Macroscopic systems in the quantum theory book by Asher Peres

[A. Neumaier]

From here:

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.

From here:

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:

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.

And on p.58:

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.

Note that Peres says that these issues are not yet fully understood!

On p.63, Peres writes:

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.

On p.424:

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?

And on the next page:

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.

The footnote quoted by Peres says:

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 of conceptual replicas of the same
system, used for statistical argumentation,

And on p.25, where Peres introduces ensembles, he says (like Gibbs 1902):

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.

 

[stevendaryl]

[Quoting Peres]
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.

To me, there is something slightly circular about how probability arises in quantum mechanics. There is no probability involved in the evolution of pure states--it's completely deterministic. Probability arises when a measurement happens, or more generally, when a microscopic variable triggers an irreversible change in a measurement device, or more generally, the environment. However, "irreversibility" is a probabilistic effect. So you need probability in order to make sense of irreversibility and you need irreversibility to get probability out of quantum mechanics.

 

[microsansfil]

There is no probability involved in the evolution of pure states--it's completely deterministic.

A non-isolated system is rarely in a pure state, right ? for all practical purposes, no physical implementation is perfect.

/Patrick

 

[DarMM]

A non-isolated system is rarely in a pure state, right ? for all practical purposes, no physical implementation is perfect.

/Patrick

Technically even isolated systems aren't in a pure state in Quantum Field Theory. It's a bit of a technical result, but essentially the type of observables you have in QFT never have pure states for any system occupying a finite volume.

 

[A. Neumaier]

To me, there is something slightly circular about how probability arises in quantum mechanics. There is no probability involved in the evolution of pure states--it's completely deterministic. Probability arises when a measurement happens, or more generally, when a microscopic variable triggers an irreversible change in a measurement device, or more generally, the environment. However, "irreversibility" is a probabilistic effect. So you need probability in order to make sense of irreversibility and you need irreversibility to get probability out of quantum mechanics.

Traditionally, one assumes probability from the start, and hence has no circularity. Only attempts to derive it without assuming it may suffer from the latter. The thermal interpretation avoids circularity by noticing that high frequency deterministic oscillations of incommensurable frequencies behave effectively like stochastic noise, so that probabilistic features and the associated irreversibility emerge in an appropriate approximation.

 

[Demystifier]

However, "irreversibility" is a probabilistic effect.

I would not agree. For example the second law of thermodynamics, in a form formulated before the discovery of statistical physics, has nothing to do with probability.

 

[A. Neumaier]

There's no necessity for [...] a quantum-classical cut (which can neither theoretically nor empirically be defined or at least be made heuristically plausible), and complementarity, whose meaning is completely obscure.

It's one of the unnecessary philosophical additions (usually called quantum-classical cut) that has no scientific foundation whatsoever!

But even Peres, who champions the minimal interpretation and is somewhat philosophy-averse, explicitly endorses the Heisenberg cut on p.26:

Why can’t we describe the measuring instrument by quantum theory too? We can, and we shall indeed do that later, in order to prove the internal consistency of the theory. However, this only shifts the imaginary boundary between the quantum world—which is an abstract concept—and the mundane, tangible world of everyday. If we quantize the original classical instrument, we need another classical instrument to measure the first one, and to record the permanent data that will remain available to us for further study.

If you want to avoid the cut you need to explain how one can apply the minimal interpretation of the quantum state of a macroscopic system (rather than the assembly of the microsystems it contains) to obtain definite measurement results from single measurements.

 

[stevendaryl]

I would not agree. For example the second law of thermodynamics, in a form formulated before the discovery of statistical physics, has nothing to do with probability.

But that was because they didn't actually understand it. Macroscopic irreversibility in the presence of reversible microscopic laws has to be a probabilistic effect.

 

[A. Neumaier]

But that was because they didn't actually understand it. Macroscopic irreversibility in the presence of reversible microscopic laws has to be a probabilistic effect.

It has to be an effect of approximation. This approximation is traditionally phrased in probabilistic terms, but there is no logical necessity for this.

 

[vanhees71]

Well, again you use the technique to make a bold claim, the H theorem is unrelated to probability theory, without telling what instead is to be used to derive it.

 

[A. Neumaier]

Well, again you use the technique to make a bold claim, the H theorem is unrelated to probability theory, without telling what instead is to be used to derive it.

H theorems are purely mathematical results about the reduced dynamics of an open quantum system. For example, for an open system ($\hbar=1$) where the density operator satisfies a Lindblad equation
$$\dot\rho = i[\rho,H] +\lambda(2A\rho A^*-A^*A\rho-\rho A^*A)$$
with real $\lambda>0$, it is easy to show that
$$\partial_t ~Tr~ \rho^2=-\lambda ~Tr~(\rho A-A\rho)^* (\rho A-A\rho)\le 0,$$
with strict inequality unless $\rho$ commutes with $A$. Thus $Tr~\rho^2$ is strictly monotone decreasing, which implies dissipation. (A conservative system conserves $Tr~\rho^2$.)

If $A$ is diagonalizable with nondegenerate spectrum, it implies that in a basis where $A$ is diagonal, $\rho(t)$ tends to a diagonal matrix as $t\to\infty$, which is decoherence.

This is pure linear algebra; nowhere any probabilistic concept entered.

 

[vanhees71]

Yes, and all these mathematical manipulations make only physical sense within the probabilistic standard interpretation until you deliver another convincing interpretation.

BTW: for the H-theorem, I'd expect you'd argue with the von Neumann entropy,
$$S=-\mathrm{Tr}(\rho \ln \rho).$$

 

[A. Neumaier]

all these mathematical manipulations make only physical sense within the probabilistic standard interpretation until you deliver another convincing interpretation.

They make sense without probability in the thermal interpretation, which convinces me more than the standard interpretations.

for the H-theorem, I'd expect you'd argue with the von Neumann entropy,

My argument for dissipation is significantly more elementary (just expand both sides of the claimed equality to see that it is true), and has no probabilistic interpretation.

But all this is strictly speaking off-topic here - the real question in this thread is:

Why does Peres, whom you took to be representative for the minimal interpretation:

Indeed, I think Peres' book is among the best if it comes to interpretation (perhaps only Weinberg's chapter on the issue is better than that).

explicitly address problems as existing that you wipe away in blissful ignorance? Weinberg also says
(in the interpretation chapter of his QM book from 2013, p.88 and p.95),

My own opinion is that these interpretations, like the Copenhagen interpretation, remain unsatisfactory. [...] My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws