Steven Weinberg on the interpretation of quantum mechanics

[A. Neumaier]

TL;DR Summary

Why Steven Weinberg finds that today there is no interpretation of quantum mechanics that does not have serious flaws.

I don't know, what precisely it is what Weinberg thinks is missing, because in his book he just says that which interpretation is "correct" is an open question, but I did not see clearly what he thinks is missing from what to be expected of a physical theory to describe beyond what QT successfully describes.

I think Weinberg is quite clear about this:

On p.87 of the second edition of his quantum mechanics book, he says,

what is known as the Born rule [...] entails a departure during measurement from the dynamical assumptions of quantum mechanics. [...] If the time-dependent Schrödinger equation described the measurement process, then whatever the details of the process, the end result would be some definite pure state, not a number of possibilities with different probabilities.

and on p.88:

This is clearly unsatisfactory. If quantum mechanics applies to everything, then it must apply to a physicist’s measurement apparatus, and to physicists themselves. On the other hand, if quantum mechanics does not apply to everything, then we need to know where to draw the boundary of its area of validity. Does it apply only to systems that are not too large? Does it apply if a measurement is made by some automatic apparatus, and no human reads the result?[...] There has emerged in recent years a clearer picture of what actually happens in a measurement. This has been largely due to the attention given to the phenomenon of decoherence. But as I will try to show, even with this clarification, there still seems to be something important missing in our present understanding of quantum mechanics.

After having discussed decoherence, he says on p.92:

There seems to be a wide-spread impression that decoherence removes all obstacles to this class of interpretations of quantum mechanics. But there is still a problem with the Born rule [...] The “derivation” given above, based on Eq. (3.7.8), is clearly circular, because it relies on the formula for expectation values as matrix elements of operators, which is itself derived from the Born rule. So where does the Born rule come from? There are two main approaches to this question, that are often called instrumentalist and realist, each with its own drawbacks.

For the instrumentalist approach (apparently your view of the matter), he states on p.92f this drawback:

But if these probabilities are taken to be the probabilities of obtaining various results when people make observations, then this approach brings people into the laws of nature. This is not a problem for those physicists who, as did Bohr, view the laws of nature as no more than a set of methods for ordering and surveying human experience. They are certainly that, but it would be sad to give up the hope that they are something more, that the laws of nature are in some sense “out there” in objective reality, the same laws (aside from language) for whoever studies them, and the same whether or not anyone is studying them. [...] The problem arises precisely because we want to be able to understand scientists along with everything else scientifically, and for that very reason, we need to keep humans (scientists, observers, or anyone else) out of the laws of nature, which by definition are unexplained.

Then he states what seems to be his main concern - for him, essential for a flawless foundation is a foundation that does not need to refer to measurements (which do not exist independent of the human technology):

Only if the laws are expressed in impersonal terms, whether particle trajectories or wave functions or something else that does not refer to people making observations, can we hope to come to a scientific understanding of what is going on when people do observe nature or make a measurement.

On p.95f he discusses coarse-graining, your way of handwaving the classical world into the quantum picture, and then criticises on p.96:

The problem here is not that the choice is not unique, but rather, that it can only be made by people. [...] So the Born rule in the decoherent-histories approach seems to bring people into the laws of nature, as is apparently inevitable for any instrumentalist approach.

After that he discusses in detail the drawbacks of the realist approach, criticism that you probably share, so there is no point in reiterating these here.

These considerations fully justify (in his eyes) his conclusion on p.102 that

today there is no interpretation of quantum mechanics that does not have serious flaws.

 

[EPR]

If you need a human being to introduce the Born rule to nature and get classical outcomes, the interpretation is likely flawed.

 

[Morbert]

The problem here is not that the choice is not unique, but rather, that it can only be made by people. [...] So the Born rule in the decoherent-histories approach seems to bring people into the laws of nature, as is apparently inevitable for any instrumentalist approach.

