Why Wave Function: Exploring Its Physical Interpretation

[RUTA]

I think the emerging modern view is its the simplest probabilistic theory that allows continuous transformations between pure states which when you think about it is what is really needed to model physical systems:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Thanks for posting this, Bill. I meant to do so earlier and ... . Anyway, it's work like this that makes me skeptical about the possibility of replacing quantum physics with classical approaches.

 

[bhobba]

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

If you are expressing a personal opinion it is flawed that's OK. But if you think in any kind of objective way that would be accepted by all mathematicians/physicists, or even most, it is flawed then you are sadly mistaken. All interpretations suck in their own special way it is true but it is purely a matter of opinion if any/all are flawed.

I believe decoherence solves the measurement problem for all practical purposes, meaning no experiment can ever show that you can't assume the pure state has been transformed into a mixed state and that the combined system and measurement apparatus is in the state it is observed to be prior to observation. You may not like that particular view because it doesn't explain how the state is selected or exactly where the collapse occurred, or even why there is any measurement outcome at all, but logically it is unassailable. It is purely a matter of philosophical debate rather than any kind of objective 'truth' if it has a flaw. Most certainly it whispers in your ear something more is going on and we like would a way of explaining the 'gaps' but whispering in your ear and actually being a flaw are not the same thing.

Thanks
Bill

 

[George Jones]

Steven Weinberg has written graduate-level quantum mechanics book that has just been published,

https://www.amazon.com/dp/1107028728/?tag=pfamazon01-20

and in it, Weinberg says

""My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation.""

 

[bhobba]

"My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation.""

Note the 'not universally shared'

Of course Weinberg is worthy of respect - but he does not speak for all physicists.

If QM is flawed is purely a matter of opinion - not actual fact.

My view is QM whispers in your ear there is something more going on - but that is far from it being a fact.

Thanks
Bill

 

[chill_factor]

what I find interesting is that the Schrodinger Equation does not look like a wave equation; it has a 1st order derivative to time, but 2nd order to position. That to me looks like a diffusion equation. Does that have any significance?

 

[bohm2]

what I find interesting is that the Schrodinger Equation does not look like a wave equation; it has a 1st order derivative to time, but 2nd order to position. That to me looks like a diffusion equation. Does that have any significance?

I think this is the model/perspective that the Grossing et al. group endorse:

The Quantum as an Emergent System
http://www.nonlinearstudies.at/files/ggEmerQuM.pdf

Historically, it had already been Schrödinger himself who pointed out the close resemblance of his time-dependent equation with the classical diffusion equation...

Emergence and Collapse of Quantum Mechanical Superposition:Orthogonality of Reversible Dynamics and Irreversible Diffusion
http://arxiv.org/ftp/arxiv/papers/1004/1004.4596.pdf

A lot of this group's work and most of their publications can be found here:

http://www.nonlinearstudies.at/

 

[akhmeteli]

Are you aware of this one: http://arxiv.org/abs/quant-ph/0111119?

Never heard of it. Looks like it has never been published. I looked at it briefly, and so far I am unimpressed. First, it is not obvious for me that entanglement necessarily implies violation of Einstein-Bell locality. Second, it looks like they start with plane electromagnetic waves and prove that the Bell inequalities are violated for some states constructed on the basis of such waves. However, violations of the Bell inequalities do not necessarily imply violation of Einstein-Bell locality - you need an extra condition: some events must be outside of each other’s light cones. I cannot imagine how this can happen for plane waves. So it looks like their proof may have a “locality loophole”:-) But again, I did not look into details of the article.

Anyway, since QM and QFT work, I think it's rather incumbent upon those who believe QM and QFT can be replaced by some classical formalism to make that happen, not for the quantum community to show it can't. And as of now, the people who believe classical formalism can account for all quantum phenomena have a looooooooooooong way to go.

I agree. But these are two different things: 1) proving that QM and QFT can be replaced by some classical formalism, and 2) proving that some features of a specific phenomenon believed to be an epitome of quantum can be reproduced in classical mechanics. I think 2) was done in Couder experiment for the two-slit experiment, but, as I emphasized earlier, maybe not much more. Nevertheless, the experiment seems very interesting and useful.

