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Journal of Quantum Information Science

Reply to “Comments on ‘There Is No Axiomatic System for the Quantum Theory’”

Koji Nagata

Published Jan 1, 2014• 1 citation
Publisher

Abstract

Barros discusses that [Jose Acacio de Barros, Int. J. Theor. Phys. 50, 1828 (2011)] Nagata derives inconsistencies from quantum mechanics [K. Nagata, Int. J. Theor. Phys. 48, 3532 (2009)]. Barros considers that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables. Here we discuss the fact that there is a contradiction within the quantum theory. We discuss the fact that only one expected value in a spin-1/2 pure state 〈σx〉rules out the reality of the observable. We do not accept extra assumptions about the reality of observables. We use the actually measured results of quantum measurements (raw data). We use a single Pauli observable. We stress that we can use the quantum theory even if we give up the axiomatic system for the quantum theory.

DOI
10.4236/jqis.2014.44018

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Comments

Bernard d’Espagnat

This chapter discusses some comments, and the rules of quantum mechanics. The quantum mechanics is universally valid for all the ensembles to which the more general formalism just alluded to is applicable. Any ensemble of systems the specification of which involves no reference to the results of future measurements that are to be performed on these systems obeys the quantum rules. One of the views most often expressed by the supporters of the "Copenhagen interpretation" is that quantum mechanics is a complete theory. The main motivation for the assumption is that the splitting of ensemble and subensembles cannot be made in any straightforward manner. However, this assumption implies the existence of particular, hitherto unknown forces, and it is therefore quite generally considered as unattractive. Thus the probabilities, or statistical distributions, that conventional quantum mechanics introduces into physics are inherently different from those found in classical mechanics, for example, in the kinetic theory of gases.

CRC Press eBooks•Mar 5, 2018•0 citations
Barros discusses that [Jose Acacio de Barros, Int. J. Theor. Phys. 50, 1828 (2011)] Nagata derives inconsistencies from quantum mechanics [K. Nagata, Int. J. Theor. Phys. 48, 3532 (2009)]. Barros considers that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables. Here we discuss the fact that there is a contradiction within the quantum theory. We discuss the fact that only one expected value in a spin-1/2 pure state 〈σx〉rules out the reality of the observable. We do not accept extra assumptions about the reality of observables. We use the actually measured results of quantum measurements (raw data). We use a single Pauli observable. We stress that we can use the quantum theory even if we give up the axiomatic system for the quantum theory.
Jose Acacio de Barros discusses as follows [{Jose Acacio de Barros, Int. J. Theor. Phys. {\bf 50}, 1828 (2011)}]. Nagata claims to derive inconsistencies from quantum mechanics [{K. Nagata, Int. J. Theor. Phys. {\bf 48}, 3532 (2009)}]. Jose Acacio de Barros considers that the inconsistencies do not come from quantum mechanics, but from extra assumptions about the reality of observables. Here we discuss the fact that there is a contradiction within the quantum theory. We discuss the fact that only one expected value in a spin-1/2 pure state ⟨σx⟩\langle\sigma_x\rangle⟨σx​⟩ rules out the reality of the observable. We do not accept extra assumptions about the reality of observables. We use the actually measured results of quantum measurements (raw data). We use a single Pauli observable. We stress that we can use the quantum theory even if we give up the axiomatic system for the quantum theory.
We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions within the formalism of von Neumann's projective measurement cannot coexist with the proposition concerning the existence of the directions. Therefore, we have to give up either the existence of the directions or the formalism of von Neumann's projective measurement. Hence there is a crucial contradiction within the Hilbert space formalism of the quantum theory. This implies that there is no axiomatic system for the quantum theory. This also reveals that we need new physical theories in order to explain the handing of raw experimental data. We discuss that this crucial contradiction makes the quantum-theoretical formulation of Deutsch's algorithm questionable.
A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ``smuggled'' in. That argument is examined here and shown, I believe, to be defective.
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.
This chapter discusses some comments, and the rules of quantum mechanics. The quantum mechanics is universally valid for all the ensembles to which the more general formalism just alluded to is applicable. Any ensemble of systems the specification of which involves no reference to the results of future measurements that are to be performed on these systems obeys the quantum rules. One of the views most often expressed by the supporters of the "Copenhagen interpretation" is that quantum mechanics is a complete theory. The main motivation for the assumption is that the splitting of ensemble and subensembles cannot be made in any straightforward manner. However, this assumption implies the existence of particular, hitherto unknown forces, and it is therefore quite generally considered as unattractive. Thus the probabilities, or statistical distributions, that conventional quantum mechanics introduces into physics are inherently different from those found in classical mechanics, for example, in the kinetic theory of gases.