Dyson's View Of Wavefunction Collapse

[bhobba]

I came across an interesting quote from Freeman Dyson: (start of quote):

The Collapse Of The Wave-Function
Four and seven years ago, Erwin Schrödinger invented wave functions to describe the behaviour of atoms and other small objects. According to the rules of quantum mechanics, the motions of objects are unpredictable. The wave-function tells us only the probabilities of the possible motions. When an object is observed, the observer sees where it is, and the uncertainty of the motion disappears. Knowledge removes uncertainty. There is no mystery here.

Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant. (end of quote)'

I must say for years now, I have held the same view suggested by Gleason's Theorem. But Dyson is saying it is different to my musings.

If his (and my view) are correct, then what is the concern of collapse? I realise it is an interpretation issue. What confuses me is that introducing collapse seems to make things more complex. You see articles, papers, and discussions about it. I find it a bit strange.

 

[Demystifier]

If you say that wave function is just a description of probability, problems don't go away. It begs question, if wave function is not physical, then what is? The PBR theorem says that if there is some objective physical reality at all, some $\lambda$ which is not just probability, then wave function is also a part of $\lambda$, and not just a description of probability.

See also footnote 2 in my https://arxiv.org/abs/2205.05986.

 

[bhobba]

Anyway, if you say that wave function is just a description of probability, problems don't go away. It begs question, if wave function is not physical, then what is?

The result of the observation. I also believe the quantum field is physical, but a paper I have linked to in the past found - that in the non-relativistic limit, the quantum field is not exactly the same as the state.

Not that it makes much difference, really - it just changes the question to why the outcome is probabilistic. Gleason would suggest it is because the outcomes are the observables' eigenvalues. But then, why is that so? Really - has anything been resolved?

Thanks
Bill

 

[martinbn]

In another place I saw Dyson advocating the many worlds interpretation. Anyway, if you say that wave function is just a description of probability, problems don't go away. It begs question, if wave function is not physical, then what is? The PBR theorem says that if there is some objective physical reality at all, some $\lambda$ which is not just probability, then wave function is also a part of $\lambda$, and not just a description of probability.

See also footnote 2 in my https://arxiv.org/abs/2205.05986.

And if there isn't any $\lambda$?

 

[javisot20]

Not that it makes much difference, really - it just changes the question to why the outcome is probabilistic. Gleason would suggest it is because the outcomes are the observables' eigenvalues. But then, why is that so? Really - has anything been resolved?

It is a complicated question, it is likely that a mechanic based on UP (uncertainty principle) would not be expected to be the same as other types of mechanics not based on UP.

What do we understand by physical?
Physical reality is the set of all physical truths. A physical truth is something that I can construct theoretically and confirm experimentally. Therefore, physical reality is the set of everything that we can construct theoretically and confirm experimentally.

So is the wave function and collapse a physical object or not? -Well, it is an object that we can build theoretically and confirm experimentally, but it is not the only object capable of performing the same function. (I have heard Spanish-speaking physicists talk about collapse as an obsolete concept in modern physics)

 

[Demystifier]

And if there isn't any $\lambda$?

Then the PBR theorem is not applicable.

 

[Demystifier]

The result of the observation.

What do you mean by observation? Does detection by an apparatus count as observation, or is it necessary that a conscious being is involved? What is your take on recent extended Wigner friend thought experiments?

 

[martinbn]

Then the PBR theorem is not applicable.

Then why did you bring it up!

 

[Demystifier]

Then why did you bring it up!

Because people who argue that wave function is not physical often tacitly assume that something else is physical.

 

[martinbn]

Because people who argue that wave function is not physical often tacitly assume that something else is physical.

There is nothing in the quote to suggest that Dyson makes such an assumption.

 

[Demystifier]

There is nothing in the quote to suggest that Dyson makes such an assumption.

I read between the lines.

 

[Morbert]

What do you mean by observation? Does detection by an apparatus count as observation, or is it necessary that a conscious being is involved? What is your take on recent extended Wigner friend thought experiments?

Asher Peres (in "Quantum Theory: Concepts and Methods") says an apparatus is well-described if i) It is appropriately correlated with the system of interest and ii) It is well-described by a Liouville density derived from its Wigner function. An observation is a test carried out by a reliable apparatus.

