Weekly Papers on Quantum Foundations (12)

Authors: Lionel Brits

Accounting for Born’s rule from first principles remains an open problem among the foundational issues in quantum mechanics. Proponents of the many-worlds interpretation have argued that histories that violate Born’s rule have vanishing norms, and so are unphysical. This argument has only been made explicit for contrived situations involving measurements on infinitely many identically prepared systems. We extend this result to arbitrary preparations and show that in a system with infinitely many degrees of freedom the universal wavefunction contains no such histories.

Crowther, Karen and Linnemann, Niels and Wuthrich, Christian (2019) What we cannot learn from analogue experiments. [Preprint]
Baker, David John (2019) On Spacetime Functionalism. [Preprint]
Jaeger, Gregg (2017) “Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia. Entropy, 19. pp. 1-11.
Jaeger, Gregg (2019) Are Virtual Particles Less Real? Entropy, 21. pp. 1-17. ISSN 1099-4300
Jaeger, Gregg (2018) Developments in Quantum Probability and the Copenhagen Approach. Entropy, 20. pp. 1-19.
Redhead, Michael (2019) A Simplified Version of Gödel’s Theorem. [Preprint]

Authors: T. N. Palmer

Bell’s Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality. Invariant set theory is a finite theory of quantum physics which violates the Bell inequality exactly as does quantum theory: in it neither Free Choice nor Local Causality hold, consistent with Bell’s Theorem. However, within the proposed theory, the mathematical expressions of both Free Choice and Local Causality involve states which, for number-theoretic reasons, cannot be ontic (cannot lie on the theory’s fractal-like invariant set IU in state space). Weaker versions of Free Choice and Local Causality are proposed involving only the theory’s ontic states. Conventional hidden-variable theories satisfying only these weaker definitions still obey the Bell inequality. However, invariant set theory, which violates the Bell inequality, satisfies these weaker definitions. It is argued that the weaker definitions are consistent with the physical meaning behind free choice and local causality as defined in space-time, and hence that Free Choice and Local Causality are physically too strong. It is concluded that the experimental violation of the Bell inequality may have less to do with free choice or local causality \emph{per se}, and more to do with the presence of a holistic but causal state-space geometry onto which quantum ontic states are constrained.

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