rotating frame of the lab where the experiments take place.
Figure 1: Peripherally rotating frame of reference.
The Sagnac experiment [8-12] is usually explained from the perspective of an inertial frame anchored to the center of rotation since the mathematical formalism is simpler from that perspective. In this section, we will use the results derived in the previous section in order to produce an equally straight forward explanation from the perspective of a frame attached to the periphery of the rotating device. Based on the prior results, the observer co-moving with the rotating frame measures the perimeter of a circle of radius r to be 2πr, both wave-fronts cover the same distance, 2πr, so the time difference between the clockwise and counterclockwise light fronts is calculated as (absolute speeds are used):
We can now explain the null result of the Michelson Morley experiment [13-21] in the rotating frame of the lab co-rotating with the Earth. The elapsed time in the direction of motion is:
The Kennedy-Thorndike experiment exploits the fact that the Earth bound laboratory has a variable speed due to the combined effect of Earth rotation around its axis and Earth revolution around the Sun . The laboratory speed has contributions from the revolution of the Earth with respect to the Sun-centered frame, ve = 30km/s and Earth’s daily rotation vd so:
Once again, while the transition times in the rotating frame is different from the ones calculated for idealistic inertial frames, the measured values of the experiment are null, exactly as predicted by the above theory.
In the following, all calculations explaining the outcome of the Hammar experiment [23,24] are made from the point of view of the rotating Earth-bound frame and all employ the theory of special relativity in rotating frames. The clockwise ( tcw ) and counterclockwise (tccw) time of light propagation are (Figure 2):
Figure 2: Instrument motion with shielded arm moving parallel to the “aether wind”. The light source as well as the screen where interference occurs between the two light beams is located in point “A”. Also, a half-silvered mirror is used as a light splitter.
Citation: Sfarti A (2019) Special Relativity Optical Experiments Explained from the Perspective of a Peripherally Rotating Frame. J Light Laser Curr Trends 2: 004.
Copyright: © 2019 Adrian Sfarti, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.