I do not think he defends this conclusion very successfully. For context:

The problem here is not that the choice is not unique, but rather, that it can only be made by people. Of course, the answers to questions depend on what questions we choose to ask, in classical as well as in quantum mechanics, but in classical physics the necessity of choice can be evaded because in principle we can choose to measure everything. It cannot be evaded in this way in quantum mechanics because in general many of these choices are incompatible with each other. For instance, we can choose to leave the eigenvalues of J x or J y or J z unaveraged at a given time, but we can’t leave all three unaveraged, because there is no state in which all three have definite non-zero values. So the Born rule in the decoherent-histories approach seems to bring people into the laws of nature

I'm with him up until the last sentence. Decoherent histories implies we must use different frameworks of alternative histories to answer different questions, but what does it mean to say the laws of nature change depending on the choice of framework?

He says that in classical physics such a choice can be evaded, but we can still choose regardless. E.g. I can choose to compute the likelihoods of 6 possible outcomes of a dice roll {1,2,3,4,5,6} or I can choose to compute the likelihoods of the 2 possible outcomes {1-3,4-6}. By choosing the latter over the former, I have not posited new laws of nature.

I have seen other physicists make similar objections (e.g. Adrian Kent).

 

[vanhees71]

I don't need a human being to introduce Born's rule. Born's rule just tells us with which probability an (ideal) measurement of an observable yields one of its possible results (eigenvalue of the measured observable's representing self-adjoint operator).

The quoted arguments from Weinberg's book are well-known, but I don't see the points. First of all, why should the application of Born's rule, giving me the probabilities for the outcome of measurements mean that I have to assume a "Heisenberg cut", i.e., the invalidity of the dynamical laws of quantum mechanics? All that happens are the interactions of the measured object with a usually macroscopic measurement device, and these follow the dynamical laws of quantum mechanics. The classical behavior of the measurement device is explained by quantum-many-body theory. There's no necessity for dynamical laws beyond what's anyway postulated in the standard formulae of QT. Weinberg himself seems also to think along this lines, as shows his use of the Lindblad equations derived from the standard dynamical rules to describe the dynamics of an open quantum system, in recent years.

The next argument is about the statement of Born's rule as a fundamental postulate. I also never understood, why it should be necessary to derive this postulate from the other (kinematical and dynamical) postulates at all. For me it's simply an additional postulate which summarizes some decades of experience with the application of more or less well-defined quantum theories until this version (a la Heisenberg, Born, Jordan and Schrödinger and Dirac) which is the final form valid until today in application to describe real-world measurements. Any successful physical theory is based on experience, i.e., the use of models and theory to observations and (with some luck) finally finding a compact formulation in terms of postulates. Why it should be necessary to prove Born's rule, which is indeed necessary to write the expectation values Weinberg quotes in the derivation of the decoherence phenomenon in the form one has to write them to get to this result. Born's rule is simply one of the basic postulates of the theory. The only justification, as for any postulate, and any application of the theory to observations/experiments based on these postulates, is the success in describing the findings of these observations. Of course, it can be interesting to investigate in which sense a single postulate may be derivable from the others, but it seems that there's no way to derive Born's rule from the other postulates alone, as Weinberg writes in this chapter of his textbook. So for me this just indicates that Born's rule seems to be an independent postulate of QT. For me that's it. Weinberg comes to the conclusion that there's something else needed to satisfactorily understand QT, but that's precisely what I don't understand.

Finally: Where does the coarse-graining (quantum many-body statistical physics) bring the observer into the game? Since when is a box containing with diabatic walls held at a certain temperature conaining a gas an observer? This is all that's needed to define a thermal-equilibrium state for which the gas's macroscopic (in this case thermodynamic) observables (temperature, pressure,...) behave as expected (according to some ideal or real gas law) from classical thermodynamics. It's just a great success that quantum statistics is so successful to describe all kinds of phenomenological constitutive laws (equations of state, susceptibilities, transport coefficients, thermal fluctuations, electrodynamic dispersion relations in media,...) based on statistical laws (coarse graining) derived from the underlying fundamental laws of the elementary constituents.

 

[Demystifier]

The quoted arguments from Weinberg's book are well-known, but I don't see the points.

So you think the book is a gem, but you don's see the point of one important part of the book. Interesting!

 

[A. Neumaier]

it seems that there's no way to derive Born's rule from the other postulates alone, as Weinberg writes in this chapter of his textbook. So for me this just indicates that Born's rule seems to be an independent postulate of QT. For me that's it. Weinberg comes to the conclusion that there's something else needed to satisfactorily understand QT, but that's precisely what I don't understand.

