Interpretations of Quantum for a Graduate Student

  • #1

Main Question or Discussion Point

Hi,

I'm a physics PhD student who is a little curious about interpretations of quantum mechanics (specifically Aharanov's Time-Symmetric theories and Relational interpretations, but others as well). I am interested specifically only in interpretations that are valid in QFT (I can't say I much see the point in considering non-relativistic interpretations) and I'd like to see some of the actual mathematical machinery of these interpretation (not just vague qualitative descriptions). I was wondering if anyone could point me to some of this sort of stuff (be it a book, an arxiv review paper, etc.). The more comprehensive and newbie friendly the better. I'd rather not be forced to go to the original papers since they are always quite terse, dense and pedantic.
 

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  • #2
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Hi maverick,

From what I understand, different philosophical interpretations of quantum mechanics are just different ways of talking about the same physics. For example, you might have learned about the Schrodinger picture; operators time independent, states changing in time, and the Heisinberg picture; operators time dependent, state time independent. These would be examples of alternative 'interpretations' of quantum mechanics; however, they give equivalent physical predictions.If we formulated the theory in a different way, such that it had different physical predictions, then it would be falsifiable and we could test whether or not our new interpretation is right. A historical example of this would be Bell's Inequality (its somewhere in Sakurai's quantum mechanics book) which gives a scenario of two different interpretations of quantum mechanics giving different physical results, and the one which survives is the one we use today.

I guess my point is, if you really want to start learning things relevant to QFT, I wouldn't waste time with extraneous philosophical interpretations and go straight to the most important mathematical interpretation of QM from a QFT perspective- the path integral. Many books do a good job; my favorite is Schredniki's QFT book(don't worry its in the beginning), but Sakurai does it pretty well also. A good understanding of the path integral is the key (and honestly almost all you really need) into being able to draw feynman diagrams and do typical QFT calculations. And if you go to high energy theory, everything from super symmetry to string theory is born from a path integral.
 
  • #3
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Hi maverick,

From what I understand, different philosophical interpretations of quantum mechanics are just different ways of talking about the same physics. For example, you might have learned about the Schrodinger picture; operators time independent, states changing in time, and the Heisinberg picture; operators time dependent, state time independent. These would be examples of alternative 'interpretations' of quantum mechanics; however, they give equivalent physical predictions.If we formulated the theory in a different way, such that it had different physical predictions, then it would be falsifiable and we could test whether or not our new interpretation is right. A historical example of this would be Bell's Inequality (its somewhere in Sakurai's quantum mechanics book) which gives a scenario of two different interpretations of quantum mechanics giving different physical results, and the one which survives is the one we use today.

I guess my point is, if you really want to start learning things relevant to QFT, I wouldn't waste time with extraneous philosophical interpretations and go straight to the most important mathematical interpretation of QM from a QFT perspective- the path integral. Many books do a good job; my favorite is Schredniki's QFT book(don't worry its in the beginning), but Sakurai does it pretty well also. A good understanding of the path integral is the key (and honestly almost all you really need) into being able to draw feynman diagrams and do typical QFT calculations. And if you go to high energy theory, everything from super symmetry to string theory is born from a path integral.
You're making unwarranted assumptions. How do you know the OP isn't already learned in standard formulations of QFT? Also, it is dismissive and ignorant to suggest that interpretation is irrelevant to QFT.

Maverick, to answer your question, there are a few major alternative formulations of QM (over and above the one's you listed): (1) De Broglie-Bohm pilot-wave theory, (2) Dynamical collapse models (e.g. GRW and CSL), (3) The Many-World's interpretations, (4) Stochastic field theory.

To my knowledge, the only considerable efforts that have been made for field-theoretic generalizations are in (1) and (4).

