Discretisation of the Bloch Sphere, Fractal Invariant Sets and Bell’s Theorem

Abstract: Max Planck famously introduced the notion of discretised packets of energy, quanta, thus kickstarting the development of our most successful theory of physics, replacing classical theories in which energy varies continuously. Despite its success, however, the concepts of reality and local causality are deeply problematic in quantum mechanics. Such problems may lie at the heart of why it has been so difficult to synthesise quantum and gravitational physics. Motivated by these issues, we apply Planck’s discretisation insight again, but this time to the continuum of quantum mechanics’ state space - complex Hilbert Space. A particular discretisation is discussed - one which draws on number theoretic properties of trigonometric functions. This leads to a model of quantum physics which is necessarily superdeterministic in character, that is to say violates the Statistical Independence assumption in Bell’s Theorem. Because of this, the model does not need to invoke concepts of indefinite reality or nonlocality to explain the violation of Bell’s inequality

mathematical physicsgeneral physicsquantum physics

Audience: advanced learners

( paper )

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QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

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