The Generalized Uncertainty Principle. New Bounds and Trends

TL;DR

This paper explores a generalized form of the Heisenberg uncertainty principle inspired by quantum gravity theories, constrains the associated parameters using experimental data, and discusses implications for high-energy physics.

Contribution

It introduces a new effective field theory approach to the generalized uncertainty principle and provides the first experimental bounds on the new scale parameter.

Findings

High-energy experiments can potentially detect deviations from the standard uncertainty principle.

The paper constrains the new scale parameter using Compton scattering data.

Theoretical subtleties in modified commutation relations are discussed.

Abstract

The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However, as suggested by some quantum gravity models and string theory, this basic principle no longer holds true in the presence of a minimal length, possible the Plank length, and modifications of the commutation have been proposed i.e., of the form $[\hat{x}^\mu, \hat{p}^\nu ] = -i\hbar(1 + \beta_0 \, \hat{p}^2/\Lambda^2 )\eta^{\mu\nu}$(plus possible additional terms). In this work we will consider the previous modified uncertainty principle in terms of an effective field theory, comment upon some theoretical subtleties that are often overlooked in the literature, and constrain, for the first time, the $\Lambda$ scale with the Compton high-energy experimental data. Our findings suggest that high-energy experiments are potentially sensitive to these corrections and could serve as an effective framework for probing possible violations of the Heisenberg uncertainty principle