2014/12/31 by Andrew J. P. Garner, Markus P. Müller, Oscar C. O. Dahlsten
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #General relativity #Kochen–Specker theorem #Problem of time #Quantum #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Relational quantum mechanics #Rendering (computer graphics) #Simultaneity #Subspace topology #Theory of relativity #gr-qc #quant-ph
paper · pdf · doi:10.1098/rspa.2017.0596
published as Proc. R. Soc. A 2017 473 20170596 · Authors' accepted manuscript
openalex publication_date 2017/12/01 · arxiv created 2017/12/08 · arxiv updated 2017/12/11 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05
The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.