I QM: Interesting View - Get the Inside Scoop

[gentzen]

I suppose I am close to one of those, thinking it is just a generalised probability theory. To me, the 'puzzle' is from symmetry principles alone; you can derive Schrodihgers equation (Chapter 3 Ballentine).

It is fine for me, if you believe that this is the 'puzzle'. Now do you believe that serious inquiry into your part of the 'puzzle' could be useful at all? And I don't necessarily talk about serious inquiry from you personally. But what would you do if vanhees71 would inquiry into your puzzle much more deeply than Ballentine, and came up with a solution of the puzzle that in certain ways would be better than previous solution attempts?

I personally believe that one result of all the money spent on quantum computing and quantum information science will be that some bright young researchers will develop an improved understanding of foundational questions in quantum mechanics. Not some superstar Zen like understanding unachievable for mere mortals like you and me, but a concrete understanding like Craig Gidney’s approach to distinguish between “before-hand experience” descriptions vs. “in-the-moment experience” descriptions, his analysis of the Frauchiger-Renner paradox, or Itai Bar-Natan's reappraisal of dephasement. It is fine for me if somebody disagrees with my concrete examples. But if the very possibility that serious inquiry could lead to concrete progress on foundational questions is denied, then I fear that we accidentally deny ourself a significant part of the possible return on investment.

 

[A. Neumaier]

We are indeed now a step further, being already in the middle of the transformation of an academic puzzle, which is now solved towards having now a theory applicable in the sense of engineering, i.e., the results are now used to construct new technology like quantum cryptography and quantum computers.

But people working in quantum cryptography and quantum computers routinely refer to the collapse. For example the widely used textbook by Nielsen and Chuang mentions it first on p.15:

For example, if measurement of |+> gives 0, then the post-measurement state of the qubit will be |0>. Why does this type of collapse occur? Nobody knows.

I find it bizzar in such a situation there are still people not satisfied with quantum theory because of these now solved philosophical quibbles.

These people include Nobel price winners such as t'Hooft and Weinberg. The former is still alive; the latter died a few weeks ago, but he wrote excellent books until shortly before his death. This shows that your view that the foundations of measurement are resolved is not mainstream consensus.

 

[A. Neumaier]

you take the classical Hamiltonian and replace energy etc., with the appropriate operators. It works - but why?

Because there is something called the classical limit. Quantization is the converse - the inherently ambiguous approach to infer a smooth function of $\hbar$ from its limit $\hbar\to 0$. One can always do it up to ambiguities of order $O(\hbar)$, reflected in quantization by the operator ordering ambiguity. Thus there is no mystery at all.

 

[vanhees71]

I personally believe that one result of all the money spent on quantum computing and quantum information science will be that some bright young researchers will develop an improved understanding of foundational questions in quantum mechanics. Not some superstar Zen like understanding unachievable for mere mortals like you and me, but a concrete understanding like Craig Gidney’s approach to distinguish between “before-hand experience” descriptions vs. “in-the-moment experience” descriptions, his analysis of the Frauchiger-Renner paradox, or Itai Bar-Natan's reappraisal of dephasement. It is fine for me if somebody disagrees with my concrete examples. But if the very possibility that serious inquiry could lead to concrete progress on foundational questions is denied, then I fear that we accidentally deny ourself a significant part of the possible return on investment.

I personally believe that there will not such new interpretation. It will just confirm the quantum theory as it is. The main results will (hopefully) be new technology in computing and communication helping to solve real scientific problems (as the invention of the digital computers from the 1940ies on brought a huge progress in our ability to solve well-formulated theoretical problems by numerical calculation not feasible by analytic calculations as accurately as possible numerically) and provide new technology for practical purposes (safe communication through quantum cryptography which is pretty important given that "cyber crime" becomes more and more a very serious issue).