For (1), here is a major review article (also ask Demystifier for papers on his QFT-related work):

Pilot-wave theory and quantum fields
Authors: Ward Struyve
Comments: 65 pages, no figures, LaTex; v2 minor changes, some extensions; v3 minor improvements; v4 some typos corrected
Journal-ref: Rep. Prog. Phys. 73, 106001 (2010)
http://arxiv.org/find/quant-ph/1/au:+Struyve_W/0/1/0/all/0/1

For (2), I refer you to these papers:

Structural aspects of stochastic mechanics and stochastic field theory
Francesco Guerra
Physics Reports
Volume 77, Issue 3, November 1981, Pages 263-312
http://www.sciencedirect.com/scienc...9122cd0ec4a251d71e1ea7b6110b298b&searchtype=a

Field theory and the future of stochastic mechanics
Nelson, Edward
Stochastic Processes in Classical and Quantum Systems: Proceedings of the 1st Ascona-Como International Conference, Held in Ascona, Ticino (Switzerland), June 24–29, 1985. Editor: S. Albeverio, G. Casati, D. Merlini, Lecture Notes in Physics, vol. 262, p.438-469
http://adsabs.harvard.edu/abs/1986LNP...262..438N

QED Revisited: Proving Equivalence Between Path Integral and Stochastic Quantization
Authors: Helmuth Huffel, Gerald Kelnhofer
Comments: 11 pages
Journal-ref: Phys.Lett. B588 (2004) 145-150
http://arxiv.org/abs/hep-th/0312315

Relating Field Theories via Stochastic Quantization
Authors: Robbert Dijkgraaf, Domenico Orlando, Susanne Reffert
Comments: References added
Journal-ref: Nucl.Phys.B824:365-386,2010
http://arxiv.org/abs/0903.0732

For whatever it's worth, I am also a PhD graduate student (at Clemson University), and (4) and (1) are my areas of research focus and interest.
 
  • #4
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Well I guess I was speaking as a phenomenologist, so I personally don't find models that describe the same physics in a new way that interesting unless such models turn out to describe some new physics. I didn't mean to dismiss those researching alternative interpretations, but the point I'm trying to make is that it would be a better investment of time as a typical particle theory student to study new and unfamiliar physics, as opposed to the same physics in a new light. And I apologize for assuming any ignorance of the OP.
 
  • #5
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Well I guess I was speaking as a phenomenologist, so I personally don't find models that describe the same physics in a new way that interesting unless such models turn out to describe some new physics.
Well then you may be interested to know that (1), (2), and (4), do predict new physics.

I didn't mean to dismiss those researching alternative interpretations, but the point I'm trying to make is that it would be a better investment of time as a typical particle theory student to study new and unfamiliar physics, as opposed to the same physics in a new light.
OK, but how do you know that the OP is a particle theory student? Maybe he's currently undecided, or is working in condensed-matter theory, or quantum gravity, or statistical mechanics, or many other possible fields. Not all theorists who are versed in QFT are particle theorists.
 
  • #6
tom.stoer
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  • #7
Fredrik
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When I decided to try to understand "the" MWI a few years ago, I was having a hard time understanding the stuff I read. The more I understood, the more I was able to see how bad those articles were. Many of them contained serious mistakes, and none of them bothered to define terms like "theory" and "interpretation". The ones that tried to define the MWI did it by modifying QM so that it could no longer make predictions about results of experiments. I consider that a mutilation of QM, not an interpretation of it.

I haven't read much about other interpretations, and a part of the reason for that is that I now expect a vast majority of articles about interpretations to be of low quality. In particular I expect most of them to fail to properly define the interpretations they're talking about. So the best advice I can give you is to lower your expectations about the quality of the material you're going to read.

You mentioned the term "time symmetric", so you might be interested in the consistent histories approach. I've been meaning to read this article for a long time, but haven't really gotten around to it.
 
  • #8
A. Neumaier
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I am interested specifically only in interpretations that are valid in QFT (I can't say I much see the point in considering non-relativistic interpretations) and I'd like to see some of the actual mathematical machinery of these interpretation (not just vague qualitative descriptions). I was wondering if anyone could point me to some of this sort of stuff (be it a book, an arxiv review paper, etc.). The more comprehensive and newbie friendly the better. I'd rather not be forced to go to the original papers since they are always quite terse, dense and pedantic.
The most down to earth interpretation (i.e., the main stream view) is given in

A. Peres,
Classical interventions in quantum systems.
I. The measuring process
Phys. Rev. A 61, 022116 (2000).
http://arxiv.org/pdf/quant-ph/9906023
II. Relativistic invariance
Phys. Rev. A 61, 022117 (2000)
http://arxiv.org/pdf/quant-ph/9906034

A. Peres,
Quantum information and relativity theory
Rev. Mod. Phys. 76, 93–123 (2004)
http://arxiv.org/pdf/quant-ph/0212023

After having read that, you'll probably be immune against many potential infections in this area.
 
