A solution to the soccer ball problem for generalised uncertainty relations

TL;DR

This paper introduces a novel method for deriving generalized uncertainty relations that avoids the issues of previous approaches, notably resolving the 'soccer ball problem' by allowing macroscopic total momenta without modifying the Heisenberg algebra.

Contribution

It presents a new approach to generate GURs compatible with fundamental principles without altering the Heisenberg algebra, addressing key problems in quantum gravity models.

Findings

Provides a consistent framework for GURs without modified commutation relations

Resolves the 'soccer ball problem' for macroscopic momenta

Maintains compatibility with the equivalence principle and Poincaré invariance

Abstract

We propose a new method for generating generalised uncertainty relations (GURs) including the generalised uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalised uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar{\' e} invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multiparticle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the "soccer ball problem" that plagues current approaches to GURs.