QM: Interesting View - Get the Inside Scoop

[A. Neumaier]

Why do we have these endless discussions?

Because Bell also wanted other things not in your quote. He wanted foundations completely free of the notion of measurement. All interpretations that provide this are controversial.

 

[vanhees71]

If you have a 1-photon state it gets either absorbed (as a whole) or is let through (as a whole). The probability is given by Malus's law, $P=\cos^2 \theta$, where $\theta$ is the angle of the polarization filter relative to the polarization direction of the photon.

 

[A. Neumaier]

If you have a 1-photon state it gets either absorbed (as a whole) or is let through (as a whole). The probability is given by Malus's law, $P=\cos^2 \theta$, where $\theta$ is the angle of the polarization filter relative to the polarization direction of the photon.

But if it gets through its polarization has changed. This is the collapse!

 

[vanhees71]

Because Bell also wanted other things not in your quote. He wanted foundations completely free of the notion of measurement. All interpretations that provide this are controversial.

This leads to a lot of confusion, because physics is all about measurements (i.e., observations), and a good theory predicts the outcome of measurements for a given experimental setup ("preparation"). I don't know for sure, but I think Bell somehow hoped to find his LHV model class confirmed and quantum theory refuted by the Bell-test experiments. Fortunately, however, rather quantum theory holds true.

 

[A. Neumaier]

This leads to a lot of confusion, because physics is all about measurements (i.e., observations), and a good theory predicts the outcome of measurements for a given experimental setup ("preparation").

Classical physics was also all about measurements but the foundations were independent of it. Nobody had measured (or required an operational measurement procedure) the particles that were posited underlying the fields that Euler and Navier, and Stokes discussed.

Thus measurement-free foundations never lead to confusion, while with the measurement-ridden quantum foundations we have now almost 100 years of manifest confusion!

 

[vanhees71]

But if it gets through its polarization has changed. This is the collapse!

Of course, the polarization has changed. That's why we call a polarization filter a polarization filter. But it's nothing that is outside of the dynamics as described by QED. You don't need an additional vague assumption called "collapse". As we discussed zillions of times, "collapse" is a FAPP description for such situations. It's not to be taken as some additional dynamial law outside of the quantum dynamical laws in the minimal formulation.

 

[A. Neumaier]

As we discussed zillions of times, "collapse" is a FAPP description for such situations.

Just like Born's rule. Being FAPP does not make it unnecessary.

 

[vanhees71]

Classical physics was also all about measurements but the foundations were independent of it. Nobody had measured (or required an operational measurement procedure) the particles that were posited underlying the fields that Euler and Navier, and Stokes discussed.

Thus measurement-free foundations never lead to confusion, while with the measurement-ridden quantum foundations we have now almost 100 years of manifest confusion!

Of course not, because we are so used to that everyday "objects" we handle all the time that nobody thought much about these foundations (though Newton et al did a lot ;-)).

 

[gentzen]

Why do we have these endless discussions?

Perhaps because we enjoy those discussions? If you watch philosophers or mathematicians wonder about Alternatives to Axiomatic Method, then you can get the impression that they are seriously inquiring about a puzzle. They still don't reach definite conclusions, or agree with each other, but at least you don't get the impression that they have endless discussions and go round in circles. In discussions of QM interpretation, there might be some participants that seem to seriously inquire about a puzzle. (For example take RUTA's attempt to give a principle account of QM similar to principal accounts of SR.) But many participants seem to actively deny that there is any puzzle to start with, for which serious inquiry could be useful at all.

 

[WernerQH]

you don't get the impression that they have endless discussions and go round in circles

I was asking a rhetorical question in response to Arnold Neumaier's statement that "[quantum fields] explain the properties of macroscopic equipment used to define the meaning of measurements to a highly satisfactory extent". Not everybody seems to be highly satisfied.

I'm participating in the discussion because I do think that there is a puzzle. The partipants have widely divergent views what the problem is, and which part of theory space is the most promising to look for a solution. There is indeed some overlap between RUTA's ideas and mine, but in my view they do not go far enough.

 

[WernerQH]

Yes, you still need fields on the lattice (links for gauge fields, nodes for fermion fields).

I'm aware of lattice theories. It is quite the opposite of what I have in mind. In those theories you still think of a field as a continuum. You discretize it only for computational reasons. I think of a field as a coarse-grained description of a fundamentally discrete reality, much like "density" refers to an average over discrete atoms. The photon field is not continuous -- photons can be counted! There is not an event at every point in spacetime; absorption and emission events can be far apart. The picture I have in mind is that of events spread out over the spacetime continuum like grains of sand. QFT is a theory describing the statistical regularities we observe in the patterns formed by those grains.

 

[PeroK]

The question remains why there are so many competent quantum physicists who disagree.

Because they are human beings. And I don't mean this flippantly.

 

[gentzen]

Arnold Neumaier's statement that "[quantum fields] explain ... to a highly satisfactory extent". Not everybody seems to be highly satisfied.

Probably because they neither know which puzzle was solved by A. Neumaier, nor what was the special role played by quantum fields for his solution.

There is a puzzle I had for a long time which is solved by A. Neumaier's ideas and elaborations. (I am not sure how many people realize that this puzzle even existed, and that he has indeed solved it.) But he obviously wanted more, i.e. the solution of a much harder puzzle. My own guess would be that the special role of quantum fields for his solution was to bring back space and locality into the picture. (Maybe their contribution to the solution is also related to their high energy / high frequency unobservable degrees of freedom and the associated dissipation.)