  • #9
A. Neumaier
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  • #11
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The most down to earth interpretation (i.e., the main stream view) is given in

A. Peres,
Classical interventions in quantum systems.
I. The measuring process
Phys. Rev. A 61, 022116 (2000).
http://arxiv.org/pdf/quant-ph/9906023
II. Relativistic invariance
Phys. Rev. A 61, 022117 (2000)
http://arxiv.org/pdf/quant-ph/9906034

A. Peres,
Quantum information and relativity theory
Rev. Mod. Phys. 76, 93–123 (2004)
http://arxiv.org/pdf/quant-ph/0212023

After having read that, you'll probably be immune against many potential infections in this area.
This is NOT the mainstream view among physicists who specialize in the field of quantum foundations. It's not even the mainstream view of the average physicist (the average physicist doesn't even think deeply enough about these issues to have a well-formed view). It may be the predominant view among quantum information theorists, but then you need to make that explicit. Otherwise, you're misleading the OP.
 
  • #12
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I haven't read much about other interpretations, and a part of the reason for that is that I now expect a vast majority of articles about interpretations to be of low quality. In particular I expect most of them to fail to properly define the interpretations they're talking about. So the best advice I can give you is to lower your expectations about the quality of the material you're going to read.
It seems that you're committing a hasty generalization here. The fact that the MWI papers you've read were of low quality is in no way an indication of the quality of the papers on other interpretations/formulations. But don't take my word for it - have a look for yourself at the papers I cited.

To the OP, I would advise to reject Fredrik's advice about having low expectations. Just delve into the topic with an agnostic stance, and let the quality of the research as a whole color your impressions of the field.
 
  • #13
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You're making unwarranted assumptions. How do you know the OP isn't already learned in standard formulations of QFT? Also, it is dismissive and ignorant to suggest that interpretation is irrelevant to QFT.

Maverick, to answer your question, there are a few major alternative formulations of QM (over and above the one's you listed): (1) De Broglie-Bohm pilot-wave theory, (2) Dynamical collapse models (e.g. GRW and CSL), (3) The Many-World's interpretations, (4) Stochastic field theory.

To my knowledge, the only considerable efforts that have been made for field-theoretic generalizations are in (1) and (4).

For (1), here is a major review article (also ask Demystifier for papers on his QFT-related work):

Pilot-wave theory and quantum fields
Authors: Ward Struyve
Comments: 65 pages, no figures, LaTex; v2 minor changes, some extensions; v3 minor improvements; v4 some typos corrected
Journal-ref: Rep. Prog. Phys. 73, 106001 (2010)
http://arxiv.org/find/quant-ph/1/au:+Struyve_W/0/1/0/all/0/1

For (2), I refer you to these papers:

Structural aspects of stochastic mechanics and stochastic field theory
Francesco Guerra
Physics Reports
Volume 77, Issue 3, November 1981, Pages 263-312
http://www.sciencedirect.com/scienc...9122cd0ec4a251d71e1ea7b6110b298b&searchtype=a

Field theory and the future of stochastic mechanics
Nelson, Edward
Stochastic Processes in Classical and Quantum Systems: Proceedings of the 1st Ascona-Como International Conference, Held in Ascona, Ticino (Switzerland), June 24–29, 1985. Editor: S. Albeverio, G. Casati, D. Merlini, Lecture Notes in Physics, vol. 262, p.438-469
http://adsabs.harvard.edu/abs/1986LNP...262..438N

QED Revisited: Proving Equivalence Between Path Integral and Stochastic Quantization
Authors: Helmuth Huffel, Gerald Kelnhofer
Comments: 11 pages
Journal-ref: Phys.Lett. B588 (2004) 145-150
http://arxiv.org/abs/hep-th/0312315

Relating Field Theories via Stochastic Quantization
Authors: Robbert Dijkgraaf, Domenico Orlando, Susanne Reffert
Comments: References added
Journal-ref: Nucl.Phys.B824:365-386,2010
http://arxiv.org/abs/0903.0732

For whatever it's worth, I am also a PhD graduate student (at Clemson University), and (4) and (1) are my areas of research focus and interest.
Small correction - The latter set of papers is for (4), not (2).
 
