Reciprocity Independent Lorentz Transformation

TL;DR

This paper introduces a reciprocal symmetry in special relativity by defining slowness and generalizing Lorentz transformations to maintain invariance under velocity-slowness exchange.

Contribution

It proposes a reciprocal symmetry operation and extends Lorentz transformations to preserve invariance when velocities are replaced by their reciprocal slownesses.

Findings

Reciprocity operation converts velocities to slownesses.

Lorentz transformation is generalized to include slowness.

Invariance is maintained under velocity-slowness exchange.

Abstract

We have defined slowness (or reciprocal velocity, corresponding to velocity v) as cc/v, where c is the speed of light. It is observed that the relative velocity remains invariant if the velocities are replaced by corresponding slownesses i.e. relative motion in one dimension is reciprocal symmetric. Reciprocity operation, which converts a velocity to the corresponding slowness, is found. Lorentz transformation is generalized so that Lorentz invariance is maintained if velocities are replaced by corresponding slownesses.