Revising the Two Postulates of Special Relativity: Three Principles of Measurement Mechanics

Abstract

Hyoungseok Koh

Einstein’s special theory of relativity rests on two postulates, the principle of relativity and the principle of the constancy of the speed of light, which together imply that all inertial frames are physically equivalent and that a state of rest cannot be operationally distinguished from a state of uniform motion. In this paper we point out that this axiomatic system overlooks the mechanical asymmetry between massive mechanical measuring instruments (rigid rulers and atomic clocks) and massless optical measuring instruments (light rulers). In place of Einstein’s two postulates, we propose three principles of measurement mechanics: (i) the law of invariance of the two-way and borrowed peeds of light, (ii) the law of length invariance of rigid rods, and (iii) the period principle of atomic clocks. We define mechanical coordinates, established in the rest frame by rigid rulers, synchronized atomic clocks, and two-way light signals, and optical coordinates, which a uniformly moving frame equipped only with light sources and observers locally matches to the points of the rest frame. Without assuming the principle of relativity or Lorentz symmetry a priori, and applying only the law of invariance of the two-way and borrowed speeds of light and the law of length invariance of rigid rods, we derive the Lorentz transformation, its inverse, and the absolute time dilation τ=t/γ of a uniformly moving atomic clock. The formal reciprocity of the transformation is interpreted as a relativity between observers, which coexists without contradiction with the physical distinguishability of the rest frame and the uniformly moving frame. This work completes the program developed in the author’s previous studies and establishes the framework of absolute relativity as a consistent reformulation of special relativity.

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