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PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association

The Objectivity and Invariance of Quantum Predictions

Gordon N. Fleming

Published Jan 1, 1992• 4 citations
Publisher

Abstract

In a recent article Itamar Pitowsky (1991) has analyzed some measurement possibilities presented by an entangled state of three spin ½ particles. From that analysis he has concluded that the valid predictions of results of possible future measurements, made by observers who actually carry out mutually space-like separated measurements, can be incompatible with one another in the sense that their conjunction contradicts the quantum theory. From this result Pitowsky infers the inherently observer specific, or relative, character of quantum predictions as opposed to the results of actual observations or measurements, which, he claims, are covariant; i.e. (I take it) compatibly translatable from one observer to another.

DOI
10.1086/psaprocbienmeetp.1992.1.192747

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In a recent article Itamar Pitowsky (1991) has analyzed some measurement possibilities presented by an entangled state of three spin ½ particles. From that analysis he has concluded that the valid predictions of results of possible future measurements, made by observers who actually carry out mutually space-like separated measurements, can be incompatible with one another in the sense that their conjunction contradicts the quantum theory. From this result Pitowsky infers the inherently observer specific, or relative, character of quantum predictions as opposed to the results of actual observations or measurements, which, he claims, are covariant; i.e. (I take it) compatibly translatable from one observer to another.
In this work we investigate the problem of locality in theories inspired by Everett’s Relative State Theory. Specifically we address the Many Worlds by Deutsch, the Many Minds Theory by David Albert and Barry Loewer and the Relational Theory by Simon Saunders, and we carry out our inquiry in view of recent work by Meir Hemmo and Itamar Pitowsky. Our aim is, on the one hand, to clarify the remarkably important points which have been put forward within Hemmo and Pitowsky work on the issue of the interpretation of probability in Many Minds, on the other hand to argue against a remark on the Relational theory, stating that the analysis carried out on the Many Minds interpretation could be applied, mutatis mutandis, to Saunders’ theory.
In 1964, John Stewart Bell famously demonstrated that the laws of standard quantum mechanics demand a physical world that cannot be described entirely according to local laws. The present article argues that this nonlocality must be gravitationally related, as it comes about only with quantum state reduction, this being claimed to be a gravitational effect. A new formalism for curved space–times, palatial twistor theory, is outlined, which appears now to be able to accommodate gravitation fully, providing a nonlocal description of the physical world. Nonlocality and Quantum State Reduction Although quantum entanglement is a normal consequence of the unitary (Schrödinger) evolution U of a multiparticle quantum system, this evolution is nevertheless local in the sense that it is described as the continuous (local) evolution in the relevant configuration space. What the EPR situations considered by John Stewart Bell [1] demonstrated was that when widely separated quantum measurements , of appropriate kinds, are performed on such entangled states (a current record for distance separation being 143 km, for entangled photon pairs [2]), the results of such measurements (which may be probabilistic or of a yes/no character) cannot be mimicked by any local realistic model. Thus, in trying to propose a mathematical model of what is going on realistically in the physical world, one would need to face up to the actual physical process involved in quantum state reduction R, which is an essential feature of quantum measurement. For many years, my own position on the state-reduction issue has been that R would have to involve a fundamental mathematical extension of current quantum theory, giving a description of something objectively taking place ‘ out there’ in the physical world (OR: objective reduction), rather than R being the effect of some kind of ‘interpretation’ of the standard unitary quantum formalism. Moreover, the extended theory should be able to describe the one physical world that we all experience, rather than some sort of coexisting superposition of vast numbers of alternatives. To be more specific about my own viewpoint, it has long been my position that such necessary deviation from unitarity U in this OR would result from a correct melding of the quantum formalism with that of general relativity .
About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper and, following Frauchiger and Renner, I show that the Everett interpretation leads to modal contradictions in 'Wigner's-Friend'-type scenarios that involve 'encapsulated' measurements, where a super-observer (which could be a quantum automaton), with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system (also possibly a quantum automaton) after that system measures the spin of a qubit. In this sense, the Everett interpretation is inconsistent.