Compact Extra Dimensions in Quantum Mechanics

TL;DR

This paper introduces undergraduate students to compact extra dimensions in physics by demonstrating their effects in quantum mechanics and discussing Kaluza-Klein excitations, making complex concepts accessible at an introductory level.

Contribution

It presents an accessible approach to teaching about extra dimensions using undergraduate physics concepts and proposes practical exercises for student engagement.

Findings

Low-energy physics is insensitive to compact extra dimensions.

Kaluza-Klein excitations can be predicted using relativistic wave equations.

An educational exercise based on the particle in a box is proposed.

Abstract

Extra-dimensions are a common topic in popular descriptions of theoretical physics with which undergraduate student most often have no contact in physics courses. This paper shows how students could be introduced to this topic by presenting an approach to two basic consequences of the presence of compact extra-dimensions based on undergraduate-level physics. The insensibility of low-energy physics to compact extra dimensions is illustrated in the context of non-relativistic quantum mechanics and the prediction of Kaluza-Klein excitations of particles is discussed in the framework of relativistic wave-equations. An exercise that could be used as a follow-up to the "particle in a box" is proposed.