Three +1 Faces of Invariance

TL;DR

This paper critically examines the concept of invariance in relativity, clarifying misconceptions about proper length and highlighting the true invariants like proper distance, proper time, and rest mass, offering new insights into relativistic invariants.

Contribution

It distinguishes between authentic and non-authentic invariants in relativity and clarifies the relationship among proper length, proper distance, proper time, and rest mass.

Findings

Proper length is not a true invariant.

Proper distance, proper time, and rest mass are genuine invariants.

Mass-time analogy offers new perspective on the twin paradox.

Abstract

A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as relativistic invariants under space-time rotations. Only observables in the first three categories are authentic invariants, whereas the single "invariant" - proper length - in the fourth category is actually not an invariant. The proper length has little is anything to do with proper distance which is a true invariant. On the other hand, proper distance, proper time, and rest mass have more in common than usually recognized, and particularly, mass - time analogy opens another view of the twin paradox.