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Is wave function a real physical thing?

  1. Dec 21, 2014 #1
    Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object? I know that it's widely known that it's just an equation however some researchers say that they have proof that it's real.
    Here is the link.
    http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
    Does this prove that wave function is a real physical object after all?
     
  2. jcsd
  3. Dec 21, 2014 #2
    Thanks for sharing the article, it is really interesting.

    To your question: The wave equation conventionally is not considered "real". Rather, its square gives the probability.

    -------------------

    Örsan Yüksek
     
  4. Dec 21, 2014 #3

    atyy

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    No, this does not show that the wave function is real. It only shows it under some assumptions, which are not obviously required. Counterexamples to a real wave function have been constructed: http://arxiv.org/abs/1201.6554, http://arxiv.org/abs/1303.2834.

    There is also the interesting comment in http://arxiv.org/abs/0706.2661 that Wiseman suggests that even within Bohmian Mechanics, the wave function is not necessarily real - this was highlighted to me by Bohm2: "Inspired by this pattern, Valentini has wondered whether the pilot-wave (and hence ontic) nature of the wave function in the deBroglie-Bohm approach might be unavoidable [77]. On the other hand, it has been suggested by Wiseman that there exists an unconventional reading of the deBroglie-Bohm approach which is not ψ-ontic [78]. A distinction is made between the quantum state of the universe and the conditional quantum state of a subsystem, defined in Ref. [79]. The latter is argued to be epistemic while the former is deemed to be nomic, that is, law-like, following the lines of Ref. [80] (in which case it is presumably a category mistake to try to characterize the universal wave function as ontic or epistemic)."
     
  5. Dec 21, 2014 #4
    The article is dated November 2011. So, I would think any question about its importance would be settled by now.
     
  6. Dec 21, 2014 #5

    bhobba

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    Its the well known and important PBR theorem:
    http://lanl.arxiv.org/pdf/1111.3328v3.pdf

    Note what the paper says:
    'The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

    Both Copenhagen and the Ensemble interpretation reject exactly that assumption.

    Indeed more work has been done clarifying it eg:
    http://arxiv.org/abs/1203.4779

    It turns out for every model where it holds you can find one that evades it and conversely.

    Thanks
    Bill
     
  7. Dec 21, 2014 #6

    atyy

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    Of course, such a rejection is unscientific. Consequently, there are flavours of Copenhagen that do not reject such an assumption.
     
  8. Dec 21, 2014 #7

    Nugatory

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    This article is way better than most (not surprising, as Nature is a source way better than most) in that it includes a link to the actual work being discussed: http://lanl.arxiv.org/abs/1111.3328. It's a preprint, and a final version of the paper (sadly, behind a paywall) was published in 2012. Googling for "PBR theorem" will find some more discussion since then.

    Getting a paper through peer review and into publication doesn't automatically establish the paper as truth. Instead it starts the process of connecting the new insight to what is already understood, working out the implications across various fields of study, seeing where the new insight can shed new light on previously intractable problems, discovering what we can build on top of it.

    So, no, this paper does not prove that the wave function is a real physical object. It does provide a serious argument and a proof by example that there is something new to say on the subject.
     
  9. Dec 21, 2014 #8
    So what do you personally think, do you think the wave function is real and physical, or just a mathematical tool?
     
  10. Dec 21, 2014 #9

    Nugatory

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    I neither know nor care. The question will only become interesting when someone can:
    1) Clearly define exactly what the words "real and physical" mean.
    2) Clearly define exactly what the words "just a mathematical tool" mean.
    3) After these terms have been defined, describe an experiment that will produce different results if the wave function is real and physical than if it just a mathematical tool.

    It's not impossible that this could happen. In 1935 Einstein posed a then-unanswerable question about quantum mechanics (google for "EPR paper"); thirty years later John Bell (google for "Bell's theorem") proposed definitions and an experiment that could settle the question; and since then the experimental results have been coming in. The question is now largely settled.