Well, unlike you he sees the clash between

• the unitary dynamics for closed systems (therefore necessarily including any measurement device and its environment, and therefore ultimately the whole universe), where there is no Born rule, and
• the nonunitary dynamics implied by Born's rule, that (at the present time) cannot be derived from the former.

On the other hand you claim

1. that unitary relativistic QFT is universally valid (with exception of some unsettled problems in quantum gravity) and
2. that the quantum mechanics of the whole universe is meaningless, since without Born's rule there is no relation to experiment.

Now one cannot consistently hold both. If some unitary QFT is universally valid (i.e., constitutes complete foundations) it describes exactly a closed physical system. But the only truly closed physical system is the whole universe, since any proper part of it is coupled to its environment, and replacing the latter by an artificial heat bath or even dropping it entirely (the two common ways to account for it) constitute approximations.

Thus your proclaimed foundation is inconsistent:

• Either 1. must be dropped and reality deviates from an exact unitary description. But then the Schrödinger equation becomes an approximate equation, not the fundamental one that current quantum mechanics (including QFT with its emphasis on unitary representations of the Poincare group) presupposes. (This is the line GRW models take, hoping for gravity to account for the lack of unitarity. But these models are nonrelativistic and don't encompass QFT.)
• Or 2. must be dropped and the quantum mechanics of the whole universe is exactly described by some unitary relativistic QFT. But then the meaning of the state of the universe cannot be interpreted in terms of Born"s rule, which requires an interaction with an external measurement device. But nothing external to the universe interacts with it, since the universe is a closed system. (Here the thermal interpretation gives a natural meaning to the state of the universe, and Born's rule is seen there as an approximation only.)

While you happily live with this inconsistency, Weinberg acknowledges it frankly.

 

[A. Neumaier]

@vanhees71:

While you happily live with this inconsistency, Weinberg acknowledges it frankly.

So does Peres in Chapter 12.10 of his book, who otherwise champions your minimal statistical interpretation.
On p.424f he writes:

Real life seldom follows the idealized preparation-observation pattern presented throughout this book. [...] any macroscopic object, such as a star, involves an enormous number of identical subsystems with almost identical properties, in particular identical positions, within the accuracy of our instruments. Thus, a macroscopic object effectively is assembly, 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. It was then asserted that any operator which can be written by a theorist can also be measured in the laboratory. This fiction was needed in order to establish a formal framework for quantum theory. Now, our goal is different: we want to use a classical language for describing, with a good approximation, macroscopic phenomena.

Thus Peres characterizes the minimal statistical interpretation as dogmatic fiction, while labeling the approach to macroscopic quantum physics discussed in Section 12 as pragmatic - involving handwaving arguments (only 'mimicking' instead of 'being' an ensemble) not fully compatible with the minimalistic dogma.

By the way, Peres also acknowledges (on p.26f) that the minimal statistical interpretation needs the Heisenberg cut:

However, this only shifts the imaginary boundary between the quantum world - which is an abstract concept - and the mundane, tangible world of everyday. [...] The internal consistency of the theory will simply mean that if an instrument is quantized and observed by another instrument, whose description remains classical, the result obtained by the second instrument must agree with the result that was registered by the first one, when the first one was described classically.

 

[Morbert]

Well, unlike you he sees the clash between

• the unitary dynamics for closed systems (therefore necessarily including any measurement device and its environment, and therefore ultimately the whole universe), where there is no Born rule, and
• the nonunitary dynamics implied by Born's rule, that (at the present time) cannot be derived from the former.

According to decoherent histories, these are alternative complementary descriptions, not examples of contradictory dynamics. We can describe a system with a single history representing unitary time evolution, or a family of alternative stochastic histories. Each description focuses on different complementary properties of the system, but they do not contradict each other.

 

[Mary Conrads Sanburn]

A. Neumaier said:
"Why Steven Weinberg finds that today there is no interpretation of quantum mechanics that does not have serious flaws."

