Lorentz invariant intrinsic decoherence

TL;DR

This paper explores a Lorentz invariant model of intrinsic decoherence caused by quantum gravity effects, modifying Schrödinger dynamics with implications for uncertainty principles and field dispersion relations.

Contribution

It introduces a Lorentz invariant extension of intrinsic decoherence models using semigroup representations, aligning with quantum gravity and string theory insights.

Findings

Modifies the uncertainty principle

Alters field dispersion relations

Maintains Lorentz invariance

Abstract

Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr\"{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum gravity and string theory .