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The Hidden Error in the Standard Quantum Mechanics

Jiří Souček

Published Jul 1, 2015• 0 citations
OpenAlex

Abstract

In the standard Quantum Mechanics (QM) there exists certain assumption (which I call the von Neuman axiom, see [1]) stating that an ensemble in the pure state is homogeneous. This means that all members of this ensemble are in the same individual state. Equivalently we can say that each pure state is an individual state (the term individual state means the state of an individual system). The von Neumann axiom is really hidden in QM: everyone who says “let us consider the system in the state ψ ” unconsciously uses this axiom. In this note I am going to show that the von Neumann axiom is false. This also means that the standard interpretation of the wave function as the state of the individual system is in general false. In the ontic/epistemic terminology this means that the ontic interpretation of the wave function cannot be true. There are four arguments for this statement (all these arguments are known): The classical argument The Bell inequality (BI) argument The Collapse argument The duplicity argument

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In the standard Quantum Mechanics (QM) there exists certain assumption (which I call the von Neuman axiom, see [1]) stating that an ensemble in the pure state is homogeneous. This means that all members of this ensemble are in the same individual state. Equivalently we can say that each pure state is an individual state (the term individual state means the state of an individual system). The von Neumann axiom is really hidden in QM: everyone who says “let us consider the system in the state ψ ” unconsciously uses this axiom. In this note I am going to show that the von Neumann axiom is false. This also means that the standard interpretation of the wave function as the state of the individual system is in general false. In the ontic/epistemic terminology this means that the ontic interpretation of the wave function cannot be true. There are four arguments for this statement (all these arguments are known): The classical argument The Bell inequality (BI) argument The Collapse argument The duplicity argument
In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur–Vaidman bomb detector and the extended Wigner’s friends scenario.
In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector and the extended Wigner's friends scenario.
In this article we consider the variant of quantum mechanics (QM) which is based on the non-realism. There exists the theory of the modified QM introduced in [1] and [2] which is based on the non-realism, but it contains also other changes with respect to the standard QM (stQM). We introduce here the other non-realistic modification of QM (n-rQM) which contains the minimal changes with respect to stQM. The change consists in the replacement of the von Neumann`s axiom (ensembles which are in the pure state are homogeneous) by the anti-von Neumann`s axiom (any two different individual states must be orthogonal). This introduces the non-realism into n-rQM. We shall show that experimental consequences of n-rQM are the same as in stQM, but these two theories are substantially different. In n-rQM it is not possible to derive (using locality) the Bell inequalities. Thus n-rQM does not imply the non-locality (in contrast with stQM). Because of this the locality in n-rQM can be restored. The main purpose of this article was to show what could be the minimal modification of QM based on the non-realism, i.e. that the realism of stQM is completely contained in the von Neumann's axiom.
Some interpretations of quantum mechanics try to describe the probabilistic nature of quantum measurements in a way that allows a system in a pure state to always have precise (if not simultaneously knowable) values for all its observable variables. In what might be called a simple ensemble interpretation, the quantum mechanical state vector is assumed to define a statistical ensemble of identically prepared systems, each of which has precise values for all its observable variables, and the act of measurement is equivalenced to a straightforward sampling of that ensemble. It is shown here, in a manner that should be suitable for a first course in quantum mechanics, that a simple ensemble interpretation is not possible for some quantum systems, and hence is untenable as a general premise. The analysis is essentially a repackaging of the Bell argument against hidden variables, although hidden variables are never invoked here.
Many works intended to introduce interpretive issues in quantum mechanics present John von Neumann as having a view in which measurement produces a physical collapse in the system being measured. In this paper I argue that such a reading of von Neumann is inconsistent with what von Neumann actually says. I show that much of what he says makes no sense on the physical collapse reading, but falls into place if we assume he does not have such a view. I show that the physical collapse view is based on an understanding of ‘state’ which von Neumann does not share. 1. Introduction2. The standard reading of von Neumann3. The standard reading of von Neumann and Chapter VI4. The Chapter VI argument5. The Chapter V argument6. The Chapters III and IV argument7. Conclusion
Introduction To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical ‘dispersion free’ states would be specified not only by the quantum mechanical state vector but also by additional ‘hidden variables’ – ‘hidden’ because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate. Whether this question is indeed interesting has been the subject of debate. The present paper does not contribute to that debate. It is addressed to those who do find the question interesting, and more particularly to those among them who believe that ‘the question concerning the existence of such hidden variables received an early and rather decisive answer in the form of von Neumann's proof on the mathematical impossibility of such variables in quantum theory.’ An attempt will be made to clarify what von Neumann and his successors actually demonstrated. This will cover, as well as von Neumann's treatment, the recent version of the argument by Jauch and Piron, and the stronger result consequent on the work of Gleason. It will be urged that these analyses leave the real question untouched.