Steven Weinberg
Framingham, Massachusetts
Nov 28, 1935 – Apr 3, 2020
Plant Memorial Trees Opens send flowers

Obituary
McCarthy, McKinney & Lawler Funeral Home Obituary
Steven Weinberg was born on Thursday, November 28, 1935 and passed away on Friday, April 03, 2020. Steven Weinberg was a resident of Massachusetts at the time of passing.He was a scientist who sought to understand the world as it is, not as he wishes it would be. And that is indeed the highest calling of a scientist - to learn how this mysterious and wondrous world actually works.
Art Weisman
May 25, 2020 | Miami, FL | Student

https://www.legacy.com/obituaries/name/steven-weinberg-obituary?pid=195909719

 

[PeterDonis]

Obituary

This isn't the Steven Weinberg whose views are being discussed in this thread.

 

[A. Neumaier]

According to decoherent histories, these are alternative complementary descriptions, not examples of contradictory dynamics. We can describe a system with a single history representing unitary time evolution, or a family of alternative stochastic histories. Each description focuses on different complementary properties of the system, but they do not contradict each other.

As visible from my quotations, Weinberg criticises this state of affairs by saying that having to choose which complementary aspect is considered as factual makes the foundations dependent on human activity. You may not mind this but he and I do. Which description applies should be determined by the state of the system including us physicists, rather than be an external add-on.

 

[A. Neumaier]

This isn't the Steven Weinberg whose views are being discussed in this thread.

Indeed, our Steven Weinberg was born May 3, 1933.

 

[Demystifier]

This isn't the Steven Weinberg whose views are being discussed in this thread.

Fortunately, our Steven Weinberg is still alive.
https://en.wikipedia.org/wiki/Steven_Weinberg

 

[Demystifier]

While you happily live with this inconsistency, Weinberg acknowledges it frankly.

It's fascinating that the three QM books that @vanhees71 appreciates the most, namely Ballentine, Weinberg and Peres, all deeply disagree with @vanhees71 on interpretational issues.

 

[A. Neumaier]

It's fascinating that the three QM books that @vanhees71 appreciates the most, namely Ballentine, Weinberg and Peres, all deeply disagree with @vanhees71 on interpretational issues.

Dirac's textbook, which has explicit collapse, as well.

Perhaps @vanhees71 should publish his lecture notes, so that he can point to at least one textbook that agrees with him.

 

[Demystifier]

Perhaps @vanhees71 should publish his lecture notes, so that he can point to at least one textbook that agrees with him.

If they give him to teach basic QM (rather than QFT), I'm sure he will.

 

[atyy]

It's fascinating that the three QM books that @vanhees71 appreciates the most, namely Ballentine, Weinberg and Peres, all deeply disagree with @vanhees71 on interpretational issues.

For me, Ballentine and Peres never state the issue sharply. I can understand how one can miss it when reading their books (I love Peres despite this flaw). Weinberg does.

 

[Morbert]

As visible from my quotations, Weinberg criticises this state of affairs by saying that having to choose which complementary aspect is considered as factual makes the foundations dependent on human activity. You may not mind this but he and I do. Which description applies should be determined by the state of the system including us physicists, rather than be an external add-on.

Decoherent histories frames neither as more or less correct than the other. We don't have to chose one as factual over the other, or more correct than the other.

 

[vanhees71]

So you think the book is a gem, but you don's see the point of one important part of the book. Interesting!

The book is indeed a gem, but not because of this part (though it also contains some important analyses like the strong indication of the independence of the Born rule from the other postulates).

I'm only wondering why Weinberg starts to not to stick to physics and only physics anymore. That was what I usually understood is his entire approach. Usually he has been very critical against "philosophy". Now he is starting to fall into this philocophical trap of claiming that there are open points in the interpretation of QT.

His newest textbook on (mostly non-relativistic) astrophysics is free of philosophy again (and also a gem).

 

[Demystifier]

I'm only wondering why Weinberg starts to not to stick to physics and only physics anymore. That was what I usually understood is his entire approach. Usually he has been very critical against "philosophy". Now he is starting to fall into this philocophical trap of claiming that there are open points in the interpretation of QT.

You should understand him. You also stick to physics and only physics, and yet you discuss philosophy a lot.

 

[vanhees71]

Well, unlike you he sees the clash between

• the unitary dynamics for closed systems (therefore necessarily including any measurement device and its environment, and therefore ultimately the whole universe), where there is no Born rule, and
• the nonunitary dynamics implied by Born's rule, that (at the present time) cannot be derived from the former.