 

[vanhees71]

But people working in quantum cryptography and quantum computers routinely refer to the collapse. For example the widely used textbook by Nielsen and Chuang mentions it first on p.15:These people include Nobel price winners such as t'Hooft and Weinberg. The former is still alive; the latter died a few weeks ago, but he wrote excellent books until shortly before his death. This shows that your view that the foundations of measurement are resolved is not mainstream consensus.

You can repeat it as often as you like and quote many textbooks concerning the collapse, it doesn't become more convincing: It depends on the setup whether you realize a von Neumann filter measurement (or, better said, preparation) or not. If you realize one there's no need for dynamics outside quantum theory to understand the filter process. That's all I'm saying.

Of course, Weinberg's last books are as brilliant as ever. What's completely ununderstandable to me is, why he was disatisfied with his own view in his (for me the most brilliant of all his brilliant textbooks) Quantum Theory of Fields book. There he explains at length that there is no problem with "non-locality" due to the fact that one makes the assumption of micro-causality together with Poincare invariance to build a theory that is local in the interactions but still of course containing the observed correlations between far-distant parts of quantum systems described by entanglement.

His attempts along the lines of thought by Hawking didn't succeed, and that's no surprise either in view of the work by Banks, Susskind, and Peskin.

For a very convincing modern view on quantum theory from the quantum information point of view, see

J. Rau, Quantum Theory - An Information Processing Approach, Oxford University Press, Oxford, 1 edn. (2021)
https://doi.org/10.1093/oso/9780192896308.001.0001.

 

[A. Neumaier]

It depends on the setup whether you realize a von Neumann filter measurement (or, better said, preparation) or not. If you realize one there's no need for dynamics outside quantum theory to understand the filter process.

The first sentence is true. The second sentence is false - nobody so far has given a convincing derivation.

For a very convincing modern view on quantum theory from the quantum information point of view, see

J. Rau, Quantum Theory - An Information Processing Approach, Oxford University Press, Oxford, 1 edn. (2021)

The book does not even touch the problems in relating a quantum detector to its measurement results. It simply avoids the measurement problem. Rau simply piles up the assumptions needed to talk about quantum information circuits. In particular, on p.108, Rau postulates the collapse, though without using the dirty name 'collapse':

Upon measurement, a statistical operator must be updated. We consider first the special case of pure states. [...] the post-measurement state results from an orthogonal projection
of the pre-measurement state onto the subspace associated with x:

Moreover, on page vi, Rau writes

Technology has made huge progress, which was recognized in 2012 with the Nobel Prize (to David Wineland and Serge Haroche) ‘for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems’.

But the statistical interpretation is completely silent about properties of an individual quantum system since it talks only about properties of ensembles of many identically prepared systems.

This kind of inconsistency is ignored by you but not by people like Weinberg. That's why your view is not mainstream.

 

[vanhees71]

It's not an inconsistently but an observed fact.

 

[A. Neumaier]

It's not an inconsistently but an observed fact.

I agree that it is an observed fact that the statistical interpretation is completely silent about properties of an individual quantum system since it talks only about properties of ensembles of many identically prepared systems. Thus the statistical interpretation cannot describe the quantum properties of an individual quantum system.

 

[vanhees71]

It describes the observable properties of an individual quantum system, particularly the probabilities of observables that don't take determined value by the preparation. You may question that this is a complete description, but there's no hint that it's not complete.

 

[martinbn]

I agree that it is an observed fact that the statistical interpretation is completely silent about properties of an individual quantum system since it talks only about properties of ensembles of many identically prepared systems. Thus the statistical interpretation cannot describe the quantum properties of an individual quantum system.

It may be that it is in principle impossible to describe the quantum properties of an individual quantum system, or even meanigless to talk about them. So, this need not be a deficiency of this interpretation.

 

[bhobba]

Because there is something called the classical limit. Quantization is the converse - the inherently ambiguous approach to infer a smooth function of $\hbar$ from its limit $\hbar\to 0$. One can always do it up to ambiguities of order $O(\hbar)$, reflected in quantization by the operator ordering ambiguity. Thus there is no mystery at all.

