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arXiv:hep-th/9305162 · Physical Review Letters

Lorentz-invariant ‘‘elements of reality’’ and the joint measurability of commuting observables

Lev Vaidman A

Published May 31, 1993• 65 citations
arXivHTMLPDF

Abstract

It is shown that joint measurements of certain commuting operators, performed on pre- and postselected quantum systems, invariably disturb each other. This result is applied to recent assertions that quantum theory has no realistic Lorentz-invariant interpretation (even without requiring locality).
DOI
10.1103/physrevlett.70.3369

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The concept of ``elements of reality" is analyzed within the framework of quantum theory. It is shown that elements of reality fail to fulfill the product rule. This is the core of recent proofs of the impossibility of a Lorentz-invariant interpretation of quantum mechanics. A generalization and extension of the concept of elements of reality is presented. Lorentz-invariance is restored by giving up the product rule. The consequences of giving up the ``and" rule, which must be abandoned together with the product rule, are discussed.
We examine a gedanken experiment described by Hardy, which purports to prove that the ``elements of reality'' corresponding to Lorentz-invariant observables cannot themselves be Lorentz invariant without violating quantum mechanics. We consider a number of criticisms of this proof and show that these criticisms are not convincing. We demonstrate that the contradiction, which arises in the gedanken experiment and forms the basis of Hardy's proof, has nothing to do with realism, but is a consequence of the well-known noncovariance of the reduction postulate. A reexamination of the gedanken experiment, using a more appropriate formalism, helps to clarify its implications. We conclude with a brief appraisal of realist interpretations of quantum mechanics in the relativistic domain.
Based on (i) the physical principle of local causality and (ii) a certain notion of elements of reality, Einstein, Podolsky, and Rosen put forward an argument showing that physical instances may exist in which two noncommuting observables can be joint elements of the physical reality. Here, we introduce a new criterion of joint reality. We demonstrate that according to this criterion, quantum mechanics generally prevents noncommuting observables from having joint elements of reality. In addition, we introduce a measure to quantify the extent to which the criterion is violated and explore the implications of such a measure in connection with incompatibility and correlations. Our findings suggest new manners of interpreting quantum phenomena.
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not select a preferred Lorentz frame as a Newton-Wigner measurement would do. The result indicates that there exists a Lorentz invariant notion of quantum measurement and sheds light on the issue of the localization of a relativistic particle. The framework considered is that of single-particle mechanics as opposed to field theory. The result may be taken as support for the interpretation postulate of the spacetime-states formulation of single-particle quantum theory.
In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be able to represent localized measuring devices and localized events? After briefly reviewing these difficulties we discuss a strategy for eliminating the tension, namely by interpreting quantum theory in a realist way. To implement this strategy we use the ideas of the modal interpretation of quantum mechanics. We then consider the question of whether the resulting scheme can be made Lorentz invariant.