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Wave-Particle Duality

  1. Sep 8, 2011 #1
    I was originally taught (and believed) that all matter was neither a wave nor a particle but in fact exhibited properties of both. However after reading QED (by Feynman) and The Cosmic Code (I forget who wrote that), both seemed to say (Feynman directly and The Cosmic Code more subtlety) that all matter were in fact particles, the probability amplitudes of the particle at a given x,y,z coordinate being given by a wave. Now this seems to suggest that they are not both particles and waves, is this correct or am I misunderstanding this?
     
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  3. Sep 8, 2011 #2

    Ken G

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    I'm not sure I see a fundamental difference between saying "they are both particle and wave" and saying "they are particles, but they act like waves." The second statement seems more useful, and is how I think about it, but doesn't exactly make the first statement wrong. In any event, if you are happy with saying that the objects "are" particles, and wave mechanics "tells the particles what to do", then I'd say that's a workable understanding of wave-particle duality. To me, the duality is that particles don't really follow the dynamics of particles-- they follow the dynamics of waves, but waves in the short-wavelength limit actually do all the things we imagined particles should do. We just didn't expect the long wavelength limit to also come into play when appropriate.
     
  4. Sep 9, 2011 #3

    vanhees71

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    If you read Feynman, better read the true Feynman, i.e., his scientific papers or his maverlous textbooks. His other books are amusing to read but not good sources for understanding physics.

    Of course, the idea whether there is something like "wave-particle duality" or even more general "complementarity" is not subject to hard science but philosophy, and thus more of a personal opinion than physics. These concepts go back to Bohr, who dominated the "philosophy of quantum mechanics" for a (too) long time.

    My personal opinion is that to understand quantum theory one should not indulge into that philosophical mode too early but rather read no-nonsense approaches like Dirac's textbook. There you won't find any of these early ideas on "wave-particle duality" or "complementarity" but simply quantum theory, presented as a precisely defined mathematical formalism to describe matter including its atomistic structure. One doesn't need all the Copenhagen esoterics to understand (or better to misunderstand) its meaning. Just stick to the formalism and use the Born's probabilistic rule to interpret the physical meaning of state vectors (Minimal Statistical Interpretation). Everything that goes beyond this Minimal Statistical Interpretation leaves the save ground of hard sciences and enters the realm of personal beliefs and philosophy.
     
  5. Sep 9, 2011 #4
    I was thinking a lot, what is a right way to answer such question. Technical questions are easier in some sense, for the most question of newbies an answer is interpretation-dependent. So proving ANY answer is not fair, because it narrows the view.
     
  6. Sep 9, 2011 #5

    vanhees71

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    With respect to the issue of "interpretation" it's a good job of a quantum-theory teacher to "narrow the view" first. The ideal is to first learn the hard facts about quantum theory (Hilbert-space formalism + minimal statististical interpretation) and to work with it on hand of simple but realistic examples, including how the theory is confronted with reality, i.e., real lab experiments. Nowadays there's a plethora of exciting experiments on the foundations of quantum theory (also many of them use photons, and photons are not so simple, but there are also a lot using massive particles like electrons in quantum dots or neutrons in neutron interferometers) one can analyse in an grad (or advanced undergrad) course on quantum theory (of course, it's hard to imagine to do the experiments yourself, but you can use real data).

    Then, when the students are familiar with the hard facts, one should of course also treat the issue of "interpretation" and look on some of them (Copenhagen, Princeton, de Broglie-Bohm, many worlds,...).
     
  7. Sep 9, 2011 #6
    Mmm, not sure I agree with respect to QED, which is a marvellous little book to read and re-read even for physicists who've already waded through textbooks on QM and use aspects of it regularly. Feynman in particular had a great gift of understanding, and a unique ability to communicate that understanding in words even including the questions he still wrestled with.
     
  8. Sep 9, 2011 #7

    Ken G

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    I agree about starting with the experiments, but I don't agree about starting with the formal theory. That would be like introducing students to classical mechanics by starting with the Lagrange formalism. The reason we still teach Newton's laws is that they are less "black boxy" and more mechanistic/intuitive. The formal approach is more axiomatic and powerful, but just seems like black magic, and never was that more true than Dirac-style quantum mechanics! The approach of connecting with classical physics, Bohr-esque, actually has a lot going for it. But I agree it can also sow misconceptions, so I feel a good way to go about things is to view quantum mechanics as the unification of classical wave and particle mechanics. Not so much that quantum is something totally new that comes from left field, but rather, we had been doing both particle and wave mechanics wrong all this time, and so we did not understand that they were unifiable. Expressed in that light, it makes contact with what the students already know. There is not much need for philosophical interpretations when one simply asserts the properties of particles, and the action of waves, and views quantum mechanics (properly, in my view) as their unification. How the unification is carried out can be expressed very formally, but what is being accomplished does not have to be.
    Grad level courses are another story-- there you can indeed get hip-deep in the formalism, and the more advanced experiments than just the Young slits and the energy levels of hydrogen!

