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Physical Review Letters

Nonlocality of a Single Photon Revisited

Lucién Hardy

Published Oct 24, 1994• 252 citations
Publisher

Abstract

A proposal to demonstrate the nonlocality of a single photon is described. This is accomplished without using inequalities, and in a way that brings out a very curious feature of quantum mechanics. Unlike the first proposal to investigate the nonlocality of a single photon due to Tan, Walls, and Collett, this proposal does not require supplementary assumptions, and therefore rules out the whole class of local hidden variable interpretations.

DOI
10.1103/physrevlett.73.2279

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A proposal to demonstrate the nonlocality of a single photon is described. This is accomplished without using inequalities, and in a way that brings out a very curious feature of quantum mechanics. Unlike the first proposal to investigate the nonlocality of a single photon due to Tan, Walls, and Collett, this proposal does not require supplementary assumptions, and therefore rules out the whole class of local hidden variable interpretations.
A factual inconsistency of the nonlocality theory is demonstrated via a careful analysis of the conceptual and formal contents of Bell's theorem and the inequalities associated with it. The conceptual inconsistency of the theory follows from the consideration that it is, in principle, impossible to formulate quantum mechanics in terms of local hidden variables. The formal inconsistency of the nonlocality theory follows from the facts that: (i) nonlocality is not a physical property that can be represented by a function or an operator; (ii) it is impossible to derive Bell's inequality in a mathematically consistent way; and (iii) Bell's definition of locality is incorrect. Therefore, Bell's theorem cannot serve as the foundation for the introduction of the nonlocality notion in quantum mechanics.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.