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arXiv:quant-ph/0111047

Time, Quantum Mechanics, and Probability

Simon W. Saunders

Published Nov 7, 2001• 24 citations
arXivHTMLPDF

Abstract

A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's approach, based on the difficulties of interpreting probability in its terms, are considered in detail, but found to be wanting.

DOI
10.48550/arxiv.quant-ph/0111047

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A "geometric" intepretation of probability is proposed, modelled on the treatment of tense in 4-dimensional spacetime. It is applied to Everett's approach to quantum mechanics, as formulated in terms of consistent histories. Standard objections to Everett's approach, based on the difficulties of interpreting probability in its terms, are considered in detail, but found to be wanting.
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I discuss the meaning of probability in the Everett‐Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future‐tense proposition is identified with its truth value in a many‐valued and context‐dependent logic. In short, probability is degree of truth. These ideas relate to traditional naive ideas of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open.
I discuss the problems of probability and the future in the Everett-Wheeler understanding of quantum theory. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. I construct a lattice of tensed propositions, with truth values in the interval [0,1][0,1][0,1], and derive logical properties of the truth values given by the usual quantum-mechanical formula for the probability of histories.
There are currently several versions of Everett's relative state interpretation of quantum mechanics, responding to a number of perceived problems for the original proposal. One of those problems is whether Everett's idea is in accord with the standard 'probabilistic' interpretation implicit in the Born rule. I argue in defence of what appears to be Everett's original view on this. The contribution I aim to make is a more complete discussion of the central issues of the identity of objects and observers over time and how the concept of expectation can be applied when all 'possible' outcomes of a measurement process are regarded as actually occurring.