I don't believe QM and QFT (quantum physics) are flawed as physics, since we use them successfully in many varied applications. Quantum physics does strike me as flawed mathematically and conceptually.

I think we should make a distinction between a precise physical law and an approximation (and maybe this is exactly what you’re doing). Is the Coulomb law flawed as physics? No, as “we use [it] successfully in many varied applications.” But it is just an approximation and fails for fast processes. We cannot imagine physics without approximations, but typically we know they are just approximations, although they can be good, or very good, or excellent approximations. So we have a crucial question: is standard quantum theory a precise law or an approximation? One may ask: does it matter, if it works so well? I think it does matter, as physics is important even beyond any applications, as it is a basis of philosophy (certainly, not the only basis). For example, we make philosophical conclusions about fundamental locality or nonlocality of Nature based on physics. But I cannot understand how nonlocality can be approximate. Nature is either local or nonlocal. So is standard quantum theory a precise law? I don’t think it can be a precise law, as it contains mutually contradicting postulates (unitary evolution and the theory of measurements). Furthermore, it is shown in http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports) how the Born rule can be derived from unitary evolution in some cases, but as an approximation (maybe an excellent approximation). If (standard) quantum physics is indeed flawed mathematically, as you think (and I agree), it cannot be a precise law. That does not mean that I don’t admire quantum physics as one of the best achievements of humanity.

When I started working in foundations (18 years ago) I had the impression that most foundationalists shared this opinion. Now I'm starting to get the impression that the community is "buying in," as I see Many Worlds and quantum information theory dominating discussion and these interpretations don't suggest modifications to the formalism like, say, DeBroglie-Bohm.

Again, you are talking about (prevailing) opinions, not about facts. I agree that “sociology” of physics is important, but it cannot change the facts. As we seem to agree that standard quantum physics is indeed flawed (“strictly speaking”, in my wording, or “mathematically and conceptually”, in yours), maybe we should not delve on this issue any further? It is not our task to convince everybody.

As for Many Worlds … (I know about quantum information theory even less than about Many Worlds:-) ) On the one hand, I am no fan of this interpretation, on the other hand, it is my understanding that it puts more emphasis on unitary evolution, whereas the status of the theory of measurements is somewhat lower there than in Copenhagen. And that may be a strong point of Many Worlds, in my book, as I think the contradiction between unitary evolution and the theory of measurements should be resolved in favor of unitary evolution.

Copenhagen = shut up and calculate. http://fisica.ciencias.uchile.cl/~emenendez/uploads/Cursos/callate-y-calcula.pdf .

I am not sure I agree. Mermin’s article is not a proof. Furthermore, even in that article, after the phrase "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!", we find the following words: “In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view”. John Bell wrote somewhere (cannot find the reference) that we owe deep respect to the Copenhagen interpretation. A primitive interpretation could not dominate physics for decades.

In the physics community Copenhagen dominates. In the foundations community ... I'd say Many Worlds has a plurality ... I could be wrong, quantum information may have it. DeBroglie-Bohm is popular. Cramer's Transactional interpretation and Aharonov's two-vector formalism have advocates -- time-symmetric approaches as a whole have an active following. Fuch's quantum Bayesianism has attracted Mermin's attention: http://users.etown.edu/s/stuckeym/MerminBayesian.pdf and generated some discussion. I've been to only two conferences this year, so I may not have a good pulse. What have you seen along these lines?

I am not sure. I am afraid my contacts were not representative, but your assessment seems fair.

 

[akhmeteli]

I think the emerging modern view is its the simplest probabilistic theory that allows continuous transformations between pure states which when you think about it is what is really needed to model physical systems:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Anyway, it's work like this that makes me skeptical about the possibility of replacing quantum physics with classical approaches.