If an apparatus is only somewhat reliable, then a physicist will only be able to somewhat reproduce the predictions of QM.

[edit] - Expanded on a reliable apparatus

 

[bhobba]

What do you mean by observation? Does detection by an apparatus count as observation, or is it necessary that a conscious being is involved? What is your take on recent extended Wigner friend thought experiments?

I take it as decoherence, an example of detection by an apparatus. I have never understood the conscious being ideas. It sounds far too much like solipsism for my taste. Not familiar with Extended Wigners, friend - I must look into it.

Thanks
Bill

 

[WernerQH]

(I have heard Spanish-speaking physicists talk about collapse as an obsolete concept in modern physics)

That precisely was Dyson's point. (What Scientific Idea Is Ready For Retirement?)

What confuses me is that introducing collapse seems to make things more complex. You see articles, papers, and discussions about it. I find it a bit strange.

I share Dyson's view and used the same quote in what was probably my first post on this forum. And I agree that it is puzzling (and sad!) that such discussions are still going on in the International Quantum Year.

The root of the problem, in my opinion, is the exaggerated role of the time-dependent wave function and Schrödinger's equation. There is an almost irrepressible urge to describe a quantum object in a pseudo-Markovian (quasi-Newtonian?) fashion as having at all times some definite state evolving continuously and even deterministically. It simply doesn't square with the discontinuities and randomness that experiments seem to reveal in the real world. There's a reason why von Neumann introduced "measurement" (collapse) as a separate process besides unitary evolution. But it's an uneasy combination and, for some physicists, has created a new "measurement problem". I think Schrödinger's equation is but one piece of the mathematical apparatus of quantum mechanics, and it must not be pulled apart from the other essential component of the machinery, namely Born's rule.

It is said that the Heisenberg picture is completely equivalent to the Schrödinger picture. But this is true only if one considers the full picture, and the wave function by itself does not provide the full picture! What is the place of wave function collapse in the Heisenberg picture? In the Heisenberg picture the state (wave function) just remains constant!

I think there is real graininess (discontinuities) in the real world, and that it is correctly described by quantum theory. But it's not caused by collapsing wave functions. In my view, quantum theory must be seen as a stochastic theory.

 

[gentzen]

@bhoppa (or any other mentor): Please move this thread into the Quantum Interpretations and Foundations subforum. At least WernerQH's post above dives deep into interpretation territory, and it isn't really surprising that this question provoked this sort of reaction.

 

[PeterDonis]

And if there isn't any $\lambda$?

Then how are we even having this conversation in the first place? Surely at the very least those of us who are having this conversation are physical. So there is something that's physical. And it seems evident that, since we can communicate, there is some common medium we all live in that is physical as well.

 

[PeterDonis]

Please move this thread into the Quantum Interpretations and Foundations subforum.

Done.

 

[martinbn]

Then how are we even having this conversation in the first place? Surely at the very least those of us who are having this conversation are physical. So there is something that's physical. And it seems evident that, since we can communicate, there is some common medium we all live in that is physical as well.

I am not questioning the existence of the physical reality. But $\lambda$ is not the reality. It is a part of the discription of reality.

 

[PeterDonis]

I am not questioning the existence of the physical reality. But $\lambda$ is not the reality. It is a part of the discription of reality.

Ok, fine, but the question is still there: what would it even mean for there to be no $\lambda$?

 

[martinbn]

Ok, fine, but the question is still there: what would it even mean for there to be no $\lambda$?

I suppose to take QM as it is. There is no lambda in QM.

 

[Peter Morgan]

I came across an interesting quote from Freeman Dyson: (start of quote):

The Collapse Of The Wave-Function
Four and seven years ago, Erwin Schrödinger invented wave functions to describe the behaviour of atoms and other small objects. According to the rules of quantum mechanics, the motions of objects are unpredictable. The wave-function tells us only the probabilities of the possible motions. When an object is observed, the observer sees where it is, and the uncertainty of the motion disappears. Knowledge removes uncertainty. There is no mystery here.

Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant. (end of quote)'

I must say for years now, I have held the same view suggested by Gleason's Theorem. But Dyson is saying it is different to my musings.

If his (and my view) are correct, then what is the concern of collapse? I realise it is an interpretation issue. What confuses me is that introducing collapse seems to make things more complex. You see articles, papers, and discussions about it. I find it a bit strange.

I think of Dirac here as somewhat threading the needle between the positions identified by Don Howard in his article in Philosophy of Science 2004, Who Invented the “Copenhagen Interpretation”? A Study in Mythology (DOI, link to PDF on author's website). I take that article to argue that Bohr takes measurements to affect the results of subsequent measurements, which is mathematically the same as but otherwise rather different from the idea that the state collapses, as advocated by Heisenberg and others.
I cite Don Howard's article as part of the argument in my article in JPhysA 2022, "The collapse of a quantum state as a joint probability construction" (arXiv, DOI), which follows Bohr's idea. I think this is also a reasonable way to take seriously an idea that the quantum state is mostly for generating probabilities, which I take to be approximately Dirac's idea here and which presumably should include joint probabilities. The Deferred Measurement Principle is an idea that I have only recently realized is very similar.
From this perspective, Dirac is too precipitate when he says that "When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant", because new knowledge only removes some uncertainty; two consecutive pieces of knowledge removes more uncertainty; and so on. When we have a dataset that contains many pairs of results of consecutive measurements, we typically want to construct a joint probability distribution as a model for that data (and for the expected results of similar future experiments, whether or not we use noncommutative operators as models for those measurements.
In talks since 2022, I have argued that Naimark's Dilation Theorem is an effective alternative to Decoherence. The argument is elementary enough that I present it in a few slides:

 

[PeterDonis]

I suppose to take QM as it is. There is no lambda in QM.

But that's no answer at all to someone who is not just taking QM as it is. Which pretty much includes anyone who is considering the question Dyson is considering in the quote given in the OP. If your answer is "just take QM as it is", then you're saying this thread is pointless. Of course you're entitled to your opinion, but other people posting here don't seem to agree.

 

[martinbn]

But that's no answer at all to someone who is not just taking QM as it is. Which pretty much includes anyone who is considering the question Dyson is considering in the quote given in the OP. If your answer is "just take QM as it is", then you're saying this thread is pointless. Of course you're entitled to your opinion, but other people posting here don't seem to agree.

No, that is not my point of view. That is my understanding of Dyson's. @Demystifier said that Dyson's view still has problems and his argument was the PBR theorem. That's why I asked him, what if Dyson doesn't think that there is a lambda?

 

[bhobba]

Because people who argue that wave function is not physical often tacitly assume that something else is physical.

I assume the quantum field is physical. My concern is (I will give a link to the paper this time):

https://arxiv.org/abs/1712.06605

The conclusion is (with a few minor editorial changes suggested by Grammarly):

'I examine this limit in several approaches ( e.g., Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field theoretic description, etc.) and identify the precise issues that arise when one attempts to obtain NRQM from QFT in each of these approaches. The dichotomy of description between NRQM and QFT does not originate just from the square root in the Hamiltonian or the demand of Lorentz invariance, as it is sometimes claimed. The real difficulty arises in the necessary existence of antiparticles to ensure a particular notion of relativistic causality. Because of these conceptual issues, it turns out that one cannot obtain some of the popular descriptions of NRQM by any sensible limiting procedure applied to QFT. To obtain NRQM from QFT seamlessly, it is necessary to work with NRQM expressed in a language closer to that of QFT.'

It would seem ordinary QM is only an 'effective theory', so the reality of the state is questionable - it suggests it is just an aid to calculations - not physically real (whatever that is - I take a common-sense Feynman-type view). We know it's wrong anyway because QFT (or at least a very clever use of ordinary QM) is needed to explain spontaneous emission:

https://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

A separate thread examining this might be interesting. When I have time, I will see if I can post one.

As an aside, I am nearly 70, and after a discussion with the police, I decided to stop driving. Using Uber to go everywhere is a bit time-consuming.

