Uncertainties inherent in the decomposition of a Transformation

TL;DR

This paper discusses the inherent uncertainties in decomposing Lorentz transformations, emphasizing the role of observational frames and the necessity of a universal synchronization for resolving these ambiguities.

Contribution

It highlights the indeterminacy in Lorentz transformation composition due to observational and simultaneity differences, proposing universal synchronization as a resolution.

Findings

Lorentz transformation composition depends on the order of observational assumptions

Uncertainty in the transformation arises from frame-dependent simultaneity and measurements

Universal synchronization can resolve the inherent uncertainties

Abstract

This contribution adds to the points on the <indeterminacy of special relativity> made by De Abreu and Guerra. We show that the Lorentz Transformation can be composed by the physical observations made in a frame K of events in a frame K-prime viz i) objects in K-prime are moving at a speed v relative to K, ii) distances and time intervals measured by K-prime are at variance with those measured by K and iii) the concept of simultaneity is different in K-prime compared to K. The order in which the composition is executed determines the nature of the middle aspect (ii). This essential uncertainty of the theory can be resolved only by a universal synchronicity as discussed in [1] based on the unique frame in which the one way speed of light is constant in all directions.