On the other hand you claim

1. that unitary relativistic QFT is universally valid (with exception of some unsettled problems in quantum gravity) and
2. that the quantum mechanics of the whole universe is meaningless, since without Born's rule there is no relation to experiment.

Again, I don't care about unobservable fictions of philosophers. Among them is the unobservable idea of "a state of the entire universe". I don't need relations between fictitious theoretical entities that are in principle unobservable.

Also I still don't see, what non-unitary dynamics might be implied by Born's rule. Born's rule is not about dynamics it all. Dynamics is given by the picture-independent equations of motion of observable quantities like transition probabilities, expectation values of observables, etc. and usually realized by choosing some picture of time evolution for states and observable-operators. Born's rule is simply telling the physical probabilistic meaning of the states. There's no non-unitary dynamics implied. There's particularly no collapse necessary for anything observable.

 

[vanhees71]

@vanhees71:

So does Peres in Chapter 12.10 of his book, who otherwise champions your minimal statistical interpretation.
On p.424f he writes:

Thus Peres characterizes the minimal statistical interpretation as dogmatic fiction, while labeling the approach to macroscopic quantum physics discussed in Section 12 as pragmatic - involving handwaving arguments (only 'mimicking' instead of 'being' an ensemble) not fully compatible with the minimalistic dogma.

By the way, Peres also acknowledges (on p.26f) that the minimal statistical interpretation needs the Heisenberg cut:

For me what Peres says here indicates no problem. That's how physical theories work. You have to find some pragmatic way to use the formalism to describe a given physical situation. There's no way to "axiomatize" physics in the sense that it describes the plethora of measurement devices.

He also acknoledges that indeed a macroscopic system consists of ensembles of microscopic (open!) subsystems, over which you can average to get macroscopic observables. The statistical analysis gives you even an estimate of its accuracy by providing the statistics of the fluctuations of these macroscopic observables. For really large macroscopic systems, including real-world measurement devices in the lab, with of the order $N \simeq 10^{23}$ microscopic degrees of freedom per macroscopically relevant entity of a many-body system, the classical description is almost exact with the fluctuations being by a factor $1/\sqrt{N}$ smaller than the macroscopic quantity.

 

[A. Neumaier]

He also acknowledges that indeed a macroscopic system consists of ensembles of microscopic (open!) subsystems, over which you can average to get macroscopic observables.

No. On the contrary, to describe the difference, Peres invented the term 'assembly' (not found anywhere else in physics) and distinguishes it from ensembles. Peres explicitly says that assemblies only 'mimick' the latter - he is aware that conceptually, these are very distinct things.

Just as Gibbs ensembles of thermal sysems in statistical mechanics are not Boltzmann ensembles of atoms.

I don't care about unobservable fictions of philosophers. Among them is the unobservable idea of "a state of the entire universe". I don't need relations between fictitious theoretical entities that are in principle unobservable.

Well, why then do you care about the unobservable idea of "a state of a quantum field"? You need relations between such fictitious theoretical entities that are in principle unobservable in order to derive what is observable in principle - in the case of quantum fields, e.g., macroscopic field expectations and correlation functions.

 

[A. Neumaier]

Also I still don't see, what non-unitary dynamics might be implied by Born's rule.

This is because unlike Weinberg you reject the collapse although virtually everyone else has it. Where is Weinberg's argument on p.87 where he reasons about Born's rule faulty?

 

[vanhees71]

No. On the contrary, to describe the difference, Peres invented the term 'assembly' (not found anywhere else in physics) and distinguishes it from ensembles. Peres explicitly says that assemblies only 'mimick' the latter - he is aware that conceptually, these are very distinct things.

Just as Gibbs ensembles of thermal sysems in statistical mechanics are not Boltzmann ensembles of atoms.

Well, why then do you care about the unobservable idea of "a state of a quantum field"? You need relations between such fictitious theoretical entities that are in principle unobservable in order to derive what is observable in principle - in the case of quantum fields, e.g., macroscopic field expectations and correlation functions.

