Extending quantum mechanics entails extending special relativity

Abstract

The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QM) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum nonlocality, and implies that special relativity (SR) has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.

17 pages, 1 figure

References in corpus (18)

• An experimental test of non-local realism
• The Free Will Theorem
• The Communication Cost of Simulating Bell Correlations
• Testing spooky action at a distance
• Local deterministic model of singlet state correlations based on relaxing measurement independence
• No extension of quantum theory can have improved predictive power
• Testing quantum correlations versus single-particle properties within Leggett's model and beyond
• Hidden variable models for quantum theory cannot have any local part
• The Strong Free Will Theorem
• The Conway-Kochen argument and relativistic GRW models
• Comment on "The Free Will Theorem"
• Collapse and Relativity
• Complementary contributions of indeterminism and signalling to quantum correlations
• What is the speed of quantum information?
• The General Free Will Theorem
• Comment on "Is a system's wave function in one-to-one correspondence with its elements of reality?" [arXiv:1111.6597]
• Bell's Conjecture and Faster-Than-Light Communication
• The concept of free will as an infinite metatheoretic recursion

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