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From here:

Peres writes on p.11:

On p.63, Peres writes:

Thus Peres says that the statistics is done with conceptual ensembles, which are entirely different things than assemblies. In particular, a canonical ensemble (though not discussed in the book) is an infinite set of

The mimicking of the macroscopic ensemble by the microscopic assembly is therefore classified by Peres as only pragmatic, in a roundabout way, not in any logically convincing sense. Thus he acknowledges the problems while you, @vanhees71, insist on the absence of all problems in your version of the minimal interpretation.

From here:A. Neumaier said:In its minimal statistical interpertation, quantum mechanics is not consistent since, unlike classical mechanics, it cannot be applied to huge quantum systems such as the solar system or the whole unvierse. At least Peres, whose book champions the minimal interpretation, thinks so.

vanhees71 said:This is only what you claim. There's no doubt that QT in its minimal interpretation can very well applied to macroscopic systems. [...]Where do you find the contrary statement by Peres?

Peres writes on p.11:

And on p.58:Asher Peres said:Bohr never claimed that different physical laws applied to microscopic and macroscopic systems. He only insisted on the necessity of using different modes of description for the two classes of objects. It must be recognized that this approach is not entirely satisfactory. The use of a specific language for describing a class of physical phenomena is a tacit acknowledgment that the theory underlying that language is valid, to a good approximation. This raises thorny issues. We may wish to extend the microscopic (supposedly exact) theory to objects of intermediate size, such as a DNA molecule. Ultimately, we must explain how a very large number of microscopic entities, described by an utterly complicated vector in many dimensions, combine to form a macroscopic object endowed with classical properties.

Note that Peres says that these issues are not yet fully understood!Asher Peres said:The characteristic property of a genuine test is that it produces a permanent record, which can be described by our ordinary language, after having been observed by ordinary means, without the risk of being perturbed by the act of observation. [...]

The robustness of a macroscopic record—its stability with respect to small perturbations such as those caused by repeated observations—suggests that irreversible processes must be involved. This is a complicated issue, not yet fully understood, which will be discussed in Chapter 11.

Having thus warned the reader of the difficulties lying ahead, I now return to the formal and naive approach where a quantum test is an unexplained event, producing a definite and repeatable outcome, in accordance with well defined probability rules given by quantum theory.

On p.63, Peres writes:

On p.424:Asher Peres said:the same word “measurement” is also used with a totally different meaning, whereby numerous quantum tests are involved in a single measurement. For example, when we measure the lifetime of an unstable nucleus (that is, its expected lifetime), we observe the decays of a large number of identically prepared nuclei. Very little information can be obtained from a single decay. Likewise, the measurement of a cross section necessitates the detection of numerous scattered particles: each one of the detection events is a quantum test, whose alternative outcomes correspond to the various detectors in the experiment.

Still another kind of scattering experiment, also called a measurement, is the use of an assembly of quantum probes for the determination of a classical quantity. For example, when we measure the distance between two mirrors by interferometry, each interference fringe that we see is created by the impacts of numerous photons. A single photon would be useless in such an experiment. These collective measurements will be discussed in Chapter 12. Here, we restrict our attention to measurements which involve a single quantum test.

And on the next page:Asher Peres said:This would cause no conceptual difficulty with quantum theory if the Moon, the planets, the interstellar atoms, etc., had a well defined state ##\rho##. However, I have insisted throughout this book that ##\rho## is not a property of an individual system, but represents the procedure for preparing an ensemble of such systems. How shall we describe situations that have no preparer?

The footnote quoted by Peres says:Asher Peres said:Thus, a macroscopic object effectively is assembly, ##{}^{45}## [Footnote: See footnote 9, page 59, and related text], which mimics, with a good approximation, a statistical ensemble. [...] You must have noted the difference between the present pragmatic approach and the dogmas held in the early chapters of this book.

And on p.25, where Peres introduces ensembles, he says (like Gibbs 1902):Asher Peres said:The term assembly denotes a large number of identically prepared physical systems, such as the photons originating from a laser. An assembly, which is a real physical object, should not be confused with an ensemble, which is an infinite set ofconceptualreplicas of the same

system, used for statistical argumentation,

Asher Peres said:We imagine that the test is performed an infinite number of times, on an infinite number of replicas of our quantum system, all identically prepared. This infinite set of experiments is called a statistical ensemble. It should be clearly understood that a statistical ensemble is a conceptual notion—it exists only in our imagination, and its use is to help our reasoning.##{}^1## [Footnote: Repeating an experiment a million times does not produce an ensemble. It only makes one very complex experiment, involving a million approximately similar elements.]

Thus Peres says that the statistics is done with conceptual ensembles, which are entirely different things than assemblies. In particular, a canonical ensemble (though not discussed in the book) is an infinite set of

*conceptual*replicas of the same macroscopic quantum system, and the statistics predicted by quantum mechanics applies approximately on the level of*many*copies of this macroscopic system, never to*a single one*.The mimicking of the macroscopic ensemble by the microscopic assembly is therefore classified by Peres as only pragmatic, in a roundabout way, not in any logically convincing sense. Thus he acknowledges the problems while you, @vanhees71, insist on the absence of all problems in your version of the minimal interpretation.

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