Thanks
Bill

 

[Demystifier]

I take it as decoherence, an example of detection by an apparatus. I have never understood the conscious being ideas. It sounds far too much like solipsism for my taste. Not familiar with Extended Wigners, friend - I must look into it.

The problem with decoherence is that, if you are agnostic about interpretations of QM, it cannot explain the origin of a definite outcome. The extended Wigner friend thought experiments make this problem more explicit.

 

[Demystifier]

I suppose to take QM as it is. There is no lambda in QM.

But QM as it is has collapse. And some people, as this thread shows, want to move collapse away. If there is no collapse, and no lambda, and no any specific interpretation of QM, what remains? Something a'la Ballentine perhaps? But even he needs lambda in the chapter on Bell's theorem of his book.

 

[Demystifier]

No, that is not my point of view. That is my understanding of Dyson's. @Demystifier said that Dyson's view still has problems and his argument was the PBR theorem. That's why I asked him, what if Dyson doesn't think that there is a lambda?

In my opinion, there is no coherent view of QM that does not contain at least one thing from the following list:
1) collapse
2) some kind of lambda
3) some controversial philosophical interpretation far beyond the minimal textbook QM

So if Dyson rejects collapse, he is either incoherent, or accepts some kind of lambda, or accepts some controversial interpretation, or some combination of those.

 

[Demystifier]

Note also that I deleted my previous claims that Dyson advocated many worlds. It was Coleman.

 

[martinbn]

But QM as it is has collapse. And some people, as this thread shows, want to move collapse away. If there is no collapse, and no lambda, and no any specific interpretation of QM, what remains? Something a'la Ballentine perhaps? But even he needs lambda in the chapter on Bell's theorem of his book.

I am guessing that he needs lambda because the version of Bell's theorem he proves needs it. But he doesn't need lambda for QM.

But the topic of this thread is Dyson. And to me it seems that he doesn't think that there is lambda. He says that looking at the collapse in the way he dose makes it not problematic. Of course you can disagree with that because there is still a measurement problem. I don't know what his view is on that.

In my opinion, there is no coherent view of QM that does not contain at least one thing from the following list:
1) collapse
2) some kind of lambda
3) some controversial philosophical interpretation far beyond the minimal textbook QM

So if Dyson rejects collapse, he is either incoherent, or accepts some kind of lambda, or accepts some controversial interpretation, or some combination of those.

I don't think he rejects collapse. He rejects the terminology and the claim that it is a physical process of a physical object. I think he is OK with state reduction.

 

[Demystifier]

I don't think he rejects collapse. He rejects the terminology and the claim that it is a physical process of a physical object. I think he is OK with state reduction.

Then I'm fine with his view, but still I would be interested to see what he thinks that a physical process is.

 

[martinbn]

May be a bit off topic, but this article may help understand Dyson a bit better.

https://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

And this article, from it

I have observed in teaching quantum mechanics, and also in learning it, that students go through an experience similar to the one that Serbian physicist, Mihajlo Idvorsky Pupin describes. The student begins by learning the tricks of the trade. He learns how to make calculations in quantum mechanics and get the right answers, how to calculate the scattering of neutrons by protons and so forth. To learn the mathematics of the subject and to learn how to use it takes about six months. This is the first stage in learning quantum mechanics, and it is comparatively painless.

The second stage comes when the student begins to worry because he does not understand what he has been doing. He worries because he has no clear physical picture in his head. He gets confused in trying to arrive at a physical explanation for each of the mathematical tricks he has been taught. He works very hard and gets discouraged because he does not seem to be able to think clearly. This second stage often lasts six months or longer. It is strenuous and unpleasant.

Then, unexpectedly, the third stage begins. The student suddenly says to himself, “I understand quantum mechanics,” or rather he says, “I understand now that there isn’t anything to be understood.” The difficulties which seemed so formidable have mysteriously vanished. What has happened is that he has learned to think directly and unconsciously in quantum-mechanical language. He is no longer trying to explain everything in terms of prequantum conceptions.

