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Journal of Physics Conference Series

A new concept of QM-models and truth in quantum mechanics (QM), the new hybrid-epistemic model of QM and its observer independence, the proof of the invalidity of no-go theorems

Jiří Souček

Published Dec 1, 2019• 0 citations
Publisher

Abstract

Abstract We define a concept of a QM-model. The true theorem in QM is a statement which is true in all QM-models. In some QM-models the Bell’s theorem can be proved (e.g. in the standard model of QM) while in other QM-models the Bell’s theorem cannot be proved (e.g. in the hybrid-epistemic model of QM). The same situation is true when other no-go theorems are considered. Thus no-go theorems are not true in QM and the proof of the non-locality of QM is invalid. Then the axiomatic definition of the hybrid-epistemic (HE) model of QM is presented in all details. At the end the recent proof of the inconsistency of the standard QM-model is discussed. Our main program is to start the axiomatic study of QM (in the sense of the Hilbert’s sixth problem), to prove the invalidity of no-go theorems and to identify the right (acceptable) QM-model.

DOI
10.1088/1742-6596/1416/1/012036

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Abstract We define a concept of a QM-model. The true theorem in QM is a statement which is true in all QM-models. In some QM-models the Bell’s theorem can be proved (e.g. in the standard model of QM) while in other QM-models the Bell’s theorem cannot be proved (e.g. in the hybrid-epistemic model of QM). The same situation is true when other no-go theorems are considered. Thus no-go theorems are not true in QM and the proof of the non-locality of QM is invalid. Then the axiomatic definition of the hybrid-epistemic (HE) model of QM is presented in all details. At the end the recent proof of the inconsistency of the standard QM-model is discussed. Our main program is to start the axiomatic study of QM (in the sense of the Hilbert’s sixth problem), to prove the invalidity of no-go theorems and to identify the right (acceptable) QM-model.
In this paper we define and study the new model for quantum mechanics (QM) – the hybrid epistemic model. The new feature of this model consists in the fact that it does not contain the formal definition of the measurement process but the measurement process is one of possible processes inside of QM. The hybrid-epistemic model of QM is based on two concepts: the quantum state of an ensemble and the properties of individual systems. We show the local nature of EPR correlations in the hybrid-epistemic model of QM in all details. We define precisely the epistemic and the ontic models of QM for the goal to prove that these three models give the same empirical predictions, i.e. that they are empirically equivalent. We show that the no-go theorems (Bell’s theorem, the Leggett-Garg’s theorem and others theorems) cannot be proved in the hybrid-epistemic model of QM. This is one of the main results of this paper. We shall consider the possible inconsistences of the ontic model of QM. We introduce the property-epistemic model of QM which is the special simple case of the hybrid-epistemic model.
In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr’s view (the ontic model) and the Einstein’s view (the epistemic model).
In this paper we describe a new (complete) axiomatization of quantum mechanics (QM) in which we add axioms describing the concept of an observation. We show that new axioms are clear and evident and based on common sense. Our approach is based on the idea of the observation of properties of an individual measuring system. We distinguish two concepts of a state: the properties of an individual measuring system and the state of an ensemble of systems. Then we prove that the ontic model of QM is inconsistent. This is our main result. This implies the necessity to consider “non-realistic” models for QM in which it is not true that each wave-function describes a possible state of an individual system. Our axiomatization is based on the postulate of the existence of definite outputs of an experiment. Thus the evident reality of the existence of definite outputs implies that our axiomatization is true and verifiable.
The two previous papers developed quantum mechanical formalism from classical mechanics and two additional postulates. In the first paper it was also shown that the uncertainty relations possess no ontological validity and only reflect the formalism's limitations. In this paper, a Realist Interpretation of quantum mechanics based on these results is elaborated and compared to the Copenhagen Interpretation. We demonstrate that von Neumann's proof of the impossibility of a hidden variable theory is not correct, independently of Bell's argumentation. A local hidden variable theory is found for non-relativistic quantum mechanics, which is nothing else than newtonian mechanics itself. We prove that Bell's theorem does not imply in a non-locality of quantum mechanics, and also demonstrate that Bohm's theory cannot be considered a true hidden variable theory.
The consequences of the theorems about ontological models are studied. "Maximally ψψψ-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized in Hilbert spaces of arbitrary dimension, but which cannot occur together for d>2. I argue that current theorems do not invalidate an epistemic interpretation of quantum states. A new condition, called "functionally ψψψ-epistemic", is introduced, which, were it to be excluded, would signal the exclusion of epistemic interpretations.