  • #14
A. Neumaier
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This is NOT the mainstream view among physicists who specialize in the field of quantum foundations. It's not even the mainstream view of the average physicist (the average physicist doesn't even think deeply enough about these issues to have a well-formed view). It may be the predominant view among quantum information theorists, but then you need to make that explicit. Otherwise, you're misleading the OP.
It is the dominant view among those who theoretically analyze real measurements and need precision in the concepts since they have to apply it to real work. This makes it mainstream.

That the views (1), (2) and (4) that you advocate in post #3 and #5 are not mainstream can be seen from the fact that (as you write in #5) they predict new physics -- physics for which there is not the slightest trace of evidence. And the many worlds view (3) in your list cannot be the mainstream view about relativistic measurements, since it has (in accordance with what you write in #3) hardly any published reflections on the relativistic case. One of the few exceptions is http://arxiv.org/pdf/quant-ph/0103092 , which is quite vague....
 
  • #15
Thank you for all your great responses thus far and I'm looking through the papers cited by Maaneli and Neumaier as we speak. In regards to speculations about my level/field I'm a condensed matter theorists whose only recently started going through statistical and quantum field theory from books like Altland and Simons, Fetter and Walecka, Peski and Schroeder, etc. However, this inquiry is more of a side interest for me, I'd like to take a more active interest in interpretation. However, and I may be totally wrong here, but I don't see how an interpretation can be classified as "possible" unless it holds up in QFT. I'm curious of how many of these metaphysical difficulties are transferred to a regime with lorentz invariance and second quantization. I'm interested in these thing but I know I'll just get lost if I try and learn from a treatment that gets bogged down in the mathematical minutae of perturbation expansions and renormalization. So I'm looking for a fairly gentle introduction (The occasional Gaussian integral or propogator or such is, of course, fine). However, I also don't want a qualitative discussion. As byzheng mentioned the example of schrodinger picture vs. heisenberg picture (vs. interaction picture), these are conceptual differences with identical mathematics, HOWEVER, they produce a change in notation that makes the concepts more intrinsic to the math. This is the kind of stuff I wouldn't mind seeing for a given interpretation (not just vague discussions). I'm particularly interested (based on VERY scant introduction) in the interpretations of Aharanov (time-symmetric theories) and in general those interpretations that jive with relativity and do away with the measurement paradox (i.e. no collapsing wavefunction). Again, thanks for the replies thus far
 
  • #16
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It is the dominant view among those who theoretically analyze real measurements and need precision in the concepts since they have to apply it to real work.
I'm not even sure that's true. In fact, Schlosshauer paints a picture of the field that seems to contradict your assertion:

"Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. "

Decoherence, the measurement problem, and interpretations of quantum mechanics
Authors: Maximilian Schlosshauer
Comments: 41 pages. Final published version
Journal-ref: Rev.Mod.Phys.76:1267-1305,2004
http://arxiv.org/abs/quant-ph/0312059


That the views (1), (2) and (4) that you advocate in post #3 and #5 are not mainstream can be seen from the fact that (as you write in #5) they predict new physics -- physics for which there is not the slightest trace of evidence.
Well I didn't claim that those views are mainstream. In fact, I was very careful with my words - I said that they are the major *alternative* interpretations and formulations of QM. And this is a statement that can be verified by looking up the conference talks at any quantum foundations conference, and also by doing a literature search.

BTW, the fact that there is no evidence for the predicted new physics is because these new predictions are beyond the limits of current experimental capabilities. But all that means is that we need to wait a little longer before the necessary experiments can be done.


And the many worlds view (3) in your list cannot be the mainstream view about relativistic measurements, since it has (in accordance with what you write in #3) hardly any published reflections on the relativistic case. One of the few exceptions is http://arxiv.org/pdf/quant-ph/0103092 , which is quite vague....
I think you're putting words into my mouth. I did not even claim that the many-worlds view is a mainstream view about relativistic measurements.
 