The duration and severity of the second stage are decreasing as the years go by. Each new generation of students learns quantum mechanics more easily than their teachers learned it. The students are growing more detached from prequantum pictures. There is less resistance to be broken down before they feel at home with quantum ideas. Ultimately, the second stage will disappear entirely. Quantum mechanics will be accepted by students from the beginning as a simple and natural way of thinking, because we shall all have grown used to it. By that time, if science progresses as we hope, we shall be ready for the next big jump into the unknown.

 

[Peter Morgan]

That precisely was Dyson's point. (What Scientific Idea Is Ready For Retirement?)


I share Dyson's view and used the same quote in what was probably my first post on this forum. And I agree that it is puzzling (and sad!) that such discussions are still going on in the International Quantum Year.

The root of the problem, in my opinion, is the exaggerated role of the time-dependent wave function and Schrödinger's equation. There is an almost irrepressible urge to describe a quantum object in a pseudo-Markovian (quasi-Newtonian?) fashion as having at all times some definite state evolving continuously and even deterministically. It simply doesn't square with the discontinuities and randomness that experiments seem to reveal in the real world. There's a reason why von Neumann introduced "measurement" (collapse) as a separate process besides unitary evolution. But it's an uneasy combination and, for some physicists, has created a new "measurement problem". I think Schrödinger's equation is but one piece of the mathematical apparatus of quantum mechanics, and it must not be pulled apart from the other essential component of the machinery, namely Born's rule.

It is said that the Heisenberg picture is completely equivalent to the Schrödinger picture. But this is true only if one considers the full picture, and the wave function by itself does not provide the full picture! What is the place of wave function collapse in the Heisenberg picture? In the Heisenberg picture the state (wave function) just remains constant!

I think there is real graininess (discontinuities) in the real world, and that it is correctly described by quantum theory. But it's not caused by collapsing wave functions. In my view, quantum theory must be seen as a stochastic theory.

Thank you for the URL for Dyson's quote on Edge.org.
A Stochastic Process is commonly defined as a collection of random variables indexed by time, which I suppose is only a starting point for a more elaborate stochastic theory that would be as complete as quantum field theory. In the first instance, I suggest there are three more-or-less clear differences: a quantum field is commonly defined as an operator-valued distribution indexed by time and space(1), which generate a noncommutative(2) algebra of measurement operators, and there are two measures of dispersion, both kT for thermal noise and ℏ for quantum noise(3).
We can accommodate (1) and (3) into a classical formalism quite straightforwardly, by working with a random-variable-valued distribution indexed by space and time(1), and by noticing that quantum noise is Lorentz invariant whereas thermal noise, which is a symmetry property that can be adopted into classical physics(3). Noncommutativity can be thought of as classically natural, as a way of accommodating different experimental contexts into a single formalism instead of taking each initial condition as a different model universe, but of course that is a considerable extension.
Although I agree that there is a real graininess in the experimental data I suggest that it is not a graininess that survives in a stochastic formalism when we consider the fine-grained signals out of an apparatus. At a timescale that is sub-picosecond, say, every measured signal exhibits a finite rise time. In any case, at such scales and with extreme amplification there is always too much noise to be sure of much except the fine-grained signal convolved with a relatively coarse-grained window function, which is as smooth as the window function we choose.
In the article I linked to above, in JPhysA 2022 (arXiv, DOI there), I introduced a new kind of 'picture', which I call the super-Heisenberg picture, which is not related to the Heisenberg picture and Schrödinger picture by a unitary transformation. I call it the super-Heisenberg picture because it absorbs the collapse of the quantum state as well as the unitary evolution into the measurement operators, in contrast to the Heisenberg picture, which absorbs only the unitary evolution into the measurement operators. Applid in the QFT setting, that results in a Hilbert space formalism that can be thought of as (a)a commutative QFT; as (b)a commutative algebraic model of a stochastic theory with (1) and (3) added; or as (c) a QFT with (2) subtracted. There are connections with Koopman's Hilbert space formalism for classical mechanics, for anyone who knows that construction.

 

[Demystifier]

May be a bit off topic, but this article may help understand Dyson a bit better.

https://www.damtp.cam.ac.uk/user/tong/em/dyson.pdf

And this article, from it

I see your point, but how to explain that, in the last 30 years or so, the interest in quantum foundations increases, rather than decreases? There is more and more mature physicists who think that QM as such is not sufficiently clear, that there is something to understand about QM which is not explained by its formalism.