Of course. It strongly suggests it - but as far as I can see, that's all:
https://arxiv.org/pdf/1201.0150.pdf

This is not about the well-known ordering issue - it is why the fundamental idea works. I have a sneaky suspicion QFT may have something to say on it - you can comment on that better than me. Some think QFT does not strictly imply QM:
https://arxiv.org/pdf/1712.06605.pdf

I also think the work of Gell-Mann and Hartle on a semi-classical limit provides even stronger evidence, but my understanding is that issues with it remain. I believe researchers will resolve them, but right now, the program looks incomplete.

Thanks
Bill

 

[A. Neumaier]

It describes the observable properties of an individual quantum system, particularly the probabilities of observables that don't take determined value by the preparation.

No.

How can a foundation that is explicitly only about properties of ensembles of many identically prepared systems (look at the postulates in your lecture notes), can say anything about properties of a single quantum dot, where the only visible ensemble is the quantum dot at different moments in time, where the state monitored changes from moment to moment and is surely not identically prepared?

Assuming the first and then claiming the second is a leap of faith (in your minority quantum religion). It may be justified by the experimental practice but it is certainly not justified by your postulates of which you claim that they are a complete foundation of quantum mechanics.

It may be that it is in principle impossible to describe the quantum properties of an individual quantum system, or even meaningless to talk about them. So, this need not be a deficiency of this interpretation.

But experimentalists prepare and measure routinely individual quantum systems called quantum dots, and they analyze their properties using shut-up-and-calculate (i.e., the handwaving interpretation of) quantum mechanics. The Nobel prize 2012 was awarded for this work!

 

[A. Neumaier]

Of course. It strongly suggests it - but as far as I can see, that's all:
https://arxiv.org/pdf/1201.0150.pdf

That some people query the limit just means that it cannot be applied under all circumstances.
Although $\hbar$ is a constant in Nature, it is a parameter in the models, where one can take the limit for all macroscopic quantities of interest. There are many rigorous papers on various aspects of this. Thus it is not just a strong suggestion but a mathematical fact of most models used.

 

[vanhees71]

No.

How can a foundation that is explicitly only about properties of ensembles of many identically prepared systems (look at the postulates in your lecture notes), can say anything about properties of a single quantum dot, where the only visible ensemble is the quantum dot at different moments in time, where the state monitored changes from moment to moment and is surely not identically prepared?

Assuming the first and then claiming the second is a leap of faith (in your minority quantum religion). It may be justified by the experimental practice but it is certainly not justified by your postulates of which you claim that they are a complete foundation of quantum mechanics.

But experimentalists prepare and measure routinely quantum dots, and analyze their properties using shut-up-and-calculate quantum mechanics. The Nobel prize 2012 was awarded for this work!

So just give an example what expermimentalists prepare and measure routinely that cannot be described by minimally interpreted QT. Which of Wineland's and Haroche's experimental results cannot be described by standard minimally interpreted QT? I've no clue what you are referring to. At least I cannot find any from the description of the Nobelist's work by the Academy:

https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2012_02.pdf

 

[A. Neumaier]

So just give an example what expermimentalists prepare and measure routinely that cannot be described by minimally interpreted QT. Which of Wineland's and Haroche's experimental results cannot be described by standard minimally interpreted QT? I've no clue what you are referring to. At least I cannot find any from the description of the Nobelist's work by the Academy:

https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2012_02.pdf

Consider the description of Figure 1:

Its quantum state (both its internal state and its motion) is controlled by interaction with laser pulses as exemplified for the case of Be+. On the right, a photon is (or several photons are) trapped in a high-Q microwave cavity. The field state is measured and controlled by interaction with highly excited Rb atoms.

They measure and manipulate the field state of a single photon, obtaining time series of measurement that are interpreted with the flexible and time-honored handwaving interpretation of quantum mechanics - not with the minimal version you advocate! Nowhere is the required ensemble of identically prepared systems that would allow one to begin applying your postulates.