    But unless and until something like that happens here .. Your question (which in the literature goes by the term "psi-ontic versus psi-epistemic") is sterile except when someone has something new to say. The PBR theorem may be such a thing, but it's way too soon and there is way too little experimental data to know.
     
  11. Dec 21, 2014 #10
    re
    The PBR theorem only rules out Ψ-epistemic models. So one can't assume that the wavefunction is just our knowledge about some underlying ontic state. Such models are ruled out by PBR (given a few reasonable assumptions). So, either one must accept the wave function as being ontic or accept non-realism (i.e. Ψ does not represent some deeper underlying reality as per instrumental/Copenhagen-type interpretations).

    Having said that, one of the reasonable assumptions of the PBR theorem which has been most questioned by some authors is the Preparation Independence assumption. Leifer goes into a lot of detail of this PBR assumption in his most recent paper on this topic:

    Is the quantum state real? A review of Ψ-ontology theorems
    http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf
     
    Last edited: Dec 21, 2014
  12. Dec 21, 2014 #11

    bhobba

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    Exactly.

    Gleason's theorem, by showing the state follows from the properties of observables, suggests the exact oppose:
    https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

    See post 137.

    Who is right? Blowed if I know - opinions are like bums - everyone has one - it doesn't make it right. What we need is experiment to decide.

    Thanks
    Bill
     
  13. Dec 21, 2014 #12

    bhobba

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    Personally I find what Gleason says very persuasive - its simply a requirement of non-contextuality - without going into what that is exactly. Its just a mathematical tool that helps calculate the probabilities of outcomes. But that's just my opinion and without experiment to decide it means diddly squat.

    Thanks
    Bill
     
  14. Dec 21, 2014 #13
    Just to add to this topic, 3 experiments have actually been done to test the ontic/epistemic status of the wave function:

    Can different quantum state vectors correspond to the same physical state? An experimental test
    http://lanl.arxiv.org/pdf/1211.0942.pdf[/B]

    Experimentally probing the reality of the quantum state
    http://lanl.arxiv.org/pdf/1211.1179.pdf

    Measurements on the reality of the wavefunction
    http://arxiv.org/pdf/1412.6213.pdf

    The last one was just published today. Unfortunately, as Leifer points out there are limitations in all these type of experiments:
    http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf
     
  15. Dec 22, 2014 #14

    atyy

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    I view things differently. There already are proposals to test deviations from quantum mechanics such as http://arxiv.org/abs/1407.8262 and http://arxiv.org/abs/1410.0270. I view the PBR theorem and other similar investigations as analogous to the Weinberg-Witten theorem, which is also "sterile" in that it does not point to any specific deviation from quantum general relativity. Yet the Weinberg-Witten theorem is usually not considered sterile, but an important no-go theorem.
     
  16. Dec 22, 2014 #15
    It always amazes me when physicists need to have defined the object and tools of their discipline, shouldn't they know what it is they are subjecting to study, and what they are using to analyze it(mathematical tools, right?)
    I mean imagine a doctor who gets asked about a possible disease and treatment of a patient, that claims that just to start doing something requires somebody giving exact and clear definitions of disease, medical instruments and patient(like he shoudn't have some notion after years of study), and to any definition the reply was: "That's philosophy, not medicine".
    Even more amazing is when this bewilderment is quite often used to to suggest there is not such an object, not realizing that would deny physics as the study of physical phenomena.

    Again, this seems befuddled. Not requiring an experiment, rather the part about the goal of the experiment. Shouldn't the goal of a good experiment serve to ascertain whether or not the wavefunction(that is, the mathematical model) describes accurately and completely the physics, that is, the phenomena we observe? My understanding is that in general this is what experiments are for.

    The truth is that the OP question is not well formulated from the start. If we only understand the wave function in statistical terms of states of the system it is too easy to run into trouble, why not stop ignoring that NRQM is currently superseded by QFT as a model of nature? In QFT the wavefunction is not very useful in the way it is described in NRQM, it is not describing a (position eigenvector projection of a) state anymore, since there are no states except for the vacuum, it is an operator(functional) instead, in a particular configuration of field disturbances where Schrodinger space of positions(also remember position is no longer an operator here) picture is not very illuminating nor useful .
     
