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Quantum Mechanics Just Got Less Complicated - Really?

  1. Dec 19, 2014 #1

    bhobba

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    I came across the following from a post in another thread:
    http://phys.org/news/2014-12-quantum-physics-complicated.html#jCp

    The wave particle duality the same as the uncertainty principle in disguise?

    Posting in this forum there is zero doubt they are two of the most misunderstood principles of QM.

    My suspicion is that connection will require a bit of tweaking on what the concepts mean - but will reserve my final opinion until I can get a hold of the article.

    One positive is that article makes a reasonable fist of stating the principles correctly which is a bit unusual in the popular press.

    Thanks
    Bill
     
  2. jcsd
  3. Dec 19, 2014 #2
  4. Dec 19, 2014 #3

    bhobba

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    Its not something that can be violated anyway. The correct statement is sometimes QM particles behave like waves, and sometimes like classical particles but most of the time its neither. To know when that sometimes is and exactly what like means you have to invoke the full QM theory.

    People often get confused about it and IMHO its best consigned to the dustbin.

    QM objects behave like - QM objects. Best to face it squarely without crux's.

    Thanks
    Bill
     
    Last edited: Dec 19, 2014
  5. Dec 19, 2014 #4
    Here is the preprint on arxiv: http://arxiv.org/abs/1403.4687
    Equivalence of wave-particle duality to entropic uncertainty
    Patrick J. Coles, Jędrzej Kaniewski, and Stephanie Wehner
    (Submitted on 19 Mar 2014 (v1), last revised 16 Sep 2014 (this version, v2))

    Abstract:
    Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle’s path inside the interferometer. This idea has been formulated quantitively as an inequality, e.g., by Englert and Jaeger, Shimony, and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg’s uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.
     
  6. Dec 19, 2014 #5

    bhobba

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    Had a quick squiz.

    It said:
    'Yet Feynman’s quote seems to suggest a belief that quantum mechanics has but one mystery and not two separate ones'

    It has but one mystery - the laws of QM. They can be explained in multiple ways - or simply postulated.

    All the rest is simply personal opinion.

    That said it is interesting in that its being quite precise about some of these things like wave-particle duality - which elevates the discussion somewhat.

    Thanks
    Bill
     
    Last edited: Dec 19, 2014
  7. Dec 20, 2014 #6

    vanhees71

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    Well, from the phys.org article I don't even see what's a breakthrough here, because that what I learned in my quantum-theory-1 lecture, when we started with the usual heuristics of the formulation of non-relativistic QT as "wave mechanics" a la Schrödinger. The uncertainty relation between position and momentum is very natural since the wave function in momentum representation is the Fourier transform of the wave function in position representation and of course vice versa since the inverse of the Fourier transformation is a Fourier transformation (with a simple sign change in the exponential) too. Now it's easy to prove that the width of a wave packet in position representation is (at least qualitatively) proportional to the inverse width in momentum representation and vice versa. So "wave-particle duality" and the position-momentum uncertainty are very naturally connected in the wave-mechanics representation of quantum theory.

    Now, fortunately our professor had thought much more carefully about the foundations of QT, and very soon he told us that there is no wave-particle duality but just quantum kinematics and dynamics + the Born rule, i.e., the probabilistic meaning of the quantum theory. Also the connection to information theory (with the von-Neumann-Shannon-Jaynes entropy as a measure for missing information, given a probability distribution, which turns out to be the same as thermodynamic entropy). So there is no surprise for me here, but of course, I've to read the original paper first to get a more qualified opinion.

    Another question is, how "complicated" quantum theory is. This is a very subjective question of course. As a student, I had the feeling that quantum mechanics 1 (non-relativistic quantum theory) is "less complicated" than classical electromagnetism, as far as the formalism and the math is involved. It's much simpler a task to solve the Schrödinger equation or manipulate Hilbert-space vectors in terms of "bras and kets" and "operators" than to solve a complicated charge-current-field problem with boundary conditions and what not in classical electromagnetism.

    On the other hand, quantum theory is "more complicated" than any classical physics, because the latter usually describes directly observables in a deterministic way. There may be auxiliary quantities for convenience and elegance of calculation (like the scalar and vector potentials in electromagnetism, which are not observable but used to derive the observable electromagnetic field finally), but in principle everything in the formalism is pretty easily mapped to what's measured in the lab.

    That's not so easy in QT, as we all know from all our lively discussions on interpretation in this forum and the sometimes seemingly pretty bizarre implications of entanglement (possibility of postselection as in the quantum-eraser experiment, the strong correlations of totally indetermined quantities as the polarizations of polarization entangled photons in this and the quantum-teleportation experiment, or (for me the most fascinating example) the possibility to separate properties of the same particle at separate locations as in the Chesire-cat experiment with neutrons). Usually, after reading the papers of such experiments, I can pretty easily follow the formal analysis of these experiments with pretty simple calculations in quantum theory, but the phenomena as such are not so easy to comprehend intuitively. The reason is of course, that in our everyday experience we deal with macroscopic objects in interaction with the environment, so that coherence and entanglement are "washed out" or "course grained" by our quite unprecise persception of the objects around us.
     
  8. Dec 21, 2014 #7
    As I was reading the news I had the same thought. While the wave-particle duality explains how radiation behaves like a particle and a wave, the uncertainty principle says that we cannot know both the position and momentum of a particle at a given time. What would we gain by saying that the "two peculiar features of the quantum world previously considered distinct are different manifestations of the same thing" if we know that the uncertainty principle is related to the wave-particle duality?

