Faculty of Physics
M.V. Lomonosov Moscow State University
Regular Article

Derivation of all linear transformations that meet the results of Michelson-Morley’s experiment and discussion of the relativity basics

R. -. Szostek

Moscow University Physics Bulletin 2020. N 6.

  • Article

The paper presents a formal proof that the mathematics on which the Special Theory of Relativity (STR) is based is currently misinterpreted. The evidence is based on an analysis of the importance of parameter e(v). Understanding the meaning of this parameter was achieved by analyzing the general form of transformation, for which the Lorentz transformation is only a special case. If e(v) ≠ 0 then the clocks in inertial systems are desynchronized. Measurements, e.g. one-way speed, using such clocks do not give real values. The article shows that there are infinitely many different transformations in which one-way speed of light is always equal to c. The Lorentz transformation is only one of those infinitely many transformations. In this article, the whole class of linear transformations of time and coordinate was derived. Transformations were derived on the assumption that conclusions from Michelson-Morley’s and Kennedy-Thorndikea’s experiments are met for the observer from each inertial frame of reference, i.e. that the mean velocity of light in the vacuum flowing along the way back and forth is constant. It was also assumed that there is at least one inertial frame of reference, in which the velocity of light in a vacuum in each direction has the same value c, and the space is isotropic for observers from this distinguished inertial frame of reference (universal frame of reference). Derived transformations allow for building many different kinematics according to Michelson-Morley’s and Kennedy-Thorndikea’s experiments. The class of transformations derived in the study is a generalization of transformations derived in the paper [10], which consists in enabling non-zero values of parameter e(v). The idea of such a generalization derives from the person, who gave me this extended transformations class for analysis and publication.

Received: 2019 November 13
Approved: 2021 March 23
02.90.+p Other topics in mathematical methods in physics
03.30.+p Special relativity
R. -. Szostek
$^1$Rzeszów University of Technology Department of Quantitative Methods
Issue 6, 2020

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