Abstract
A Hilbert-space model for quantum logic follows from space-time structure in theories with consistent state collapse descriptions. Lorentz covariance implies a condition on space-like separated propositions that if imposed on generally commuting ones would lead to the covering law, and such a generalization can be argued if state preparation can be conditioned to space-like separated events using EPR-type correlations. The covering law is thus related to space-time structure, though a final understanding of it, through a self-consistency requirement, will probably require quantum space-time.
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Svetlichny, G. The Space-Time Origin of Quantum Mechanics: Covering Law. Foundations of Physics 30, 1819–1847 (2000). https://doi.org/10.1023/A:1003797204134
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DOI: https://doi.org/10.1023/A:1003797204134