In the handwaving interpretation of quantum mechanics, one freely uses whatever concepts, intuition, and arguments seem suitable to bridge the theory-experiment chasm, employing conventional handwaving without bothering about logical soundness.

The handwaving interpretation of quantum mechanics is surely the best of all, since it is very easy to apply and cannot be refuted, due to its vagueness and the ground shifting allowed by its practitioners. From your many arguments over the years I know very well that while you pay lip service to (and defend with religious zeal) the minimal statistical religion you practice in fact like almost everyone else mostly the handwaving religion.

 

[vanhees71]

What's described in Fig. 1 is the preparation of the system, a trapped ion or a single photon in a cavity. What's measured on this single ion (or in this particular case 3 ions) is the fluorescent light emitted by these ions excited by a laser field. This "image of the fluorescence" is due to many photons emitted in such transitions. So what's measured is rather the reflection of a coherent laser state of light than a single photon. If you'd observe a single transition and a single photon, you'd just excite (at most) one pixel on the CCD cam.

The same holds true for the CQED measurements:

Photons produced by a coherent source are coupled to the cavity via a waveguide. The atoms are sent
one at a time into the cavity at a controlled velocity and thereby have a controlled time of
interaction. In most experiments performed by Haroche’s group, the atom and field have
slightly different frequencies. An atom traveling in the cavity does not absorb photons, but
its energy levels shift due to the dynamical Stark effect, inducing a phase variation of the
microwave field.

In neither of these example you need more than standard statistically interpreted quantum theory to describe the experimental results.

 

[A. Neumaier]

What's measured on this single ion (or in this particular case 3 ions) is the fluorescent light emitted by these ions excited by a laser field. This "image of the fluorescence" is due to many photons emitted in such transitions.

But this does not explain why you are allowed to interpret the result as having measured the state of the ion - which is the object of interest. According to the statistical interpretation, having measured the many photons only tells something about their state!

 

[vanhees71]

Yes, but their state is entangled with the state of the ion in the cavity!

 

[Lord Jestocost]

It may be that it is in principle impossible to describe the quantum properties of an individual quantum system, or even meanigless to talk about them. So, this need not be a deficiency of this interpretation.

When “Statistical interpretation” is used in the way Ballentine means it, there is a fundamental deficiency of this interpretation. In Abner Shimony’s words (in “Symposia on the Foundations of Modern Physics 1992 - The Copenhagen Interpretation and Wolfgang Pauli” (edited by K. V. Laurikainen and C. Montonen)):

“There is, for example, Ballentine, whom I mentioned yesterday. He says: ‘I am not a hidden variable theorist, I am only saying that quantum mechanics applies not to individual systems but to ensembles.’ I didn't put this down separately because I simply do not understand that position. Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables. So I fail to see how one can have Ballentine's interpretation consistently. That is, one can always stop talking and not answer questions, but that is not the way to have a coherent formulation of a point of view. But to carry out the coherent formulation of a point of view, as I think Einstein had in mind, you certainly have to supplement the quantum description with some hypothetical extra variables.” [bold by LJ]

 

[A. Neumaier]

Yes, but their state is entangled with the state of the ion in the cavity!

So what? None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled. Entanglement is not even mentioned in your postulates! You are just handwaving!

 

[A. Neumaier]

None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled.

The state of the single ion is not even defined since according to your postulates, the state is not a property of the single system but one of the ensemble!

 

[A. Neumaier]

Of course. It strongly suggests it - but as far as I can see, that's all:
https://arxiv.org/pdf/1201.0150.pdf

Actually, the physically correct way to state the dynamical classical limit is as a limit where the ''classical point particles'' are the center of mass of bound states with a large number of protons. Examples are cannon balls or planets. Then the classical dynamics follows without difficulties. I treated it in Section 2.3 of my book

A. Neumaier, Coherent Quantum Physics: A Reinterpretation of the Tradition, de Gruyter, Berlin 2019.

 

[bhobba]

I have had a chance to have a look at a preview on Amazon. I generally like to buy books by Mentors/Science Advisors here. IMHO it is both provocative and good. Written at a nice level that undergrads can generally understand. It is a worthwhile addition to the literature on QM foundations, and I will eventually get a copy. Just have so much reading to catch up on at the moment. Thanks for making me aware of it.

