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How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics

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Many people here know that I am a “Bohmian”, i.e. an adherent of a very non-orthodox interpretation of quantum mechanics (QM). Indeed, in the past I have published a lot of papers on Bohmian mechanics in peer reviewed journals from 2004 to 2012. So how can I not worry and love orthodox QM? As a “Bohmian”, shouldn’t I be strictly against orthodox QM?

No. If, by orthodox QM, one means instrumental QM (which is well explained in the book “Quantum Theory: Concepts and Methods” by A. Peres), then orthodox QM is fully compatible with Bohmian QM. I am not saying that they are equivalent; indeed Bohmian QM offers answers to some questions on which instrumental QM has nothing to say. But I am saying that they are compatible, in the sense that no claim of instrumental QM contradicts any claim of Bohmian QM.

But still, if instrumental QM has nothing to say about certain questions, then why am I not worried? As a “Bohmian”, I certainly do not consider those questions irrelevant. So how can I not worry about it when it says nothing about questions that I find relevant?

The answer is that I stopped worrying and learned to love orthodox QM precisely because I know about Bohmian QM. But let me explain it from the beginning.

I always wanted to study the most fundamental aspects of physics. Consequently, as a student of physics I was much more fascinated by topics such as particle physics and general relativity than about topics such as condensed-matter physics. Therefore, my graduate study in physics and my PhD were in high-energy physics. Nevertheless, all the knowledge about quantum field theory (QFT) that I acquired as a high-energy physicists did not help me much to resolve one deep puzzle that really bothered me about QM. The thing that bothered me was how could Nature work like that? How could that possibly be? What could be a possible physical mechanism behind the abstract rules of QM? Should one conclude that there is no mechanism at all and that standard QM (including QFT) is the end of story?

But then I learned about Bohmian QM, and that was a true revelation. It finally told me a possible story how could that be. It didn’t definitely tell how it is (there is no direct evidence that Bohmian mechanics is how Nature actually works), but it did tell how it might be. It is comforting to know that behind the abstract and seemingly paradoxical formalism of QM may lie a simple intuitive mechanism as provided by Bohmian QM. Even if this mechanism is not exactly how Nature really works, the simple fact that such a mechanism is possible is sufficient to stop worrying and start to love instrumental QM as a useful tool that somehow emerges from a more fundamental mechanism, even if all the details of this mechanism are not (yet) known.

However, something important was still missing. Bohmian QM looks nice and simple for non-relativistic QM, but how about relativistic QFT? In principle, Bohmian ideas of that time worked also for relativistic QFT, but they did not look so nice and simple. My question was, can Bohmian ideas be modified such that it looks nice, simple and natural even for relativistic QFT? That question motivated my professional research on Bohmian QM and I published a lot of papers on that.

Nevertheless, I was not completely satisfied with my results. Even though I made several interesting modifications of Bohmian QM to incorporate relativistic QFT, neither of those modifications looked sufficiently simple and natural. Moreover, in arXiv:1309.0400, the last specialized paper on Bohmian mechanics I have written, a referee found a deep conceptual error that I was not able to fix. After that, I was no longer trying to modify Bohmian QM in that way.

Nevertheless, a partial satisfaction came from a slightly different angle. In an attempt to make sense of local non-reality interpretation of QM, I developed a theory of solipsistic hidden variables which is a sort of a hybrid between Bohmian and Copenhagen QM. In this theory an observer does play an important role, in the sense that Bohmian-like trajectories exist only for degrees of freedom of the observer and not for the observed objects. That theory helped me to learn that, in order to understand why do we observe what we observe, it is not necessary to know what exactly happens with observed objects. Instead, as solipsistic hidden variables demonstrate, in principle it can be understood even if the observed objects don’t exist! It was a big conceptual revelation for me that shaped my further thinking about the subject.

But it does not mean that I became solipsist. I don’t believe that observed objects don’t exist. The important message is not that observed objects might not exist. The important message is that the exact nature of their existence is not really so important to explain their observation. That idea helped me a lot to stop worrying and learn to love orthodox QM.

But that was not the end. As I said, in my younger days, my way of thinking was largely shaped by high-energy physics and not by condensed-matter physics. I thought that condensed-matter physics cannot teach me much about the most fundamental problems in physics. But it started to change in 2010, when, by accident, I saw in Feynman Lectures on Physics that Bohmian mechanics is related to superconductivity (see here) That suddenly made me interested in superconductivity. But superconductivity cannot be understood without understanding other more basic aspects of condensed-matter physics, so gradually I became interested in condensed-matter physics as a field. One very interesting thing about condensed-matter physics is that it uses QFT formalism which is almost identical to QFT formalism in high-energy physics, but the underlying philosophy of QFT is very different. Condensed-matter physics taught me to think about QFT in a different way than I was used to as a high-energy physicists.

