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Physical Review Letters

Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories

Lucién Hardy

Published May 18, 1992• 739 citations
Publisher

Abstract

First, we demonstrate Bell's theorem, without using inequalities, for an experiment with two particles. Then we show that, if we assume realism and we assume that the ``elements of reality'' corresponding to Lorentz-invariant observables are themselves Lorentz invariant, we can derive a contradiction with quantum mechanics.

DOI
10.1103/physrevlett.68.2981

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Cambridge University Press eBooks•Aug 31, 2016•1 citation
First, we demonstrate Bell's theorem, without using inequalities, for an experiment with two particles. Then we show that, if we assume realism and we assume that the ``elements of reality'' corresponding to Lorentz-invariant observables are themselves Lorentz invariant, we can derive a contradiction with quantum mechanics.
The singlet state of two spin-32\frac{3}{2}23​ particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.
This thesis addresses some of the consequences of giving quantum mechanics a realist interpretation. We consider three main topics: wave-particle duality, locality, and Lorentz invariance. First we show that classical particles alone or classical waves alone cannot explain all single particle quantum phenomena. Then we consider the possibility that a quantum particle is composed of a particle and a wave, both being taken to exist objectively. We are able to demonstrate the reality of empty waves (that is, waves without a particle) if we make three realist motivated assumptions. The main part of this thesis concerns locality. In 1964 Bell demonstrated that a local realist interpretation of quantum mechanics is not possible by deriving a set of inequalities that apply to two particle systems. More recently Greenberger, Home, and Zeilinger have demonstrated this for systems with more than two particles without the need for inequalities. We present a new way to derive Bell inequalities for two particles and show how this can be extended to systems with more than two particles. A number of proposals for experiments to test local realism are put forward. In particular, we show how it is possible to demonstrate the nonlocality of a single photon. A new demonstration of Bell's theorem is presented for two particles but without inequalities. A realizable quantum optical version is proposed and inequalities are proposed which would be required in a non-ideal experiment. Finally, the question of Lorentz invariance is considered. We define a condition for the existence of elements of reality and a condition for the Lorentz invariance of these elements of reality. Then we show that, by considering a particular gedanken experiment, we obtain a contradiction demonstrating that Lorentz-invariant realistic interpretations of quantum theory are not possible.
Having elsewhere refuted Bell’s theorem irrefutably with elementary mathematics, we here advance Einstein’s ideas similarly with a classical Lorentz-invariant theory, observationally-indistinguishable from quantum mechanics. Given that our elementary theory is straight-forward and non-mysterious, we provide an Einsteinian—a specifically local and truly realistic—advance toward understanding the classical nature of physical reality at the quantum level. We thus resolve Bell’s dilemma in Einstein’s favor: as Bell half-expected, he and his supporters were being rather silly.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.