arXiv:quant-ph/0306069

Classical and quantum spaces as rough images of the fundamental prespace

Andrei Yu. Khrennikov

Published Jun 10, 2003• 2 citations

Abstract

In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf prespace.} Quantum mechanics cannot be reduced to classical one. Both classical and quantum representations induce reductions of prespace information.

DOI: 10.48550/arxiv.quant-ph/0306069

Related papers

Växjö Interpretation of Quantum Mechanics

Andrei Yu. Khrennikov

We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the possibility to use Statistical Contextual Realist Interpretation of quantum formalism. In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...), recently (quant-ph/0306003 and 0306069) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces are rough images of the fundamental {\bf prespace.} Quantum mechanics cannot be reduced to classical one. Both classical and quantum representations induce reductions of prespace information.

arXiv:quant-ph/0202107Feb 19, 200210 citations

Vaxjo Interpretation of Quantum Mechanics

Andrei Yu. Khrennikov

We present critical arguments against individual interpretation of Bohr’s complementarity and Heisenberg’s uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the possibility to use Statistical Contextual Realist Interpretation of quantum formalism. In spite of all no-go theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...), recently (quant-ph/0306003 and 0306069) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces are rough images of the fundamental prespace. Quantum mechanics cannot be reduced to classical one. Both classical and quantum representations induce reductions of prespace information. ”Often we enter the unknown edifice of a new scientific discipline through a lesser gate that leads us into a side passage. It may take us a long while to find our way to the main portal and to view the whole structure in its proper perspective”. E. Schrödinger 1

Feb 19, 200214 citations

Contextual approach to quantum mechanics and the theory of the fundamental prespace

Andrei Yu. Khrennikov

We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables—in the standard quantum model these are the position and momentum observables. This representation has all distinguishing features of the quantum model. Our representation is not standard model with hidden variables. In particular, this is not a reduction of the quantum model to the classical one.

arXiv:quant-ph/0306003Journal of Mathematical PhysicsFeb 12, 200429 citations

No "No-Go"

Andrei Yu. Khrennikov

In spite of the very common opinion we show that QM is not complete and that it is possible to create prequantum models providing finer description of physical reality than QM. There exists (at least in theoretical models) dispersion free states and the Heisenberg uncertainty principle can be violated. Thus in spite of all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found a realist basis of quantum mechanics. I think that our model would totally satisfy A. Einstein who was sure that QM is not complete and a finer description is possible.

arXiv:quant-ph/0308166Aug 29, 20030 citations

How to (Un-) Quantum Mechanics

C. Baumgarten

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the Hamiltonian formulation of classical analytical mechanics is based on abstract generalized coordinates and momenta: It is a mathematical rather than a philosophical framework. If the metaphysical assumptions ascribed to classical mechanics are dropped, then there exists a presentation in which little of the purported difference between quantum and classical mechanics remains. This presentation allows to derive the mathematics of relativistic quantum mechanics on the basis of a purely classical Hamiltonian phase space picture. It is shown that a spatio-temporal description is not a condition for but a consequence of objectivity. It requires no postulates. This is achieved by evading spatial notions and assuming nothing but time translation invariance.

arXiv:1810.06981Oct 12, 20182 citations

Kochen-Specker Theorem and Games

Laura Mančinska

One of the statements one would hear pretty early in any quantum mechanics course is that for quantum particles there are properties which do not have definite values. For example, if we measure |+〉 in standard basis, the best we can do to describe the outcome is to say, that with probability 1/2 we will get 0 and with probability 1/2 we will get 1. Yet one could wonder, is this really the way things are or is it just because our description of this quantum particle is incomplete, but in fact there are some hidden variables inside every quantum system that contain enough information to tell the outcome of measurement (see Fig. 1). However, many people disdain the idea of hidden variables, so there has been rather long history of theorems that forbid theories involving hidden variables. Usually if one wants to prove some no hidden variables theorem he has to assume something about the hidden variables theories he is going to forbid. One of such assumptions is non-contextuality, which means that the outcome we get after measuring with an observable is the same regardless of what other observables we choose to measure at the same time. The first theorem forbidding hidden variables theories is due to von Neumann in 1932. Then for a third of a century everyone cited von Neumann’s work carelessly, till Bell in 1966 indicated that there was an unreasonable assumption in von Neumann’s proof and urged for further examination of the problem (see [6] and [1] for more historical details). Bell also constructed a hidden variables model for one qubit that could assign the outcome of any observable in a way consistent with quantum mechanics. He also proved two theorems that forbid non-contextual hidden variables theories using counterexamples with larger quantum systems. Yet surprisingly he himself thought that hidden variables do exists and considered these theorems only as characterizations of the hidden variables theory we should look for. In this essay we will discuss several versions of one of the two Bell’s theorems. The theorem we will consider was also independently proven by Kochen and Specker in 1967 (see [5]), hence it is called Bell-Kochen-Specker theorem. For shortness and in order not to mix this theorem with another Bell’s theorem from now on we will refer to it as Kochen-Specker theorem. We will be interested in proving several versions of this theorem and the following lemma will turn out to be of great use:

Jan 1, 20070 citations