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arXiv:1110.4549

Comment on `Underlining some limitations of the statistical formalism in quantum mechanics' by Fratini and Hayrapetyan

András Bodor, Diósi, Lajos

Published Oct 20, 2011• 1 citation
arXivHTMLPDF

Abstract

We point out that Fratini and Hayrapetyan ignored the randomness of mixing, a basic request to prepare a statistical ensemble rather than an ensemble in general. Their analysis is irrelevant for standard statistical ensembles, their conclusions about the limitations of standard theory become unjustified.
DOI
10.48550/arxiv.1110.4549

Related papers

Underlining some limitations of the statistical formalism in quantum mechanics: Reply to the Comment of Bodor and Diósi

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In a paper of us, it is showed that Density Matrices do not provide a complete description of ensembles of states in quantum mechanics, since they lack measurable information concerning the preparation of the ensembles. Bodor and Diósi have later posted a comment on that article, which agrees on some points of it but disagrees on some others. This reply is intended to clarify the discussion.

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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.

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Comments on the paper "Foundation of statistical mechanics from symmetries of entanglement" by S. Deffner and W. Zurek

Robert Alicki

The authors of the recent paper [1] boldly claim to discover a new fully quantum approach to foundation of statistical mechanics: "Our conceptually novel approach is free of mathematically ambiguous notions such as probability, ensemble, randomness, etc." The aim of this note is to show that this approach is neither specific for quantum systems nor really conceptually different from the standard textbook arguments supporting microcanonical or canonical ensembles in statistical mechanics.

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Use and misuse of variances for quantum systems in pure or mixed states

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Underlining some limitations of the statistical formalism in quantum mechanics

F. Fratini, A G Hayrapetyan

We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic in which they differ is shown to be the variance of the spin along a given direction. We conclude that the statistical description of an ensemble of states as given by its density matrix, although sufficient in many cases, should be considered incomplete, as it does not fully describe the measurable characteristics of the ensemble. A discussion a posteriori on the problem is provided.

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Reply to “Comment on ‘Spin and statistics in nonrelativistic quantum mechanics: The spin-zero case’ ”

Murray Peshkin

The preceding Comment states that I have assumed the conclusion in my proof from nonrelativistic quantum mechanics that spin-zero particles must be bosons, and that the theory presented is different from standard quantum mechanics. I show here that neither of those statements is true.

Physical Review A•Oct 14, 2003•14 citations
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.
The authors of the recent paper [1] boldly claim to discover a new fully quantum approach to foundation of statistical mechanics: "Our conceptually novel approach is free of mathematically ambiguous notions such as probability, ensemble, randomness, etc." The aim of this note is to show that this approach is neither specific for quantum systems nor really conceptually different from the standard textbook arguments supporting microcanonical or canonical ensembles in statistical mechanics.
As a consequence of the place ascribed to measurements in the postulates of quantum mechanics, if two differently prepared systems are described with the same density operator \r{ho}, they are said to be in the same quantum state. For more than fifty years, there has been a lack of consensus about this postulate. In a 2011 paper, considering variances of spin components, Fratini and Hayrapetyan tried to show that this postulate is unjustified. The aim of the present paper is to discuss major points in this 2011 article, and in their reply to a 2012 paper by Bodor and Diosi claiming that their analysis was irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in the reply, we first try to guess their aim, then establish results useful in this context, and finally discuss the use or misuse of several concepts implied in this debate.
We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic in which they differ is shown to be the variance of the spin along a given direction. We conclude that the statistical description of an ensemble of states as given by its density matrix, although sufficient in many cases, should be considered incomplete, as it does not fully describe the measurable characteristics of the ensemble. A discussion a posteriori on the problem is provided.