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Pilot-Wave Theory Without Nonlocality

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I saw the impossible done. [1, p. 160].

a many-threads theory is ultimately just a hidden-variable theory where one simultaneously considers all physically possible worlds. [2, p. 184], original emphasis.

Abstract

It’s generally taken to be established that no local hidden-variable theory is possible. That conclusion applies if our world is a thread, where a thread is a world where particles follow trajectories, as in Pilot-Wave theory. But if our world is taken to be a set of threads locality can be recovered. Our world can be described by a many-threads theory, as defined by Jeffrey Barrett in the opening quote. Particles don’t follow trajectories because a particle in our world is a set of elemental particles following different trajectories, each in a thread. The “elements” of a superposition are construed as subsets in such a way that a particle in our world only has definite position if all its set-theoretic elements are at corresponding positions in each thread. Wavefunction becomes a 3D density distribution of particles’ subset measures, the stuff of an electron’s “probability cloud”. Current Pilot-Wave theory provides a non-relativistic dynamics for the elemental particles (approximated by Many Interacting Worlds theory). EPR-Bell nonlocality doesn’t apply because the relevant measurement outcomes in the absolute elsewhere of an observer are always in superposition.

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Notes

  1. As described by AntonyValentini [3, pp. 498–499].

  2. Following Simon Saunders [4, p. 196], Alastair Wilson uses similar terms in a different context. Saunders’ individual worlds don’t contain hidden-variables [5, 6].

  3. The term is from [7, p. 266]. See [8, p. §2.2] for further discussion.

  4. Introduced in [10, p. §2] as the Unitary Interpretation of Mind and further developed in [8].

  5. For some discussion of unusual cases see [19, p. §5].

  6. For a succinct account see [18, pp. 29–34].

  7. Quoted in [10, p. 10].

  8. The term ‘Quine atom’ is sometimes used simply to denote a set which is its own sole element. I use the term ‘Quineian individual’ for objects characterized as in the quote.

  9. See [26, p. §10] for some discussion of this type of approach to quantum theory.

  10. Hall, Deckert and Wiseman write:

    The MIW [Many Interacting Worlds] approach can only become equivalent to standard quantum dynamics in the continuum limit, where the number of worlds becomes uncountably infinite. [26, p. §1].

    Sebens argues that finitude is called for because the intelligibility of a subject’s assignment of probabilities to alternative futures is based on ‘self-locating uncertainty’ which requires a ‘basic indifference principle’ [25, p. 282], original emphasis.

  11. In [8, p. 6390] it’s suggested that a version of the Principle Principle might be justified via the Deutsch-Wallace theorem.

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Acknowledgements

I particularly want to thank Simon Saunders for a careful reading of an earlier draft which revealed a crucial error. Also a reviewer who encouraged me to say more about the details of the metaphysics and indicated a number of issues in need of resolution.

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    Paul Tappenden

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Tappenden, P. Pilot-Wave Theory Without Nonlocality. Found Phys 52, 107 (2022). https://doi.org/10.1007/s10701-022-00627-0

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