  • #17
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Thank you for all your great responses thus far and I'm looking through the papers cited by Maaneli and Neumaier as we speak. In regards to speculations about my level/field I'm a condensed matter theorists whose only recently started going through statistical and quantum field theory from books like Altland and Simons, Fetter and Walecka, Peski and Schroeder, etc. However, this inquiry is more of a side interest for me, I'd like to take a more active interest in interpretation. However, and I may be totally wrong here, but I don't see how an interpretation can be classified as "possible" unless it holds up in QFT. I'm curious of how many of these metaphysical difficulties are transferred to a regime with lorentz invariance and second quantization. I'm interested in these thing but I know I'll just get lost if I try and learn from a treatment that gets bogged down in the mathematical minutae of perturbation expansions and renormalization. So I'm looking for a fairly gentle introduction (The occasional Gaussian integral or propogator or such is, of course, fine). However, I also don't want a qualitative discussion. As byzheng mentioned the example of schrodinger picture vs. heisenberg picture (vs. interaction picture), these are conceptual differences with identical mathematics, HOWEVER, they produce a change in notation that makes the concepts more intrinsic to the math. This is the kind of stuff I wouldn't mind seeing for a given interpretation (not just vague discussions). I'm particularly interested (based on VERY scant introduction) in the interpretations of Aharanov (time-symmetric theories) and in general those interpretations that jive with relativity and do away with the measurement paradox (i.e. no collapsing wavefunction). Again, thanks for the replies thus far
You're welcome. I'd be interested in your reactions to some of the references I shared, once you've had time to look through them. BTW, I agree with your comment about an interpretation/formulation being untenable if it cannot ultimately hold up in a QFT context. I would only emphasize that, even though an interpretation/formulation may not yet have a QFT generalization, it does not mean that it is impossible. Unfortunately, one of the problems with the quantum foundations field is that many of the people who work on alternative interpretations are not well-versed in QFT, and as a result, progress in QFT extensions has been relatively slow. I would say though that this is an opportunity for young physicists like you and me to take the reigns and work these details out. :-)
 
  • #18
A. Neumaier
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I'm not even sure that's true. In fact, Schlosshauer paints a picture of the field that seems to contradict your assertion:
He says nothing about the relativistic case, so what he says is irrelevant for deciding which view of relativistic measurement theory is mainstream.
Well I didn't claim that those views are mainstream.
I didn't claim that you did. I just pointed out that the information you gave didn't support the claim you actually made:
This is NOT the mainstream view among physicists who specialize in the field of quantum foundations.
Please retract this claim, or substantiate it by giving evidence for what you consider to be (and why) the mainstream view about ''interpretations that are valid in QFT'', which is what the OP had asked for, and to which I answered.
BTW, the fact that there is no evidence for the predicted new physics is because these new predictions are beyond the limits of current experimental capabilities. But all that means is that we need to wait a little longer before the necessary experiments can be done.
It also means that we need to wait a little longer before this possibly becomes mainstream.
I think you're putting words into my mouth. I did not even claim that the many-worlds view is a mainstream view about relativistic measurements.
Neither did I claim that you did.
 
  • #19
A. Neumaier
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I'd like to take a more active interest in interpretation. However, and I may be totally wrong here, but I don't see how an interpretation can be classified as "possible" unless it holds up in QFT. I'm curious of how many of these metaphysical difficulties are transferred to a regime with lorentz invariance and second quantization. I'm interested in these thing but I know I'll just get lost if I try and learn from a treatment that gets bogged down in the mathematical minutae of perturbation expansions and renormalization.
To my knowledge, nobody ever considered foundational questions in the context of renormalization. (We don't even properly understand what renormalization means in terms of quantum states and finite-time dynamics, let alone how to interpret it in the context of measurement.)

Most interpretations get into severe difficulties once relativity is taken seriously. The only reasonably coherent (but still limited) point of view is that of Peres and his school.
So I'm looking for a fairly gentle introduction (The occasional Gaussian integral or propogator or such is, of course, fine). However, I also don't want a qualitative discussion.
You may wish to read Chapter A4 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#A4 , which discusses the interpretation of (mainly nonrelativistic) quantum mechanics, partly in quantitative terms.

For the relativistic case, beyond the work by Peres and some papers quoting it (to be found via http://scholar.google.com/ ), I think you'll have to create yourself what you hope to find.
If you do a good job, it will be a very welcome addition to the literature!
 