Thanks
Bill

 

[vanhees71]

So what? None of your minimal postulates says that when you measure many times observable X (of the photons) it counts as a measurement of the state of the single Y with which it is entangled. Entanglement is not even mentioned in your postulates! You are just handwaving!

It's not handwaving. Measurements of quantum properties are usually made by observing some macroscopic pointer observable. E.g., in the SG experiment you observe two partial beams of Ag atoms that went through a magnet by observing the corresponding traces on the observation screen. So what's literally meaured is the position of the Ag atoms when hitting this screen. That this is a separation of Ag atoms wrt. the value the corresponding spin component takes is due to the known entanglement between position and this spin component.

The observed pattern of the photons is also related to the state of the atom(s) in the trap through such an entanglement. It's well-described in the Nobel paper.

Of course, I don't mention entanglement in the postulates, because it's a consequence of the postulates. The corresponding observable non-classical properties concerning measurable correlations are not postulates but deduced from the postulates.

 

[A. Neumaier]

So what's literally measured is the position of the Ag atoms when hitting this screen.

I fully agree.

The observed pattern of the photons is also related to the state of the atom(s) in the trap through such an entanglement.

True only by handwaving and experience. But not according to your minimal foundations!

The problem with this begin already in the meaning of your statement.

Does the single atom in the trap have a well-defined state at every time?

If yes, then the state is a property of the single atom, and not of an ensemble of atoms. This flatly contradicts your postulates.

If not, what do you mean by the 'state of the atom'? Only one atom was prepared, so there is no ensemble to refer to. Thus your postulates are not applicable to this system.

Since you claim that everything in your lecture notes (and hence presumably in quantum mechanics) is derived from your minimal postulates, no consequences of entanglement apply to the single atom.

Thus your postulates are too minimal and need to be extended to allow for entangled states of single atoms to be measured by measuring instead an Ag atom.

 

[gentzen]

I'm one of those stupid people, who don't see, where the "puzzle" is.

You seem to assume that there is one single big puzzle, and that it is the same for everyone.

For example, one puzzle for me has been of historical and sociological nature:
Why does popular science get QM so badly wrong? How did it happen that the "consciousness causes collapse" interpretation got associated with the names of John von Neumann and Eugene Wigner? What was the role of Henry P. Stapp in this?

What might be characteristic about this sort of puzzle is that there is some activity I can do for investigating it more seriously, and that this is an activity that I could bear. So my guess is that different people will see various puzzles, and at least some of these puzzles will be choosen such that the one who believes this to be a puzzle also believes that there are ways to make progress on his puzzle.

I personally believe that there will not such new interpretation. It will just confirm the quantum theory as it is.

My intial reaction was that there will be no new interpretation, just improved understanding of certain questions and better (more convincing) approaches to explain them to other people. I fully agree that it will not contradict quantum theory as it is.

However, then I noticed that the quantum computing and quantum information science people basically already converged on the outline of their "new interpretation":

That is not to 'trivialise' those issues - I just think the generalised probability theory viewpoint resolves them.

I also invested effort in the past to better understand this viewpoint (based on a somewhat long series of blog post by Qiaochu Yuan - a nice fit to "bright young researcher") and even tried to explain it to a senior researcher. While doing so, I also mentioned one of my puzzles and that I believed that this viewpoint could help with it: "For quantum mechanics, the question for me is how to use concepts from probability theory for avoiding infinite information content. The first step is to switch to a probability from expectation approach, as outlined in Qiaochu Yuan's post, ..."