What's and "assembly" then? It's clear that Gibbs ensembles are just ways to think about averaging processes in this context of the coarse-grained macroscopic observables. Here the averaging is meant to be done over microscopic large macroscopic small spacetime regions by the measurement device itself. E.g., an oldfashioned ammeter measuring a DC current through a wire connected to a battery simply doesn't resolve all the thermal (and quantum) fluctuations of the electrons and thus directly measures the macroscopic current. In this sense it takes an average (or rather a sum) of many fluctuating microscopic observables (the currents made up of single electrons in the wire).

That the Gibbs ensemble averages lead to the same results as the Boltzmann ones which are indeed closer to the macroscopic behavior of a single macroscopic system than the Gibbs "gedanken ensemble" is indeed not that trivial (ergodicity etc.), but it seems to work well in comparison to experience.

States of quantum fields describe many (if not all) phenomena. Why are you claiming they are unobservable?

 

[DrChinese]

Weinberg, Lectures on Quantum Mechanics, 12.1 Paradoxes of Entanglement (talking about EPR-B): "... the observer could have measured the x-component of the spin of particle 1 instead of its z-component, and by the same reasoning, if a value h/2 or −h/2 were found for the x-component of the spin of particle 1 then also the x-component of the spin of particle 2 must have been −h/2 or h/2 all along. Likewise for the y-components. So according to this reasoning, all three components of the spin of particle 2 have definite values, which is impossible since these spin components do not commute..."

"There is a troubling weirdness about quantum mechanics. Perhaps its weirdest feature is entanglement, the need to describe even systems that extend over macroscopic distances in ways that are inconsistent with classical ideas."

"Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Clearly, Weinberg is affirming the standard post-Bell position that QM does not evidence local realism. Obviously QFT lacks local realism too. If Weinberg felt that there was theoretical support for FTL effects as the "out" for QFT, he would say as much. Or if he felt that realism should be rejected - which he strongly implies but does not say straight out - then that would be clear too. Instead, he places this discussion under the label of "Paradoxes" and refers to this as "a troubling weirdness" which QFT in no way resolves. But that interpretations attempt to answer via assumption.

So one answer to what Weinberg thinks is "missing" in QM interpretations is a clear answer to whether locality or realism (or both) should be rejected. A measurement "here" changes the state of a distant subsystem, and we have no understanding how that occurs without making assumptions that seem unacceptable or otherwise are unreasonable. At least to him.

 

[vanhees71]

I don't understand this one quote by Weinberg: "Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Where in the formalism of QT can one find this idea? I don't see it. Weinberg in his earlier textbook Quantum Theory of Fields vol. I is most lucid on the importance of the microcausality condition and the cluster decomposition principle. How he comes to the conclusion in this book on QM that the measurement in one subsystem does change the state vector for a distant isolated subsystem? I doesn't explicitly say that this change is "instantaneously". So it's not clear whether this is implied or not in this statement. Then it's a contradiction to the very principles of QFT he is so clear on in his QFT book.

As I said, I'm very puzzled by this chapter in Weinberg's QM book, particularly because Weinberg in his QFT book is so clear about all this apparent problems with measurement and "state collapse" and "Einstein causality". Has he changed his mind in the years between writing the two books and, if so, why? For that's an enigma!

 

[A. Neumaier]

What's an "assembly" then? It's clear that Gibbs ensembles are just ways to think about averaging processes in this context of the coarse-grained macroscopic observables.

The assembly is the single macrocopic probe, a real collection of interacting microscopic atoms (hence not an ensemble, which by definition consists of independent copies). The Gibbs ensemble is a fictitious collection of many independent (noninteracting) identically prepared such probes.

Here the averaging is meant to be done over microscopic large macroscopic small spacetime regions by the measurement device itself. E.g., an oldfashioned ammeter measuring a DC current through a wire connected to a battery simply doesn't resolve all the thermal (and quantum) fluctuations of the electrons and thus directly measures the macroscopic current. In this sense it takes an average (or rather a sum) of many fluctuating microscopic observables (the currents made up of single electrons in the wire).

This is not what the axioms for quantum mechanics say. According to your axioms, an ensemble is a collection of many independent (i.e., noninteracting) identically prepared systems! This is very different from the story you just made up!

That the Gibbs ensemble averages lead to the same results as the Boltzmann ones which are indeed closer to the macroscopic behavior of a single macroscopic system than the Gibbs "gedanken ensemble" is indeed not that trivial (ergodicity etc.), but it seems to work well in comparison to experience.