    Last edited: Dec 22, 2014
  17. Dec 22, 2014 #16

    bhobba

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    That's not the issue - the issue is getting any kind of agreement on things like that. It's much easier to move forward - and has proven very useful.

    Thanks
    Bill
     
  18. Dec 22, 2014 #17

    vanhees71

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    For an experimental physicist it's pretty clear what he is doing when setting up an experiment, say a particle collision at the LHC: He shoots bunches of protons head on and then counts (the part of ) particles emerging by this reaction using a bunch of detectors to figure out, which particles come out, which momenta they have, etc. Then he's doing very many such experiments to "gain statistics" and get a nice bumb in a certain reaction cross section telling him that he has indeed created something that was predicted by his theoretical colleagues using sophisticated math, like Higgs did in the 60ies when he predicted the famous scalar boson named after him. Since the CMS and ATLAS collaboration have achieved this with a pretty high statistical significance of more than 5 standard deviations, it's called a discovery and earned Higgs and Englert the Nobel prize in physics of 2013.

    The experimentalist (and to be honest almost all theorists working in this field either) doesn't bother much about the entirely philosophical question, whether there is an ontic interpretation of probabilities (and it all boils down to an ontic interpretation of probabilities since the wave function in non-relativistic quantum theory or more generally the S-matrix elements are a specific way to calculate probabilities for a given setup of the quantum objects under consideration) or not. It's simply irrelevant for physics: There's a clear experimental setup with a well-known characteristics concerning the uncertainties in the "state preparation" and the "measurement" (to know the detector characteristic and have a reliable estimate of its systematic uncertainties is the key work of an experimentalist) with a clear statistical result that can be compared to the probabilities (cross sections) calculated by the theorist within a given model, and this comparison can rule out the model or strengthen our confidence in it. The standard model is good in strengthening our confidence in it although we'd like to find deviations from it, because there are some problems we'd like to solve by finding an even better model, but so far there's no clear result contradicting the standard model (the most promising at the moment seems to be the anomalous magnetic moment of the muon, but (a) the deviation is around 3 sigmas only, which is no discovery but only evidence and (b) there's still some uncertainty concerning the hadronic contributions to the theoretical prediction which is in the same ballpark as the experimental uncertainties). That's what physics is about and not the vague question if some highly abstract Hilbert space structure is "real" ("ontic") or only descriptive ("epistemic").

    On top of this irrelevance of these metaphysical problems for physics it's also quite unsharply formulated, i.e., it's not clear from a physical point of view, what's meant by these notions. It indeed only becomes an interesting physical question, when one can find an experimental setup to distinguish between these two possibilities, but as far as I can see from all these debates, it's not even clear, what's the difference between the two in this physical hard sense of a question!
     
  19. Dec 22, 2014 #18

    atyy

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    Well, is the Weinberg-Witten theorem also "metaphysical" and addressing a problem that is unsharply formulated?
     
  20. Dec 22, 2014 #19

    vanhees71

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    The Weinberg-Witten theorem is a mathematical statement about (asymptotic free!) single-particle states in connection with the existence of a covariant conserved current carried by massless particles. It's a clear statement and a not too difficult proof, which you can even find in the Wikipedia:

    http://en.wikipedia.org/wiki/Weinberg–Witten_theorem

    It's not about some vaguely defined philosophical idea.
     
  21. Dec 22, 2014 #20

    atyy

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    It's about a vaguely defined philosophical idea called Wilsonian renormalization and effective field theory. According to Wilson, non-renormalizable theories like general relativity are acceptable as effective theories, and there are "hidden variables" or more fundamental degrees of freedom at energies near the Planck scale. The Weinberg-Witten theorem shows that the hidden variables of Wilson cannot be described by a relativistic 4 dimensional quantum field theory.
     
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