 

[vanhees71]

I'm one of those stupid people, who don't see, where the "puzzle" is. There was a serious and well-formulated puzzle for Einstein, which was inadequately (for me not at all) answered by Bohr concerning entanglement, and it's not in the EPR paper (which Einstein didn't like, exactly because of its unclear philosophical rather than physical statements). For Einstein the real issue was "inseparability", i.e., the fact that entangled states can be prepared such that far-distant well-separable parts of a system (e.g., two photons in an entangled polarization-momentum Bell state such that you can measure clearly the single photons by putting detectors far away from each other), which for themselves are totally indetermined (the single photons have utmost indetermined polarization, i.e., they are ideally unpolarized) while they still have 100% certain correlations (e.g., in the polarization singlet state, if A measured "H", with certainty B measures "V" and vice versa).

Now, indeed, Einstein was right in criticizing the Copenhagen interpretation, at least those which add a "collapse assumption" as a physical process outside of the quantum theoretical description of the dynamics, in calling this "action at a distance". His proposal famously was that there might be "hidden variables" which are not observed (or maybe even not observable at all) but provide the probabilistic description of an underlying deterministic theory due to incomplete knowledge as in classical statistics.

Then Bell formulated this philosophical quibbles in terms of truly scientific question, i.e., he made a prediction under general assumptions about what he called "local realistic theories", which is basically the assumption that all observables are in fact determined but their values for a specific system are unknown due to the unobserved "hidden variables". This lead to his famous inequality, which however is contradicted by quantum theory precisely for entangled states we know call Bell states. Now the philosophical quibbles were formulated as an experimental challenge, i.e., a true scientific statement decidable by observations, and starting with Aspect et al the issue was resolved completely with very high accuracy and statistical significance in favor of quantum theory.

For me the problem is thus completely solved as far as QT as a natural science theory is concerned. 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. As in the case of electricity and magnetism, for which Faraday predicted that once the politicians could take taxes for its use, there's a lot money invested with high prospect to earn a profit from it.

I find it bizzar in such a situation there are still people not satisfied with quantum theory because of these now solved philosophical quibbles. The real scientific puzzle is rather to find a consistent theory of the gravitational interaction than the philosophical headaches of Einstein and Bohr.

 

[Lord Jestocost]

Now, indeed, Einstein was right in criticizing the Copenhagen interpretation, at least those which add a "collapse assumption" as a physical process outside of the quantum theoretical description of the dynamics...

Sorry, but I have to correct this statement regarding the Copenhagen interpretation. As Cord Friebe et al. put it in “The Philosophy of Quantum Physics”:

"At this point, the infamous collapse of the wavefunction comes into play; however, according to the Copenhagen interpretation, it is either merely methodological, or explicitly epistemological, but in any case not to be understood as ontological." [italics in original, bold by LJ]

 

[WernerQH]

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

The puzzle is not "merely" philosophical. It has a profound effect on our thinking and how we teach physics. You may think that the formulation of QFT is an entirely different matter, but it is likely that the problems there have their roots in our imperfect understanding of what a quantum field is.

The real scientific puzzle is rather to find a consistent theory of the gravitational interaction than the philosophical headaches of Einstein amd Bohr.

I don't think gravity needs to be quantized at all. Mostly because of my inability to conceive of a coherent superposition of two different spacetime geometries. Gravity is just too different an animal.

 

[vanhees71]

Sorry, but I have to correct this statement regarding the Copenhagen interpretation. As Cord Friebe et al. put it in “The Philosophy of Quantum Physics”:

"At this point, the infamous collapse of the wavefunction comes into play; however, according to the Copenhagen interpretation, it is either merely methodological, or explicitly epistemological, but in any case not to be understood as ontological." [italics in original, bold by LJ]

Indeed, that's solving the entire problem: you take QT as what it is, i.e., a theory predicting probabilities for the outcome of random random experiments aka. measurements. I think a big part of the problem many people still see in quantum theory is the misinterpretation of the quantum state as describing some ontology. There are no self-adjoint operators on a Hilbert space and Hilbert-space vectors "out there" but particles, many-body systems, etc.

 

[haushofer]

As Ethan Siegel recently puts it:

"Although there are a myriad of interpretations of quantum mechanics that are equally as successful at describing reality, none have ever disagree with the original (Copenhagen) interpretation’s predictions. Preferences for one interpretation over another — which many possess, for reasons I cannot explain — amount to nothing more than ideology."

Ontology is not ideology.

Strange remark imho.

 

[RUTA]

I'm aware of lattice theories. It is quite the opposite of what I have in mind. In those theories you still think of a field as a continuum. You discretize it only for computational reasons.

In our model, (modified) LGT is not an approximation to a continuum reality, but the truth is actually the reverse (see our explanation of regularization, renormalization, and unification). I'm in the process of working up a detailed model for QFT along these lines based on what I now understand about QM via this Insight.

 

[bhobba]

PBut many participants seem to actively deny that there is any puzzle to start with, for which serious inquiry could be useful at all.

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). The 'mystery' is taking expectation values; you get the Hamiltonian of classical mechanics suggesting (not proving but just suggesting) to quantize a system, you take the classical Hamiltonian and replace energy etc., with the appropriate operators. It works - but why? Evidently, Dirac thought long and hard about that one as well, except, of course, he used Poisson Brackets:
https://uwaterloo.ca/physics-of-inf...iles/uploads/files/aqm_lecture_notes_10_2.pdf

Yet, I rarely hear anyone discussing that conundrum. To me, it is the central mystery, not the so-called measurement problem, collapse, and other stuff often discussed. That is not to 'trivialise' those issues - I just think the generalised probability theory viewpoint resolves them. But not everyone agrees. Such are the issues with the foundations of QM.

Thanks
Bill

 

[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.