 

[martinbn]

I see your point, but how to explain that, in the last 30 years or so, the interest in quantum foundations increases, rather than decreases? There is more and more mature physicists who think that QM as such is not sufficiently clear, that there is something to understand about QM which is not explained by its formalism.

That is a question for Dyson, I am not sure my view is entirely the same as his. There is a lot of interest in the last 30 years, but what is the progress made?

 

[Demystifier]

That is a question for Dyson, I am not sure my view is entirely the same as his. There is a lot of interest in the last 30 years, but what is the progress made?

There is no much progress, I admit. But that can be said for many other branches of physics as well. Actually, the Nobel prize in physics last year is given for a research which did not make a progress in physics at all, which indicates that physics as a whole is in crisis. But now I'm off-topic.

 

[martinbn]

There is no much progress, I admit.

But there is some, right?

 

[Peter Morgan]

That is a question for Dyson, I am not sure my view is entirely the same as his. There is a lot of interest in the last 30 years, but what is the progress made?

Working physicists have slowly been making QM seem less and less 'weird'. As Philip Ball put it in the title of one of his popular-level books, QM is becoming "Beyond Weird". It has been a drop-by-drop process that can be dismissed as just Shut-Up-And-Calculate, but IMO that kind of dismissal misses the bigger picture.
I suggest, in particular, that the distance between classical stochastic models and quantum models has been steadily eroding, so that there is now almost a flood of articles about classical-quantum models. There are now many physicists pursuing stochastic models in ways that would have been thought laughable 20 years ago.
't Hooft weathered years of ridicule for his approach to QM, but Oppenheim, Barandes, Wetterich, Khrennikov, Hossenfelder, Palmer, Carcassi, as only those who come to mind in a moment, are now developing similar ideas. Wolfram and Weinberg are well-known on the periphery of Physics, and there are many more physicists pursuing similar ideas less visibly. Nobody has succeeded in making a stochastic process 'story' compelling, but I think there's now more of a watch-this-space feeling than there was even five years ago.

What was called "quantum probability" in the 1990s is now called "Generalized Probability Theory", and the nature of that generalization is just a mathematical issue of different measurement contexts, not about physics at all. The Measurement Theory literature now is almost unrecognizably different from the literature in 1990.

I could belabor this some more, but the Oxford Philosophy of Physics Seminar was willing to listen to the approach to the relationship between classical physics and quantum physics that I suggest, so here that is: , title "A Dataset&Signal Analysis Interpretation of Quantum Field Theory".
To be clear, I only want to claim that this is progress, it's very far from perfect, but that's what you asked for: progress, not perfection. In some ways this channels SUAC and Copenhagen to construct a much more potent classical physics than we have been used to. Here's the abstract:

 

[Demystifier]

But there is some, right?

Of course.

 

[martinbn]

Of course.

Like?

 

[Morbert]

I see your point, but how to explain that, in the last 30 years or so, the interest in quantum foundations increases, rather than decreases? There is more and more mature physicists who think that QM as such is not sufficiently clear, that there is something to understand about QM which is not explained by its formalism.

This is likely due to the protean character of QM, and hence the mutual independence of different quantum foundation projects. Progress made in Everettian interpretations will not close QBism research projects.

QM does not uniquely select among equally complete projects, so instead of branches being pruned as per usual, you get a divergent mess of branches offering more and more opportunities for paper writing.

 

[Demystifier]

Like?

Better theoretical and experimental understanding of decoherence, various new no-go theorems, sharpening of various interpretations, ...

 

[Peter Morgan]

This is likely due to the protean character of QM, and hence the mutual independence of different quantum foundation projects. Progress made in Everettian interpretations will close QBism research projects.

QM does not uniquely select among equally complete projects, so instead of branches being pruned as per usual, you get a divergent mess of branches offering more and more opportunities for paper writing.

There are convergences as well as divergences. In particular, Koopman's Hilbert space formalism for classical mechanics allows a unification of classical mechanics with quantum mechanics. It has taken since the 1931 appearance of Koopman's original paper suggesting that formalism because the issues are subtle, but those subtleties are slowly coalescing.