    That might be hard to fit into most quantum courses. I never learned any philosophy in any quantum class-- even the Copenhagen interpretation was not taught, it was merely alluded to along the lines of "if you don't understand why things are this way, refer to the Copenhagen interpretation, which says in essence that you are not supposed to understand why things are this way." In my view, the other interpretations really don't get any past that, because formal black boxes are just machines for making predictions-- no matter what interpretation we attach to them.
     
  9. Sep 9, 2011 #8

    jambaugh

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    One aspect of the language is that as we consider QM the term "particle" evolves to mean something other than a classical point particle. We often say "quantum particle" to mean the phenomena of quantized mass (and other charges) which manifests the celebrated dual "classical wave" and "classical particle" attributes.

    In the end it (e.g. an electron) is neither wave nor particle but rather a repeatably observable phenomenon with no single objective ontological description that we can empirically confirm but with behavior predictable via quantum theory.
     
  10. Sep 9, 2011 #9

    Ken G

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    That is certainly the safest statement to make within the confines of physics, but I would argue that the same can be said for any physical theory, yet it does not tend to be the way we regard physics in practice. For example, we could (should?) say that classical particle trajectories modeled by Newtonian physics involve neither the ontological status of a moving particle nor a stationary particle, rather just a set of consistent experimental outcomes that unify the concepts of the attributes of a stationary particle (like rest mass) and the concepts of a moving particle (like momentum). In this sense, I would say that Zeno was millennia ahead of his time-- he understood, at some level, the ultimate failure of literal ontological descriptions (though perhaps he incorrectly attributed that failure as proof of a logical conclusion that motion is impossible, rather than the more natural conclusion that ontology is impossible). Quantum mechanics was merely the loudest of the many wake-up calls we have had over those millennia.
     
  11. Sep 9, 2011 #10

    jambaugh

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    Yes, exactly. Quantum theory forces us to recognize science as an epistemological discipline, not an ontological one.
    The classical scale is by definition the scale at which we may utilize an ontological model with its manifold of states.
    I never found much significance in the Zeno paradoxes. They seemed to me more sophistry than puzzle. If one understands infinities as place-holders for unbounded ranges of finite cases one never need argue the impossibility of physical acts base on mathematical infinities.

    It is one thing to ascribe reality to the material, i.e. grains of sand etc. It is yet another to ascribe reality to the coordinates we use to express their position.
     
  12. Sep 9, 2011 #11

    Ken G

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    Yes. But who among us really does that? I've never met anyone who said "shut up and calculate" who really did that, the lure to make the jump from "what does" to "what is" is just too great.
    I think the problem with the way many people understand Zeno's paradoxes is they interpret them at the epistemological level, as you have just done. But in my view, those paradoxes are intended at the ontological level. Zeno was one of the ones who was basically inventing logical thought, and they were asking themselves, what is the power of reason? Can we know things about reality just from pure reason? They thought they could, so they thought that ontological reasoning could reveal reality. And when you attempt that, you find that motion does have ontological problems. But instead of saying "I guess ontology is impossible in physics", Zeno said "ontology is accessed by pure reason, so motion is impossible." We may accept that his conclusion was off target, while still respecting the true brilliance of his accomplishment-- he noticed the ontological problems with the notions of classical dynamics that would be laid out and believed wholeheartedly thousands of years later, until quantum mechanics exposed the flaws that Zeno anticipated so long before.

    For example, consider what must be the all time record of prescience-- there is an effect named the "quantum Zeno effect" which no physicist before 1900 would have had the slightest inkling of. But Zeno did, at least some of the key elements. (The quantum Zeno effect is the fact that a state in constant observation must remain in an eigenstate of the observable, so can never change. I'd say Zeno is to be given a pass for not expecting that the way to circumvent the impossibility of change is indeterminacy!)
    Zeno wasn't thinking about motion as just a coordinate description, he, like many of the Greeks, felt that motion had to be an attribute of an object, if it was to be something ontologically real. Then the basic question he posed boils down to, if motion is an attribute, where does the object contain that attribute? Is a moving object a different kind of object than a stationary object, and if not, in what sense is it a moving object? The ontological description breaks down-- which you and I dismiss as not a problem for physics, except when we stray from just doing the calculation.
     
  13. Sep 9, 2011 #12
    Hi.

    I would share your interpretation in the sense that particle is point in space. Actually nobody has observed electron or other particles with size or cloud like area in space. However word particle has another meaning i.e. something that has definite trajectory of motion as in classical physics. In this sense

    Probability amplitude and particle in the latter sense are not compatible.
     
  14. Sep 12, 2011 #13

    jambaugh

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    Yes, it's an integral part of your cognitive process, perfectly appropriate for day to day living. It has taken me some years (and the guidance of a good mentor) to retrain my habits when contemplating QM.
    Yes, I begin to see your point and it is a very good one. I suppose my problem was in being first exposed to his paradoxes outside of this context.
    I'd go further and say Zeno et al didn't have the tools we take for granted now, the Arabic innovations in algebra and symbolic representation, Descartes' innovation of coordinates, etc. The things we can use to resolve these ontological issues as they then enable modern classical mechanics.

