Abstract
Proposed derivations of the Born rule for Everettian theory are controversial. I argue that they are unnecessary but may provide justification for a simplified version of the Principal Principle. It’s also unnecessary to replace Everett’s idea that a subject splits in measurement contexts with the idea that subjects have linear histories which partition (Deutsch in Int J Theor Phys 24:1–41, 1985; The Beginning of Infinity. Allen Lane, London, 2011; Saunders and Wallace in Br J Philos Sci 59:293–305, 2008; Saunders, in: Saunders, Barrett, Kent, Wallace (eds) Many worlds? Everett, quantum theory, and reality, Oxford University Press, Oxford, pp 181–205, 2010; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2012, Chapter 7; Wilson in Br J Philos Sci 64:709–737, 2013; The nature of contingency: quantum physics as modal realism, Oxford University Press, Oxford, forthcoming). Linear histories were introduced to provide a concept of pre-measurement uncertainty and I explain why pre-measurement uncertainty for splitting subjects is after all coherent, though not necessary because Everett’s original fission interpretation of branching can arguably be rendered coherent without it, via reference to Vaidman (Int Stud Philos Sci 12:245–66, 1998), Tappenden (Br J Philos Sci 62:99–123, 2011), Sebens and Carroll (Br J Philos Sci 69:25–74, 2018) and McQueen and Vaidman (Stud Hist Philos Mod Phys 66:14–23, 2019). A deterministic and probabilistic quantum mechanics can be made intelligible by replacing the standard collapse postulate with a no-collapse postulate which identifies objective probability with relative branch weight, supplemented by the simplified Principal Principle and some revisionary metaphysics.
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Notes
The pointer basis is arguably determined by the process of decoherence. See (Wallace 2012, Ch. 3) for details. The measurement idealization ignores many bizarre low amplitude branches and so takes the absolute square of amplitude for the up and down branches to sum to 1.
Roland Fraïssé argued that a splitting event gives rise to a ramifier, the lightspeed propagation of the branching of spacetime (Fraïssé 1974, 1982, 1986). Given that any splitting event creates a gravitational disturbance, this suggests an interface between general relativity and quantum mechanics. Note that the different views in McQueen and Vaidman (2019) and Sebens and Carroll (2018) turn on a difference in their interpretations of the process of branching.
An idea developed in a different way in Barrett (1999, pp. 179–84).
Further thoughts on overlap and divergence can be found in Tappenden (2019).
My thanks to Oliver Pooley for raising this question.
As reported to me by Simon Saunders, who posed the question.
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Acknowledgements
I wish to thank Jeff Barrett, David Deutsch, Douglas Campbell, Andrew F. Knight, John Ponsonby, Douglas Porpora, Simon Saunders, Mauricio Suàrez and David Wallace for useful comments. And in particular two anonymous referees for detailed and searching critiques which led to considerable revision of the original submission.
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May the spirit of Newton’s method give us the power to restore unison between physical reality and the profoundest characteristic of Newton’s teaching – strict causality.
(Einstein 1927, p. 467).
The theory based on pure wave mechanics is a conceptually simple, causal theory.
(Everett 1957, p. 462).
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Tappenden, P. Everettian theory as pure wave mechanics plus a no-collapse probability postulate. Synthese 198, 6375–6402 (2021). https://doi.org/10.1007/s11229-019-02467-4
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DOI: https://doi.org/10.1007/s11229-019-02467-4