 

[vanhees71]

According to quantum theory any system has a state at any time, described by the statistical operator $\hat{\rho}(t)$.

What do you mean by "consequences of entanglement"? The consequences of entanglement are of course again of statistical nature, describing the well-known correlations. Take again the SG experiment, just because it's most simple to discuss this issues.

The preparation of the state is getting an Ag atom out of the oven, let it go through some slits, then letting it go through the magnet. Now there is an entanglement between the position of the atom with the spin component determined by the magnet. So you can be sure when measuring this spin component of the atom at a given place to find with certainty the corresponding value of this spin component. That's the "consequence of entanglement".

Thus by counting many Ag atoms prepared in this specific way (forming an ensemble of equally prepared silver atoms) ending up at the one or the other region of screen is, according to the calculation using the postulates, a way to measure the probabilities for the outcome of a spin measurement though what's indeed is observed is just the position of the Ag atom at the one or the other region on the screen. Of course that's not directly said in the postulates, because its deducable from the postulates.

If you make different postulate for any specific experimental setup you don't have a theory but just a description of one specific application. That's why "old quantum theory" has been abandoned in favor of "new quantum theory". The former just predicted the spectrum of the hydrogen atom and failed for all other atoms if not making additional ad hoc assumptions for these other cases, leading gradually to the discovery of new quantum mechanics which allowed to predict the spectra of all atoms using generally valid concepts.

 

[A. Neumaier]

According to quantum theory any system has a state at any time, described by the statistical operator

I fully agree.

What do you mean by "consequences of entanglement"?

I mean your statement that when you measure the pointer position you actually measured the state of the trapped ion, because of entanglement. This is pure handwaving since it is neither in your postulates nor is it derived from them in your lecture notes (version of July 22, 2019), as far as I can see. If I missed the derivation of such a fundamental claim, please point me to the relevant page.

Take again the SG experiment, just because it's most simple to discuss this issues.

No, take the Nobel prize winning experiment with the single ion in the trap, since there the problem is much more obvious!

Independent of that, your minimal exposition has another flaw. The experimental results (the pointer positions) are compared are independent of anyone's knowledge - one only needs to be able to read the meter. Thus they and the probabilities computed from them are objective in the ordinary sense. On the other hand, according to the minimal interpretation (p.23 of your lecture notes) the state of the trapped ion depends on we's knowledge of the system. The same system may be in a pure or in a mixed state, depending on the knowledge of 'we' who assigns the state. Since the predicted probabilities are a direct consequence of the assigned state they depend on this subjective assignment. But because the measurements are objective, there can be (within the measurement accuracy) at most one correct assignment! Unless augmented with a recipe to assign the correct state independent of what 'we' knows, this smells very fishy...

 

[martinbn]

But experimentalists prepare and measure routinely individual quantum systems called quantum dots, and they analyze their properties using shut-up-and-calculate (i.e., the handwaving interpretation of) quantum mechanics. The Nobel prize 2012 was awarded for this work!

Not sure how this related to the statistical interpretation! They work with representatives of the ensemble, and according to the statistiacl interpretations, they do not analyse their properties, but those of the ensemble. Are you saying that this disproves the statistical interpretation?

 

[vanhees71]

This is again a purely philosophical quibble. How good my description of the preparation in terms of the quantum formalism is, is of course itself subject to experimental test. Obviously for the experiments by Haroche et al our knowledge of the state is sufficient to accurately describe the outcome. This is of course the problem of any theorist using any theory. So it applies as well to your alternative theory you called "thermal interpretation" before. Now it seems to be called "coherent quantum mechanics". So, how do you describe the SG experiment (or the experiments by Haroche and Wineland describe in the Nobel foundation's citations)?

The SG experiment is very well understood in the standard formulation because of its simplicity. You can dynamically calculate how it comes to the said entanglement between position and spin component with sufficient accuracy to understand the outcome of the experiments. So where is the problem?