Some Consequences of the Generalised Uncertainty Principle: Statistical Mechanical, Cosmological, and Varying Speed of Light

TL;DR

This paper explores the implications of Maggiore's generalized uncertainty principle, revealing effects like reduced degrees of freedom at high temperatures, varying speed of light, and potential impacts on cosmology and black hole physics.

Contribution

It introduces a novel perspective on the GUP's consequences, linking it to thermodynamics, cosmology, and black hole phenomena, and suggests it as a new form of the Heisenberg principle.

Findings

High-temperature reduction in degrees of freedom similar to string theory

Natural emergence of varying speed of light and modified dispersion relations

Potential implications for cosmology and black hole physics

Abstract

We study the dynamical consequences of Maggiore's unique generalised uncertainty principle (GUP). We find that it leads naturally, and generically, to novel consequences. In the high temperature limit, there is a drastic reduction in the degrees of freedom, of the type found, for example, in strings far above the Hagedorn temperature. In view of this, the present GUP may perhaps be taken as the new version of the Heisenberg uncertainty principle, conjectured by Atick and Witten to be responsible for such reduction. Also, the present GUP leads naturally to varying speed of light and modified dispersion relations. They are likely to have novel implications for cosmology and black hole physics, a few of which we discuss qualitatively.