I guess I am less impressed by “work like this” than you are. The reason is such work looks too successful:-) for my taste: it reproduces the theory of quantum measurements, among other things, and, therefore, the contradiction of standard quantum theory (or at least something that contradicts unitary evolution). That’s not very good, in my book. Where is the source of such “success”? I did not study the article in detail, but the source may be the assumption of definite outcomes of quantum measurements in the reasonably looking axioms. Such definite outcomes, strictly speaking, contradict unitary evolution. How do we get the appearance of definite outcomes? I think the following work gives an idea (I mentioned it earlier): http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports). Or you may wish to look at their earlier work http://arxiv.org/abs/quant-ph/0702135 (there are references to their journal articles there), which is much, much shorter.

 

[akhmeteli]

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

If you are expressing a personal opinion it is flawed that's OK. But if you think in any kind of objective way that would be accepted by all mathematicians/physicists, or even most, it is flawed then you are sadly mistaken. All interpretations suck in their own special way it is true but it is purely a matter of opinion if any/all are flawed. :-).

Yes, this is my personal opinion. But this is not just my personal opinion: the measurement problem in quantum theory is recognized as a serious problem ( http://plato.stanford.edu/entries/qt-measurement/ - you may wish to search for “insolubility theorem” there ). The problem will not disappear even if I am eaten by alligators tomorrow:-). While it is important in physics who accepts what, what I am saying has some solid and “objective” basis. Let me note that I am not talking about “all interpretations”, just about standard quantum theory. By the way, I don’t quite understand how “flawless” interpretations can “suck”, but maybe that’s just because English is not my native language:-)

I believe decoherence solves the measurement problem for all practical purposes, meaning no experiment can ever show that you can't assume the pure state has been transformed into a mixed state and that the combined system and measurement apparatus is in the state it is observed to be prior to observation. You may not like that particular view because it doesn't explain how the state is selected or exactly where the collapse occurred, or even why there is any measurement outcome at all, but logically it is unassailable. It is purely a matter of philosophical debate rather than any kind of objective 'truth' if it has a flaw. Most certainly it whispers in your ear something more is going on and we like would a way of explaining the 'gaps' but whispering in your ear and actually being a flaw are not the same thing.

I am afraid your belief that “decoherence solves the measurement problem for all practical purposes” is far from being universally accepted (http://plato.stanford.edu/entries/qm-decoherence/ , especially “2.1 Solving the measurement problem?“) If you disagree, could you somehow substantiate your point of view?

 

[RUTA]

I agree. But these are two different things: 1) proving that QM and QFT can be replaced by some classical formalism, and 2) proving that some features of a specific phenomenon believed to be an epitome of quantum can be reproduced in classical mechanics. I think 2) was done in Couder experiment for the two-slit experiment, but, as I emphasized earlier, maybe not much more. Nevertheless, the experiment seems very interesting and useful.

Definitely interesting. Not sure if it will prove useful.

I think we should make a distinction between a precise physical law and an approximation (and maybe this is exactly what you’re doing). Is the Coulomb law flawed as physics? No, as “we use [it] successfully in many varied applications.” But it is just an approximation and fails for fast processes. We cannot imagine physics without approximations, but typically we know they are just approximations, although they can be good, or very good, or excellent approximations. So we have a crucial question: is standard quantum theory a precise law or an approximation? One may ask: does it matter, if it works so well? I think it does matter, as physics is important even beyond any applications, as it is a basis of philosophy (certainly, not the only basis). For example, we make philosophical conclusions about fundamental locality or nonlocality of Nature based on physics. But I cannot understand how nonlocality can be approximate. Nature is either local or nonlocal. So is standard quantum theory a precise law? I don’t think it can be a precise law, as it contains mutually contradicting postulates (unitary evolution and the theory of measurements). Furthermore, it is shown in http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports) how the Born rule can be derived from unitary evolution in some cases, but as an approximation (maybe an excellent approximation). If (standard) quantum physics is indeed flawed mathematically, as you think (and I agree), it cannot be a precise law. That does not mean that I don’t admire quantum physics as one of the best achievements of humanity.

I believe there is a theory fundamental to quantum physics (whence quantum gravity, for example). One could divide interpretations along that line -- those that do and those that don't rely on concepts from a yet undetermined theory fundamental to quantum physics.

