Quantum Superpositions of the Speed of Light

• Published in: Foundations of physics Vol. 42; no. 11; pp. 1452 - 1468
• Main Author: Hossenfelder, Sabine
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.11.2012
• Subjects: Classical and Quantum Gravitation; Classical Mechanics; History and Philosophical Foundations of Physics; Lorentz-invariance; Philosophy of Science; Physics; Physics and Astronomy; Quantum gravity; Quantum Physics; Relativity Theory; Statistical Physics and Dynamical Systems; Lorentz-invariance; Quantum gravity
• ISSN: 0015-9018; 1572-9516; 1572-9516
• DOI: 10.1007/s10701-012-9678-0

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.