... though ergodicity is violated in many known cases. It is not ergodicity that works but the interpretation of the q-expectations (i.e., ensemble averages) as field densities.

States of quantum fields describe many (if not all) phenomena. Why are you claiming they are unobservable?

They describe many phenomena but are not observable. Experiments at CERN, say, measure not many-particle states of quantum fields but cross sections and similar things. These are computed from unobservable many-particle scattering states of the quantum fields.

If you consider the latter observble because of some observable consequences you have no right to call the state of the universe unobservable (wnatever it is) because by sufficiently coarse-graining it or by restriction to a region containing very few particles, it also has observable consequences.

 

[vanhees71]

I have not "my axioms". It's just the standard minimal set of axioms of QT, and you have to apply them of course to all kinds of real-world measurements.

If you deal with single "microscopic systems", i.e., of a single electron or two electrons colliding, of course you deal with ensembles pretty much in the Gibbs sense, and indeed what you observe in such cases are pretty random outcomes.

As an example for this case take the double-slit experiments with single electrons, demonstrating that each electron leaves one spot at a photoplate (or a modern CCD cam). The precise position each electron leaves is pretty random. Many equally prepared photons going through the slits leaves a pattern according to the predictions of QT (looking like a diffraction pattern of waves going through such a double slit). In this case you indeed need a "Gibbs ensemble" of single electrons to get enough statistics to see the interference pattern and to test with "sufficient significance" whether or not the probabilistic predictions are confirmed or not.

Of course also the experiments at CERN work that way. Also here you need to collect "events" from millions of pp collisions to get a cross section. In this sense it's also a "Gibbs-ensemble like" averaging.

The classical behavior of macroscopic systems comes about by averaging/summing over many such "microscopic events" over a microscopic large macroscopically small space-time region. "Macroscopically small" means "within the spatio-temporal resolution of the measurement device".

This also seems to be behind your enigmatic formulation of "interpretation of q-expectation values as field densities".

 

[A. Neumaier]

I have not "my axioms". It's just the standard minimal set of axioms of QT, and you have to apply them of course to all kinds of real-world measurements.

I meant the axioms as formulated in your QM lecture notes; they are your axioms, since different people formulate the axioms differently, and these differences may matter in logical arguments.

The axioms you stated work for an ensemble but say nothing about the interpretation of the state of an assembly (such as a microscopic system together with a single detector, or a single brick of iron) .
That's why Peres talks about 'mimicking' only.

If you deal with single "microscopic systems"

In our context we were not talking about these, or about the double slit, but about macroscopic quantum systems, which Peres calls assemblies.

The classical behavior of macroscopic systems comes about by averaging/summing over many such "microscopic events" over a microscopic large macroscopically small space-time region.

But this is not covered by your axioms, where the average is over independent, identically prepared systems, not over interacting subsystems of a macroscopic system defined by a mesoscopic cell decomposition. The latter is the assembly of Peres. Born's rule - which is not about interacting subsystems of a quantum system - says nothing about assemblies.

the experiments at CERN work that way. Also here you need to collect "events" from millions of pp collisions to get a cross section. In this sense it's also a "Gibbs-ensemble like" averaging.

Sure, but they measure events, not states of the quantum field. The latter are unobservable, that was my claim. They are just theoretical tools for making predictions!

 

[bhobba]

If you need a human being to introduce the Born rule to nature and get classical outcomes, the interpretation is likely flawed.

That is not what he is saying. We need a human being to introduce any theory. His issue was a particular examination of Consistent Histories in that you started with the Born Rule and ended with a version of the Born Rule, so was circular. The Born rule as shown by Gleason depends mostly on non-contextuality. His issue against instrumentalist approaches, like Consistent Histories, is it says says if we measure a state and always find it has a position close to a certain value, then we can say it has a position close to that value. See:
http://quantum.phys.cmu.edu/CQT/chaps/cqt02.pdf
'It is sometimes the case, as in the examples in Figs. 2.2, 2.3 and 2.5, that the quantum wave
function is non-zero only in some finite interval x1 ≤ x ≤ x2, In such a case it is safe to assert that the quantum particle is not located outside this interval, or, equivalently, that it is inside this interval, provided the latter is not interpreted to mean that there is some precise point inside the interval where the particle is located. '

That is not what QM says - it is non-commital until it is measured and that required human intervention. He is ill at ease with a interpretation that has human beings in it's foundations. It can be made independent of that by accepting it as an assumption of the interpretation (or perhaps by just putting the Heisenberg cut there). Despite my high respect for Wienberg, I do not agree with him on that, nor on his conclusion all interpretations have problems. But his section on interpretations is well worth a read - it is very good - but beware - it would be wise to understand something about it first.

