Quantum superpositions of the speed of light

TL;DR

This paper proposes a novel quantum superposition-based framework allowing photons to have variable speeds, including superluminal and subluminal, without violating Lorentz-invariance or introducing tachyons, thus reconciling quantum theory with modified relativistic principles.

Contribution

It introduces a new method to incorporate deviations from Lorentz-invariance into quantum field theory via photon superpositions, avoiding previous issues with explicit breaking or deformation.

Findings

Photons can exist in superpositions of different speeds without violating relativity.

Measurement collapses superpositions, restoring standard relativistic laws.

The approach avoids tachyons and explicit Lorentz violation.

Abstract

While it has often been proposed that, fundamentally, Lorentz-invariance is not respected in a quantum theory of gravity, it has been difficult to reconcile deviations from Lorentz-invariance with quantum field theory. The most commonly used mechanisms either break Lorentz-invariance explicitly or deform it at high energies. However, the former option is very tightly constrained by experiment already, the latter generically leads to problems with locality. We show here that there exists a third way to integrate deviations from Lorentz-invariance into quantum field theory that circumvents the problems of the other approaches. The way this is achieved is an extension of the standard model in which photons can have different speeds without singling out a preferred restframe, but only as long as they are in a quantum superposition. Once a measurement has been made, observables are subject to the laws of special relativity, and the process of measurement introduces a preferred frame. The speed of light can take on different values, both superluminal and subluminal (with respect to the usual value of the speed of light), without the need for Lorentz-invariance violating operators and without tachyons. We briefly discuss the relation to deformations of special relativity and phenomenological consequences.