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AIP conference proceedings

The Everett-Wheeler interpretation and the open future

Anthony Sudbery, Andrei Yu. Khrennikov, Gregg S. Jaeger, M. Schlosshauer, Gregor Weihs

Published Jan 1, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.1063/1.3578742

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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 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.
According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice of future-tense propositions, with truth values in the interval [0, 1], and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history.
I propose, in the context of Everett interpretations of quantum mechanics, a way of understanding how there can be genuine uncertainty about the future notwithstanding that the universe is governed by known, deterministic dynamical laws, and notwithstanding that there is no ignorance about initial conditions, nor anything in the universe whose evolution is not itself governed by the known dynamical laws. The proposal allows us to draw some lessons about the relationship between chance and determinism, and to dispel one source of the tendency among Everettians to introduce consciousness as a primitive element into physical description.