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Quantum Superpositions of the Speed of Light

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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.

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Notes

  1. The ‘Box-problem’ discussed in reference [20, 21] is circumvented because rather than there being two photons with different speeds, there is one photon in a superposition of different speeds. The measurement is either made in the laboratory frame, in which case the bomb blows up and the observer in the satellite agrees, or it is made in the satellite frame, in which case the bomb does not blow up and the observer in the lab agrees. The situation is entirely symmetric as long as both frames represent identical measuring processes with some relative velocity.

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Acknowledgements

I thank Ben Koch, Jakub Mielczarek, Stefan Scherer and Lee Smolin for helpful feedback and discussions, and Sean Carroll for drawing my attention to Reference [31].

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  1. NORDITA, Roslagstullsbacken 23, 106 91, Stockholm, Sweden

    Sabine Hossenfelder

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  1. Sabine Hossenfelder
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Correspondence to Sabine Hossenfelder.

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Hossenfelder, S. Quantum Superpositions of the Speed of Light. Found Phys 42, 1452–1468 (2012). https://doi.org/10.1007/s10701-012-9678-0

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