I am not sure I agree. Mermin’s article is not a proof. Furthermore, even in that article, after the phrase "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!", we find the following words: “In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view”. John Bell wrote somewhere (cannot find the reference) that we owe deep respect to the Copenhagen interpretation. A primitive interpretation could not dominate physics for decades.

Yes, you're right. Mermin says he was wrong to have characterized Copenhagen as "shut up and calculate," yet "shut up and calculate" certainly exists as an "interpretation." Therefore, Copenhagen is distinct. I've always (erroneously) conflated them, so now I will have to find a proper characterization of Copenhagen and add it to my list

 

[RUTA]

I guess I am less impressed by “work like this” than you are. The reason is such work looks too successful:-) for my taste: it reproduces the theory of quantum measurements, among other things, and, therefore, the contradiction of standard quantum theory (or at least something that contradicts unitary evolution). That’s not very good, in my book. Where is the source of such “success”? I did not study the article in detail, but the source may be the assumption of definite outcomes of quantum measurements in the reasonably looking axioms. Such definite outcomes, strictly speaking, contradict unitary evolution. How do we get the appearance of definite outcomes? I think the following work gives an idea (I mentioned it earlier): http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports). Or you may wish to look at their earlier work http://arxiv.org/abs/quant-ph/0702135 (there are references to their journal articles there), which is much, much shorter.

For those with a psi-epistemic view, the measurement problem is not an issue.

 

[akhmeteli]

For those with a psi-epistemic view, the measurement problem is not an issue.

Again, maybe we don't need to delve on this further, as we both seem to regard the measurement problem as an issue.

 

[RUTA]

Again, maybe we don't need to delve on this further, as we both seem to regard the measurement problem as an issue.

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

 

[akhmeteli]

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

 

[RUTA]

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

You don't have wave function collapse in the path integral approach because the experimental outcome is a boundary condition, i.e., there is nothing being "time evolved," so there is nothing to "collapse." One is thinking spatiotemporally (4D) rather than dynamically ((3+1)D). By assuming 4Dism is the correct fundamental description and that not all 4D situations permit a (3+1)D story, MP and violation of the Bell inequality are no longer "mysterious," i.e., those are just situations where a 4D quantum result doesn't permit a (3+1)D time-evolved story.

By the way, I've seen several threads on PF about the mystery of the big bang, e.g., how do we have conservation of energy!? But, again, one has to understand GR is a 4D solution, so not all points on the spacetime manifold need possesses a "history," and the big bang is just such a point -- there is no (3+1)D time-evolved story to tell about the "cause" of the big bang. Thus, this "mystery" results from an inappropriate desire to tell dynamical stories where they're just not applicable.

 

[rkastner]

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

Great question, and that's why I advocate a realist interpretation of the wave function (more generally, projection of the state vector on the measured observable eigenspace). In fact the state vector does describe something real and that's why the theory needs it to correctly describe reality. The state vector describes a physical possibility. This interpretation can give a natural account of the Born Rule as the square of the wf. It is the transactional interpretation, with a new 'possibilist' approach. See my new book, which you can get for a 20% discount here:

http://www.cambridge.org/us/knowledg...US&code=L2TIQM

Also see my website, transactionalinterpretation.org, for introductory and preview material.

 

[akhmeteli]

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

You don't have wave function collapse in the path integral approach because the experimental outcome is a boundary condition, i.e., there is nothing being "time evolved," so there is nothing to "collapse." One is thinking spatiotemporally (4D) rather than dynamically ((3+1)D). By assuming 4Dism is the correct fundamental description and that not all 4D situations permit a (3+1)D story, MP and violation of the Bell inequality are no longer "mysterious," i.e., those are just situations where a 4D quantum result doesn't permit a (3+1)D time-evolved story.

I took a quick look at your interpretation. What's important to me, it looks like QFT is just a continuous approximation to a fundamental discrete theory in your interpretation, so you don't seem to consider standard quantum theory a precise theory. That's where we might agree.