The Relativistic Elasticity of Rigid Bodies

TL;DR

This paper clarifies the distinction between rigid and undeformable bodies in relativity, presenting elastic laws for rigid bodies and emphasizing their importance in relativistic physics education.

Contribution

It introduces elastic laws for relativistic rigid bodies and advocates for correct terminology and teaching in relativity courses.

Findings

Rigid bodies in relativity are deformable with shock waves propagating at speed c.

The paper clarifies the distinction between rigid and undeformable bodies in relativistic context.

It proposes elastic laws for relativistic rigid bodies.

Abstract

In 1909 Born studied the "relativistic undeformable body" but made the mistake of calling it "rigid". The "rigid body" as one can find in Relativity books is, in fact, this Born "undeformable body". In Relativity it is necessary to distinguish between "rigid" and "undeformable". The "undeformable" body (in the sense of the most rigid possible) must be the "deformable" body where schock waves propagate with maximum speed c. We present in this text the elastic laws for rigid bodies. We think that these laws, which are ignored by the majority of relativists, should be taught in the elementary relativistic courses. With the approach of 2005, the centenary year of Relativity, we should like to appeal to all those who have some influence on these matters to avoid this mistake of repeatedly calling "rigid" to the "undeformable body".