Serendipity: Spacetime Invariance and Scale Effect

TL;DR

This paper explores the relationship between spacetime invariance, scale effects, and reciprocity in special relativity, proposing a new derivation of the Lorentz Factor based on scale conversion to preserve invariance.

Contribution

It introduces a novel derivation of the Lorentz Factor rooted in scale effects, enhancing understanding of spacetime invariance and reciprocity in relativity.

Findings

Scale conversion is essential for spacetime invariance.

A new derivation of the Lorentz Factor based on scale effects.

Reciprocity and causality are maintained through scale considerations.

Abstract

A logic of reciprocity between inertial frames in relative uniform motion is investigated. Relativity allows any reference frame to apply Lorentz Transformation while reciprocity would require the relative frame to use Inverse Transformation for the same event, and vice versa. After such transformations, an inseparability between relativistic measurements and the covariant scale is examined. Scale conversion has been found to be necessary to preserve spacetime invariance in Special Relativity. A new derivation of the Lorentz Factor has been found based on the scale effect. The physical meaning of the Factor is that it serves as a scale conversion ratio between relative reference frames. Reciprocity in relativity and causality of covariance in relative motion are thereby conserved. These logical conclusions harmonize intrinsic natural invariances vis-a-vis apparent observational covariances.