Time dilation and length contraction without relativity: The Bohr atom and the semi-classical hydrogen molecule ion

TL;DR

This paper demonstrates that classical semi-classical models of hydrogen systems can exhibit relativistic effects like time dilation and length contraction without relying on Einstein's relativity, using modifications of classical and quantum ideas.

Contribution

It introduces a semi-classical approach combining Maxwell's classical physics, a modified thought experiment, and Bohr quantization to reproduce relativistic effects.

Findings

Semi-classical hydrogen atom shows time dilation effects.

Hydrogen molecule ion exhibits length contraction.

Classical models can mimic relativistic phenomena without relativity.

Abstract

Recently it was shown that classical "relativistic" particle dynamics was implicit in physics going back to Maxwell. The demonstration utilized a simple modification of a 1906 thought experiment by which Einstein established the mass equivalence of energy, independently of the relativity postulates. The modified thought experiment leads directly to correct expressions for the momentum and kinetic energy of a particle at high speed. In the present paper, one additional ingredient is added, namely, the Bohr quantization rule of the old quantum theory. It is found that a semi-classical model of a hydrogen atom and a hydrogen molecule ion exhibit, respectively, time dilation and length contraction.