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Reply to ``Comments on `There is No Axiomatic System for the Quantum Theory'''

Koji Nagata, Tadao Nakamura

Published Sep 1, 2013• 0 citations
OpenAlex

Abstract

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 $\langle\sigma_x\rangle$ 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.

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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.
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.
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.
Recently, it is shown that there is a crucial contradiction within von Neumann's theory [K.Nagata and T. Nakamura, Int.J. Theor.Phys.49, 162 (2010)].We derive a proposition concerning a quantum expected 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 von Neumann's theory.We discuss that this crucial contradiction makes the theoretical formulation of Deutsch's algorithm questionable.Especially, we systematically describe our assertion based on more mathematical analysis using raw data.Our discussion, here, improves previously published argumentations very much.