Frequent Errors in Special Relativity

TL;DR

This paper questions traditional interpretations of Lorentz transformations in special relativity, suggesting potential errors in their coordinate-based interpretation and the form of the Lorentz contraction factor, proposing alternative considerations.

Contribution

It introduces a novel critique of the standard Lorentz transformations and Lorentz contraction formula, emphasizing the importance of interval-based interpretation and differential considerations.

Findings

Lorentz transformations may be misinterpreted as coordinate transformations.

The standard Lorentz contraction factor form might be incorrect under differential assumptions.

Alternative forms of the Lorentz contraction factor are proposed.

Abstract

Some reasons are given to suggest that the interpretation of the Lorentz' transformations as if they referred to coordinates instead of to intervals could be incorrect. Besides, the usual form of such transformations, by using variables that represent finite values instead of differentials, could be another error. Later it is shown that the Lorentz contraction factor must not have the form currently accepted for it if the Lorentz contraction factor is assumed to be equal to the quotient between time differentials.