The general form-invariance principle

TL;DR

This paper explores the general form-invariance principle in special relativity and classical mechanics, proposing new transformations between reference frames, including rotating and stationary rigid frames, to demonstrate the principle's applicability.

Contribution

It introduces a new transformation for rotating reference frames and extends the form-invariance principle to stationary rigid frames, broadening its theoretical scope.

Findings

The principle holds in classical mechanics.

A new transformation for rotating frames is proposed.

Form-invariance applies to stationary rigid frames.

Abstract

We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this principle are considered. A new transformation is proposed for a transition from a uniformly rotating reference frame to a reference frame whose origin is shifted from the rotation axis. Another possible formulation of this principle is given for the case of stationary rigid reference frames which differ from one another only by the position of the origin.