    Yet still I cannot give him quite as much credit as you do, given we can, at the classical level still work in an ontological picture, his unresolved problems do not quite invalidate ontological description in the same way as does quantum mechanics seeing as they do not invalidate classical mechanics.

    All that is required to resolve the issues raised by Zeno is the use of continuum time in the same way as continuum space is being used. The various "it will never occur" statements rely on the incomeasurablity of continuum space and discrete time, or on the ability to map one discrete infinity into a proper subset of another... hmmmm... (visions of the Von Neumann and Banach-Tarski paradoxes just popped into my head!)

    Then again it is at a deeper level in is pointing out the incompatibility of ontological infinities with the necessary finiteness of epistemological foundations which recurs in QM.

    Let me ferment on this a while... and I suppose we should get back to the OP topic.
     
  15. Sep 12, 2011 #14

    Ken G

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    Yes, Zeno's paradoxes are usually introduced like "here's how confused people were before there was calculus," but I don't think that gives him a fair shake. His goal was very different from the goal of an analysis involving calculus-- we was asking questions more along the lines of "what is motion really", not "how can we make a workable mathematical model of motion"? I think the question presages issues like how in relativity, motion is viewed as a relationship rather than an attribute, and in quantum mechanics, motion requires indeterminacy. Zeno wasn't quite there of course, but he might have gotten a chuckle about how those issues turned out, if we can claim to have resolved them even now (which we probably can't, given issues like the Planck length).
    But Zeno didn't have classical mechanics either, and that in a sense was his advantage not his disadvantage. He was "free" to ask the kinds of fundamental questions about motion that those who buy off on classical descriptions imagine are already resolved. To them, I would counter, if they were really resolved by classical mechanics, why didn't classical mechanics work? In other words, just because a certain question doesn't bother us any more, doesn't mean it has been resolved-- we might just be kidding ourselves! It could be argued this is what the Newtonians were doing. If I had to guess, I suspect Zeno would have held to his argument even after taking modern classical mechanics and calculus classes. He might have said "great, you have a successful quantitative model, but I'm pointing out that it can't actually be what nature is doing." And he would have been right, for whatever reason.
    But that's something different-- you are saying that one can create a physical model which does not suffer from the problems that Zeno referred to. But Zeno never said such a mathematical model was impossible, he merely said that logic dictated it could never be truly what was happening. He would have needed to maintain that the postulates of any such mathematical model had to be counter to what reality could support as the actual truth. And again, that's actually right, and it came 2500 years before Godel's proof, and before quantum mechanics.

    Here's how I like to imagine Zeno's arrow paradox. Imagine Zeno and superman were arguing, and Zeno says arrows don't actually move. To prove his point, he takes out an arrow and shoots it. Superman says, "but you just disproved your point, look the arrow is moving right now." To which Zeno replies, "are you really sure it is moving? Maybe you should take a closer look." So Superman uses his super speed to fly after the arrow, and he gets right up next to it, and says "by golly, Zeno was right-- it isn't moving at all, now that I get a nice long close look." Then it slams into a tree, so we must attribute the consequences of the undeniable fact that the tree has been hit by the arrow. To that, Zeno would simply conclude that we are suffering from the illusions of our ability to perceive, which is pretty close to saying that motion is not a fundamental attribute, it is a relationship between the observed and the observer, whose consequences are added to the object by the observer's perceptions.
    Exactly, I think that's what Zeno was really saying, though it's hard to know. To bring my diversion back to the thread, my point is that we shouldn't make so much fuss about the wave-particle duality that appears in quantum mechanics, we should make the fuss about the wave-particle disunity that appears in classical physics. It is only because we forgot to care about questions like Zeno's that we thought all was well in the classical world, the fact that we had these two very different ways to talk about motion should have been a clue that all was not well in the land of Newton.
     
    Last edited: Sep 12, 2011
  16. Sep 12, 2011 #15
    Interesting exchange about ontology vs epistemology in science. If I may I'd like to ask something about the "shut up and calculate" approach.
    To a certain point I agree this is the correct way to do science when you are dealing with something that is (or is believed to be) competely understood and mastered, but this is not usually the case and even when it seems so it might be a misleading mirage. So in my view this approach could in certain conditions block advancement in science. Let me show it with an example: In the ptolemaic system of epicycles they were getting pretty accurate results given their instruments, so as long as they were getting good predictions you could say they were applying the shut up and calculate method (they actually weren't because they attributed a very elaborated ontology to their calculations, but we can abstract that in my example), we know in retrospect their method was flawed but in their time whenever they found incompatible observations they just had to add a new epicycle, so the s.u.a.c method worked.
    What I mean to say is that limiting oneself to the purely non-ontological way can have its setbacks too,in that it prevents you from conceiving extensions or modifications to a theory that gives certain accurate predictions.
     
  17. Sep 12, 2011 #16

    Ken G

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    And to your Ptolemy->Galileo example I would add Lorentz->Einstein. When it was found that Galileo's frame change did not succeed, Lorentz found the one that did, but had Einstein just said "s.u.a.c", he would never have recast the L.T. in terms of a new principle of physics.
     
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