One of the main conceptual differences between the two schools of thought on QFT is the interpretation of particle-like excitations resulting form canonical quantization of fields. In high-energy physics, such excitations are typically interpreted as elementary particles. In condensed-matter physics, they are usually interpreted as quasiparticles, such as phonons. Since I was also a Bohmian, that led me to a natural question: Does it make sense to introduce a Bohmian trajectory of a phonon? An obvious (but somewhat superficial) answer is that it doesn’t make sense because only true particles, and not quasiparticles, are supposed to have Bohmian trajectories. But what is a “true” particle? What exactly does it mean that a photon is a “true” particle and a phonon isn’t?

It was this last question that led me to my last fundamental insight about Bohmian mechanics. As I explained in Sec. 4.3 of arXiv:1703.08341 (accepted for publication in Int. J. Quantum Inf.), the analogy with condensed-matter quasiparticles such as phonons suggests a very natural resolution of the problem of Bohmian interpretation of relativistic QFT. According to this resolution, the so-called “elementary” particles such as photons and electrons described by relativistic QFT are not elementary at all. Instead they are merely quasiparticles, just as phonons. Consequently, those relativistic particles do not have Bohmian trajectories at all. What does have Bohmian trajectories are some more fundamental particles described by non-relativistic QM. Non-relativistic QM (together with Bohmian interpretation) is fundamental, while relativistic QFT is emergent. In this way, the problem of Bohmian interpretation of relativistic QFT is circumvented in a very elegant way.

There is only one “little” problem about that idea. There is no any experimental evidence that such more fundamental non-relativistic particles actually exist in Nature. Perhaps they will be discovered one day in the future, but at the moment it is only a theory. In fact it is not even a proper theory, because it cannot tell anything more specific about the exact nature of those hypothetical non-relativistic particles.

Nevertheless, there are at least two good things about that. First, unlike most other versions of Bohmian mechanics, this version makes a testable prediction. It predicts that, at very small distances not yet accessible to experimental technology, the Nature is made of non-relativistic particles. Second, at distances visible by current experimental technology, this version of Bohmian QM says that Bohmian trajectories are irrelevant. This means that, as far as relativistic QFT is concerned, I do not need to worry about Bohmian trajectories and can love orthodox QFT, without rejecting “common sense” in the form of non-relativistic Bohmian mechanics on some more fundamental scale. That’s how I finally I stopped worrying and learned to love orthodox QM.

 

 

Theoretical physicist from Croatia
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  1. Physics Footnotes
    Physics Footnotes says:

    Thanks for the stimulating read. I too have come to the conclusion in recent years that anyone serious about the Foundations of Physics must thoroughly acquaint themselves with Bohmian Mechanics; not necessarily because it will turn out to be correct, but because it provides the most coherent and well fleshed-out alternative to the usual bare-bones view of QM.

    I find your idea of taking QM as fundamental, while QFT as emergent, particularly interesting, except for one thing. You talk of non-relativistic particles, but I'm not sure how such things could exist, since we know spacetime, even locally, is not Galilean. Wouldn't the fundamental theory, in your assumed view, have to relativistic QM rather than non-relativistic? To put it a different way, how could we have particles existing in the world which respect Galilean spacetime, but not Minkowskian spacetime, when the latter is the one we know to actually be the case (or at least to be closer to the truth than the former)?

  2. Demystifier
    Demystifier says:
    atyy

    Are you worried about the chiral fermion problem, which seems to me the remaining problem in realizing the standard model using non-relativistic QM?

    I consider it to be a technical problem, with some proposed solutions already existing. So I do not worry too much.

  3. Demystifier
    Demystifier says:
    Physics Footnotes

    since we know spacetime, even locally, is not Galilean

    What we know is that spacetime does not appear Galilean at "large" distances (e.g. distances much larger than the Planck distance). How does it appear at very small distances, we don't know that.

  4. bahamagreen
    bahamagreen says:

    "What does have Bohmian trajectories are some more fundamental particles…"

    Above, at, or below string level?
    Multiples of multiple types?
    Multiples of one type?
    One each of multiple types?
    One only of only one type? It would have to really get around, but how elegant.

  5. zonde
    zonde says:
    Demystifier

    Even if this mechanism is not exactly how Nature really works, the simple fact that such a mechanism is possible is sufficient to stop worrying and start to love instrumental QM as a useful tool that somehow emerges from a more fundamental mechanism, even if all the details of this mechanism are not (yet) known.

    Well said.