 

[A. Neumaier]

A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant.

A subjective probability is a statement of ignorance, and one can learn and make the ignorance go away.

But an objective probability is a well-defined property of an ensemble. If you observe one item of the ensemble, the probability does not change but persists.

Many physicists have the view that probability is objective!

There is nothing in the quote to suggest that Dyson makes such an assumption.

Observations are physical in Dyson's text quoted in #1, since they are taken as objective pieces of evidence. Since they do not appear in the wave function, they are additional input to reality.

What is the place of wave function collapse in the Heisenberg picture? In the Heisenberg picture the state (wave function) just remains constant!

But in the Heisenberg picture, dynamics is always unitary.

How do you describe in the Heisenberg picture two consecutive measurements of noncommuting observables? The states changes nonunitarily in between!

 

[Morbert]

But in the Heisenberg picture, dynamics is always unitary.

How do you describe in the Heisenberg picture two consecutive measurements of noncommuting observables? The states changes nonunitarily in between!

Wouldn't the Heisenberg picture just evolve the projectors unitarily? E.g. Two consecutive measurements at $t_1$ and $t_2$ would yield respective outcomes $a$ and $b$ with probability $\mathrm{tr}\Pi_a(t_1)\rho\Pi_a(t_1)\Pi_b(t_2)$

 

[WernerQH]

How do you describe in the Heisenberg picture two consecutive measurements of noncommuting observables? The states changes nonunitarily in between!

All that quantum theory is concerned with are operator products and traces over them.
We can calculate correlation functions of any order ($n$-point functions) and compare them with experimental data. What is missing, in your opinion?

 

[A. Neumaier]

Wouldn't the Heisenberg picture just evolve the projectors unitarily? E.g. Two consecutive measurements at $t_1$ and $t_2$ would yield respective outcomes $a$ and $b$ with probability $\mathrm{tr}\Pi_a(t_1)\rho\Pi_a(t_1)\Pi_b(t_2)$

Can you write down the details of how this should follow from the Heisenberg dynamics and some assumed form of Born's rule for a single measurement? Or do you need a separate axiom for the probability of 2,3,4,,... consecutive experiments?

 

[A. Neumaier]

All that quantum theory is concerned with are operator products and traces over them.

This is just the mathematical formalism, without its link to reality.

We can calculate correlation functions of any order ($n$-point functions) and compare them with experimental data. What is missing, in your opinion?

How do you get Born's rule for two consecutive measurements (which is traditionally used to compare with consecutive measurements) from these $n$-point functions?

 

[martinbn]

Observations are physical in Dyson's text quoted in #1, since they are taken as objective pieces of evidence. Since they do not appear in the wave function, they are additional input to reality.

Not sure what you mean by this and how it relates to my post! Are you saying that Dyson takes observations for lambda?

 

[gentzen]

Can you write down the details of how this should follow from the Heisenberg dynamics and some assumed form of Born's rule for a single measurement? Or do you need a separate axiom for the probability of 2,3,4,,... consecutive experiments?

It looks to me like Morbert just wrote down the formulas from the Consistent Histories formalism. Which makes sense, because those formulas take their simplest form in the Heisenberg picture.

But since there is no collapse in the Consistent Histories formalism, this may not be the answer (or formula) you are looking for.

 

[Morbert]

It looks to me like Morbert just wrote down the formulas from the Consistent Histories formalism. Which makes sense, because those formulas take their simplest form in the Heisenberg picture.

But since there is no collapse in the Consistent Histories formalism, this may not be the answer (or formula) you are looking for.

Consistent Histories uses these formulas a lot but the formulas are not exclusive to that interpretation.

They come from more general reasoning about consecutive measurements, where outcomes a then b can be computed from products of conditional probabilities $p(a|\rho)p(b|a,\rho)$ which results in expressions like the one I gave. While it can be written down with only unitary dynamics, deriving it from Born's rule without recourse to collapse or filtering seems difficult.

[edit] - And actually, you will quickly run into decoherence issues unless the degrees of freedom the measurement apparatuses are explicitly included.