    Which significant implications would this imply? Any thoughts?
     
    Last edited: Dec 21, 2014
  9. Dec 21, 2014 #8

    vanhees71

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    The point is that there is no wave-particle duality. That's an early idea from the socalled "old quantum theory", which was a collection of ad-hoc ideas to describe the behavior of atomic and subatomic particles and the interaction of electromagnetic radiation with matter that contradict the prediction of classical mechanics of point particles and the classical theory of the electromagnetic field. The physicists at the time were well aware that this "old quantum theory" is not a satisfactory physical theory and that's why "modern quantum theory" was developed and within a short time between 1925-1927 appeared in three different but mathematically equivalent formulations:

    (a) Heisenberg, Born, Jordan, Pauli: Matrix mechanics
    (b) Schrödigner: Wave mechanics
    (c) Dirac, von Neumann: Abstract Hilbert-space formalism

    All three mathematical descriptions are different representations of the same physical theory, modern quantum theory, and it's neither a classcial point-particle nor a classical field theory. It's a pretty different probabilistic description of the physical world.

    There are aspects which are analogous to classical point-particle theory and classical field theory, and there's also a classical limit of modern quantum theory: when describing situations (usually concerning macroscopic systems), where the classical theory is applicable, the classical theory can be derived from modern quantum theory. I don't see, what should be significant implications for a relation between a mathematical theorem (Robertson-Heisenberg uncertainty relations) and an idea that is outdated by modern quantum theory, for 89.5 years by now.
     
  10. Dec 21, 2014 #9
    It is not the case that we 'cannot know position and momentum at the same time'. The uncertainty principle, formally, is thus: "uncertainty of position" * "uncertainty of momentum" >= "reduced planck constant"/2. This is because position*momentum is angular momentum, and angular momentum is quantized in terms of reduced planck constant. For something that is quantized in terms of something else, your calculation will at most be misaligned from the discrete set of values by half of the grid-size.

    Know that the reduced planck constant is an extremely miniscule number, smaller in 10 magnitudes times less than even the size of quarks. It is only a theoretical, philosophical fact: In reality our practical measurements become involved long before we get that level of precision. By 'measurement' the uncertainty principle refers to interactions of particles, and the information a particle is capable of having. The fact isn't that it is impossible to measure - the fact is that the information is not there. It would be like saying that the exact position of a square of my monitor is unknowable because its position is quantized in terms of pixels.
     
  11. Dec 21, 2014 #10
    Thank you for your answers: although my post wasn't very clear as I was interpreting the theory behind the news partially wrong, you made me understood it in a clearer/simpler way.

    When I asked about the implications this would generate I was refering to the fact that the "discovery" that the uncertainty principle and the wave-particle duality are different manifestations of the same thing. But I am quite sure I understand it better now.

    Thank you for your answer. It made my understanding of the uncertainty principle much clearer.

    I realized that the principal consequence of such "discovery" is that we can explain/comprehend the concept behind the uncertainty principle (and consequently quantum physics) a little better now.
     
  12. Dec 21, 2014 #11
  13. Dec 21, 2014 #12
    The phsysical uncertainty principle, although you can discuss the math behind it (especially statistics) is more of a philosiphocal subject as ellipsis explained earlier:
    The content of the news http://phys.org/news/2014-12-quantum-physics-complicated.html#jCp is only relevant when talking about the philosophical/theoretical aspect of quantum physics.

    So there is a physical relationship between them.
     
  14. Dec 21, 2014 #13

    bhobba

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    Its an exact theorem - what philosophy you want to read into is your business.

    Thanks
    Bill
     
  15. Dec 21, 2014 #14

    bhobba

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    I cant quite follow how you get that from that link.

    Its saying its an idea that helps people at the beginner level but isn't true:
    'So there is no duality – at least not within quantum mechanics. We still use the “duality” description of light when we try to describe light to laymen because wave and particle are behavior most people are familiar with. However, it doesn’t mean that in physics, or in the working of physicists, such a duality has any significance.'

    Thanks
    Bill
     
  16. Dec 22, 2014 #15
    So, but the article don't seem only speaking about a simple metaphor. It takes physical sense as the uncertainty principle according to the article.

    Unless the article is not talking about the same thing ?

    Patrick
     
  17. Dec 22, 2014 #16

    bhobba

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    Scratching head.

    As far as I can see my quote was crystal clear.

    Thanks
    Bill
     
  18. Dec 22, 2014 #17
    You have only give your personal opinion as the authors of the article.

    Patrick
     
  19. Dec 22, 2014 #18

    bhobba

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    It states unequivocally its used to describe it like that to the layman - but it isn't really like that - there is no duality has only one meaning.

    English was not my best subject - I was much better at math - but any other reading of it really has me beat.

    Thanks
    Bill
     
  20. Dec 22, 2014 #19
    You are right. I didn't express myself well there. It is a theorem, but a theorem that gives us freedom to dicuss the philosophy behind it due to its physical nature.
     
  21. Dec 22, 2014 #20
    So I still don't understand what's going on with the paper by Boyd about the previous one by Menzel. If we all agree that the duality particle-wave is a wrong concept, showing it like Menzel et al. seemed to in their 2012 paper should not be controversial, and the August paper by Boyd overselling a return to the duality is hard to fathom.
     
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