  6. zonde
    zonde says:
    Physics Footnotes

    You talk of non-relativistic particles, but I'm not sure how such things could exist, since we know spacetime, even locally, is not Galilean. Wouldn't the fundamental theory, in your assumed view, have to relativistic QM rather than non-relativistic? To put it a different way, how could we have particles existing in the world which respect Galilean spacetime, but not Minkowskian spacetime, when the latter is the one we know to actually be the case (or at least to be closer to the truth than the former)?

    It is interesting that possibility of relativity principle not being fundamental is generally not considered.

  7. Demystifier
    Demystifier says:
    bahamagreen

    "What does have Bohmian trajectories are some more fundamental particles…"

    Above, at, or below string level?

    There are 3 possibilities:
    1) String theory is wrong. In this case the hypothetical fundamental distance ##l_{rm nr}## at which Nature starts to look non-relativistic is not related to the string scale ##l_{rm string}##.
    2) String theory is correct, but only as an effective theory. In this case ##l_{rm nr}ll l_{rm string}##.
    3) String theory is correct as the fundamental theory of everything. In this case my theory is wrong and there is no such thing as ##l_{rm nr}##.

    bahamagreen

    Multiples of multiple types?
    Multiples of one type?
    One each of multiple types?
    One only of only one type? It would have to really get around, but how elegant.

    Sorry, I don't understand the questions. Any hint?

  8. atyy
    atyy says:
    Demystifier

    There are 3 possibilities:
    1) String theory is wrong. In this case the hypothetical fundamental distance ##l_{rm nr}## at which Nature starts to look non-relativistic is not related to the string scale ##l_{rm string}##.
    2) String theory is correct, but only as an effective theory. In this case ##l_{rm nr}ll l_{rm string}##.
    3) String theory is correct as the fundamental theory of everything. In this case my theory is wrong and there is no such thing as ##l_{rm nr}##.

    I think a variant of (2) is that string theory is correct only as an effective theory, but when string theory fails, there is no more spacetime, so ##l_{rm nr}## does not exist, eg. gauge/gravity where the gauge theory is emergent from non-relativistic QM.

  9. bahamagreen
    bahamagreen says:

    Sorry, what I meant was have you excluded any of these possibilities for the more fundamental particle(s) ?

    Multiple particles of multiple types?
    Multiple particles of one type?
    One particle each of multiple types?
    One particle only of only one type?

  10. Demystifier
    Demystifier says:
    atyy

    I think a variant of (2) is that string theory is correct only as an effective theory, but when string theory fails, there is no more spacetime, so ##l_{rm nr}## does not exist, eg. gauge/gravity where the gauge theory is emergent from non-relativistic QM.

    Sure, 2) has an infinite number of versions, including this one.

  11. Demystifier
    Demystifier says:
    bahamagreen

    Sorry, what I meant was have you excluded any of these possibilities for the more fundamental particle(s) ?

    Multiple particles of multiple types?
    Multiple particles of one type?
    One particle each of multiple types?
    One particle only of only one type?

    I still don't understand what do you mean by "one particle". That the whole universe contains only one particle? That's excluded.
    Concerning the number of particle types, I cannot exclude any possibility.

  12. vanhees71
    vanhees71 says:

    What I find not so convincing about the final conclusion of the article is the fact that obviously nature is not Newtonian but relativistic, as is shown also in the domain of physics, where classical approximations are valid. There seems to be really a limiting speed, ##c##, and it seems to be universal no matter of which system is studied.

    Of course, you have also in non-relativstic (condensed-matter) physics quasiparticles with relativistic dispersion relations and a lot of quite "exotic" features (Weyl fermions, magnetic monopoles, anyons ans what not has been discovered in the sense of quasiparticles but seem not to exist on a fundamental level), but these are only valid in the quasiparticle approximation and in fact describe collective low-energy excitations of the matter as a whole. At some point the non-relativistic approximation breaks down, and you have to use relativistic models.

  13. Demystifier
    Demystifier says:
    vanhees71

    There seems to be really a limiting speed, c, and it seems to be universal no matter of which system is studied.

    It seems, but we don't know if this persists at even smaller distances than available by current experimental technology. The default hypothesis is that it persists, but a hypothesis that it doesn't is also legitimate and Bohmian mechanics is not the only motivation for such a "heretic" hypothesis. See e.g. Horava gravity.

  14. vanhees71
    vanhees71 says:

    Well, I don't see any merit of Bohmian mechanics to begin with. It just assumes unobservable "trajectories" in non-relativistic QT and otherwise predicts the same thing as QT in its minimal quantization. So this argument doesn't convince me too much. I've to check out what Horava gravity might be.

  15. Demystifier
    Demystifier says:
    vanhees71

    Well, I don't see any merit of Bohmian mechanics to begin with.

    Of course. The insight article is about how I stopped worrying and learned to love orthodox QM. It does not say that everyone should follow the same path. When all think alike, then nobody thinks much.

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