Thim’s experiment and exact rotational space-time transformations

Abstract

Abstract-Thim measured the transverse Doppler shift using a system consisting of a stationary antenna and pickup, in addition to a number of intermediate antennas mounted on the rim of a rotating disk. No such shift was detected, although the experiment should have had enough sensitivity to measure it, as predicted by the Lorentz transformations. However, using the Lorentz transformations to analyze the results of experiments involving circular motion, while commonly done, is inappropriate because such an analysis involves non-inertial frames, which are outside the range of validity of special relativity. In this paper, we re-analyze Thim's experiment using exact rotational space-time transformations, finding that his null result is consistent with theoretical predictions.

Fermi coordinates and modified Franklin transformation: a comparative study on rotational phenomena

“…Since the theoretical predictions based on MFT agree with those based on Lorentz transformations up to the second order in β, one needs to carry out the same experiment ( = 35000 rpm, R 0 = 9.3 cm) with a precision of at least 1 part in 10 14 to find any deviations in the fourth order. For the treatment of the same effect using an alternative RRT refer to [24].…”

“…Obviously their difference leads to the same relation (24). In this formulation the Sagnac effect and the so-called clock effect [28] are treated as different manifestations (null and timelike) of the desynchronization effect in axisymmetric stationary spacetimes.…”

Experiments on the CMB Spectrum, Big Jets Model and Their Implications for the Missing Half of the Universe

“…Based on the general-frame covariant blackbody distributions (1), (4), (12)- (15), it is unnatural and inconsistent with the principle of relativity to attribute the 'dipole anisotropy of the CMB' to the motion of the solar system relative to the CMB. The general-frame covariant result (15) implies that if the Lorentz invariant distribution law B(k µ U µ , T ) and the CMB temperature are isotropic in one inertial frame F , then they will both be isotropic in every inertial and rotational frames as well, according to the principle of limiting Lorentz-Poincaré invariance.…”

“…In the literature, there exists a fundamental space-time symmetry framework called limiting four-dimensional symmetry (or limiting LorentzPoincaré invariance) that can help us generalize physical laws in inertial frames to non-inertial frames of reference. [1,2] In particular, one can use this framework to derive a set of coordinate transformations between an inertial frame F and a rotating frame F r that (a) are exact, (b) simplify to the Lorentz transformations in the appropriate limit (i.e., as the orbital radius goes to infinity while the product of the orbital radius and angular velocity remains finite [15]), (c) are consistent with the results of experiments such as the Davies-Jennison experiment, Thim's experiment involving radio sources in circular motion [2,15], and high energy experiments involving unstable particles in a circular storage ring, and (d) support the analysis of the Wilson experiment. [7] These transformations can also give us the metric tensors P µν (x) necessary for generalizing the blackbody distribution to rotating and constant-linear-acceleration frames.…”

“…Let the Earth be at rest relative to the rotating frame and located at x r = ρ, y r = 0, z r = 0. The exact rotational coordinate transformations are then [15] …”