Rigid Motion in Special Relativity

Abstract
We solve the problem of rigid motion in special relativity in completeness, forswearing the use of the 4-D geometrical methods usually associated with relativity, for pedagogical reasons. We eventually reduce the problem to a system of coupled linear nonhomogeneous ordinary differential equations. We find that any rotation of the rigid reference frame must be independent of time. We clarify the issues associated with Bell’s notorious rocket paradox and we discuss the problem of hyperbolic motion from multiple viewpoints. We conjecture that any rigid accelerated body must experience regions of shock in which there is a transition to fluid motion, and we discuss the hypothesis that the Schwarzchild surface of a black hole is just such a shock front.

Keywords
rigid body; rigid motion; born rigidity; rotation; acceleration; revolution; Ehrenfest’s paradox; Bell’s rocket paradox; relativity; hyperbolic motion; Schwarzchild solution; black holes

Cite this paper
Stuart Boehmer, Rigid Motion in Special Relativity , SCIREA Journal of Physics. Volume 6, Issue 1, February 2021 | PP. 1-31. 10.54647/physics14321

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