  • #20
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He says nothing about the relativistic case, so what he says is irrelevant for deciding which view of relativistic measurement theory is mainstream.
I think we're talking past each other. I made an assertion about what are the major alternative interpretations and formulations of QM, not just relativistic measurement theory.

I didn't claim that you did. I just pointed out that the information you gave didn't support the claim you actually made
The information I gave wasn't intended to support my claim, but in any case, once you see that the claim I made was different from yours, I don't think you'll disagree with it.

Please retract this claim, or substantiate it by giving evidence for what you consider to be (and why) the mainstream view about ''interpretations that are valid in QFT'', which is what the OP had asked for, and to which I answered.
OK, on the basis of the OP's original post, I concede that your initial response was fair enough. But now that the OP has clarified that "I'm particularly interested (based on VERY scant introduction) in the interpretations of Aharanov (time-symmetric theories) and in general those interpretations that jive with relativity and do away with the measurement paradox (i.e. no collapsing wavefunction).", I would maintain that the papers you posted by Peres et. al do not satisfy the OP's criteria, since none of those papers show how the measurement paradox is solved in either the nonrelativistic or relativistic measurement theories they discuss.
 
  • #21
To my knowledge, nobody ever considered foundational questions in the context of renormalization. (We don't even properly understand what renormalization means in terms of quantum states and finite-time dynamics, let alone how to interpret it in the context of measurement.)

Most interpretations get into severe difficulties once relativity is taken seriously. The only reasonably coherent (but still limited) point of view is that of Peres and his school.
But surely whether the measurement paradox still exists in QFT in all its glory must be well known. Otherwise what is the point of considering interpretations at all until that's known.
 
  • #22
Fredrik
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But surely whether the measurement paradox still exists in QFT in all its glory must be well known. Otherwise what is the point of considering interpretations at all until that's known.
There is no measurement problem in what I would call "quantum mechanics". I would only include the assumptions that are necessary to make predictions. The measurement problem appears when you make additional assumptions on top of that. People often make such assumptions without even realizing it. These are the two most common ones: 1. The wavefunction describes what the system is "actually doing" at all times. 2. There's only one world.

I believe that these two assumptions are incompatible (and they are definitely unnecesary), but I can't prove this rigorously, or even state it in the form of a theorem, because it's not even 100% clear what those statements really mean.

So does the measurement problem "still" exist in QFT? If we make unnecessary assumptions that gets us into trouble in the context of single-particle theories, and non-interacting multiple-particle theories, they will certainly not go away when we bring interactions into the picture as well.
 
  • #23
tom.stoer
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I think a common assumption is that a quantum state describes what a system "is"; if one drops this assumption and assumes that the state describes what an observer "knows" the measurement problem is shifted from the system to the observer. This does not avoid the problem at all, but it avoids the conclusion that the "collaps of the wave function" or the "many worlds" are something physical.
 
  • #24
Fredrik
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I think a common assumption is that a quantum state describes what a system "is"; if one drops this assumption and assumes that the state describes what an observer "knows" the measurement problem is shifted from the system to the observer.
I can't say I have ever understood what the advocates of the "knowledge" interpretation mean by "knowledge of the system". To me, the choice of words strongly suggests all those things that we have learned to reject, e.g. that a particle has a well-defined position at all times and that we just don't know what it is.

I would be OK with the statement that a mathematical state represents our knowledge of the system, if "our knowledge of the system" is defined to mean something like "the set of statements about (probabilities of) results of measurements that will agree with experiment in a long series of measurements on identically prepared systems". But that can't be what they mean, because if they did, they would probably say something like that instead.

Anyone know if these people have ever defined what "knowledge of the system" means?
 
  • #25
tom.stoer
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I would like to add an idea which is influenced by the holographic principle.

Assume that we divide the universe into two disjoint sets, namely a closed region, our "system" which is equipped with a surface Hilbert space on which we model what we "know" about that system and "the rest of world" which is located outside and which serves as an "observer" who "knows" something about the system. So the artificial split introduced an artificial surface on which an artificial collaps (or according to MWI an artificial branching) will happen.

Trying to find an "ontological" interpretation of quantum mechanics (or quantum field theory) must not start from an Hilbert space but from the collection of all Hilbert constructed according to the above mentioned splits. I do not know whether this has been done so far.
 

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