Thanks
Bill

 

[DrChinese]

I don't understand this one quote by Weinberg: "Of course, according to present ideas a measurement in one subsystem does change the state vector for a distant isolated subsystem - it just doesn't change the density matrix."

Where in the formalism of QT can one find this idea?

This is one of many things you have read about Weinberg that you simply dismiss. You are of course entitled to your opinions, no issue about that. You should take care to label your opinions as your own to provide suitable notice to the reader.

I.e. do that instead of labeling standard views of quantum theory as questionable (which you did here), and quoting yourself as an authority in the counter case. I would say, for example, that Weinberg's statements - as I quoted - are fairly innocuous... and they fall closely in line with what most physicists believe. The burden is on you, my friend, not on Weinberg. Show us where Weinberg is wrong by quoting SOMEONE ELSE.

 

[Morbert]

Worth noting that Weinberg, a few sentences later, says "the phenomenon of entanglement thus poses an obstacle to any interpretation of quantum mechanics that attributes to the wave function or the state vector any physical significance other than as a means of predicting the results of measurements."

I don't think he's saying anything to challenge mainstream interpretations of QM as a local theory.

 

[Morbert]

His issue against instrumentalist approaches, like Consistent Histories, is it says says if we measure a state and always find it has a position close to a certain value, then we can say it has a position close to that value. See:
http://quantum.phys.cmu.edu/CQT/chaps/cqt02.pdf
'In such a case it is safe to assert that the quantum particle is not located outside this interval, or, equivalently, that it is inside this interval, provided the latter is not interpreted to mean that there is some precise point inside the interval where the particle is located. '

That is not what QM says - it is non-commital until it is measured and that required human intervention.

Griffiths's claims here are consistent with his presentation of QM throughout that book. He presents a realist CH interpretation as opposed to a (more common) instrumentalist one. According to his account, the states illustrated in 2.2 and 2.3 imply any history that has the particle outside the interval would have probability 0, and so (according to his account) the particle is not outside that interval regardless of whether or not an observer comes along to check.

 

[vanhees71]

I meant the axioms as formulated in your QM lecture notes; they are your axioms, since different people formulate the axioms differently, and these differences may matter in logical arguments.

Yes, since in a manuscript about quantum physics I don't write about philosophical quibbles.

The axioms you stated work for an ensemble but say nothing about the interpretation of the state of an assembly (such as a microscopic system together with a single detector, or a single brick of iron) .
That's why Peres talks about 'mimicking' only.

As I wrote in this case you calculate expectation values and fluctuations of macroscopic coarse-grained (space-time averaged) quantities and see that the fluctuations are very small compared to the expectation values, which is compatible with what's measured by your "single detector". I don't know, what an "assembly" is. So I can't comment on this.

In our context we were not talking about these, or about the double slit, but about macroscopic quantum systems, which Peres calls assemblies.

But this is not covered by your axioms, where the average is over independent, identically prepared systems, not over interacting subsystems of a macroscopic system defined by a mesoscopic cell decomposition. The latter is the assembly of Peres. Born's rule - which is not about interacting subsystems of a quantum system - says nothing about assemblies.

Sure, but they measure events, not states of the quantum field. The latter are unobservable, that was my claim. They are just theoretical tools for making predictions!

As I said, in the quantum many-body theory you have to go further and use these postulates to derive equations for macroscopic coarse-grained quantities. You end up in a hierarchy of semiclassical approximations (Kadanoff-Baym->non-Markovian transport->BUU->hydro) showing the emergence of classical laws for the said coarse-grained quantities.

What you measure related to "vacuum" QFT are squared S-matrix elements (transition probabilities), and that's what's measured in terms of cross sections. Of course, some mathematical tools like $n$-point Green's functions are not directly observable but a calculational tool to get the observable transition probabilities. Where is here a problem?