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Is there any phenomenon where the 'wave description' of the electron's motion is not applicable?

The reason for this question is to find out if there are any situations were quantum wave theories fail. If not, it seems that the Everett's multiworld analysis as described by Coleman, http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv works.

Kyle Kanos
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Per Arve
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    In classical (as in non-quantum) settings, the electron is best understood as a particle rather than a wave. – Danu Aug 25 '14 at 18:32
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    Have a look at (e.g, there's more of this around here) Is the wave-particle duality a real duality? The premise of your question seems to be that sometimes, the electron is a wave, and sometimes, it is a particle. It is neither, it is a quantum object that carries properties of both, and asking for instances where one aspect of its description is appropriate or fails is missing the point. – ACuriousMind Aug 25 '14 at 18:46
  • Electrons can't be described by waves, to begin with. They can, at most, be described by wave functions, which is an entirely different animal. As others have pointed out, as long as your electrons have large enough momentum, there is no need for a quantum mechanical description. Electrons with large momenta will, for all practical purposes, behave like point charges. – CuriousOne Aug 25 '14 at 19:56
  • @ACuriosMind I want the arguments, physical situations, not the believes. – Per Arve Aug 25 '14 at 20:03
  • @Danu I agree, there are situations where the quantum wave description is extremely clumsy compared to a classical particle description. But my question is on the fundamental level. – Per Arve Aug 25 '14 at 20:05
  • On the fundamental level, as @ACuriousMind pointed out, one should not separate the two. – Danu Aug 25 '14 at 20:21
  • There was an interesting article by Art Hobson in the American Journal of Physics (http://arxiv.org/abs/1204.4616) a few years back that advocates we abandon the particle view of fundamental constituents and move to a fields-only view. Might be interest to you. – jjgoings Aug 25 '14 at 20:40
  • @Danu I'm searching for the arguments behind the particle wave duality belief, then it is not useful to take it for granted. – Per Arve Aug 25 '14 at 21:02
  • It's an experimentally confirmed fact, not a 'belief'. – Danu Aug 25 '14 at 21:03
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    The wave-particle duality is not a belief, it is the unfortunately expressed observation that some things, when shot through slits, seem to interfere like waves, but register in detectors like particles. It is also very difficult to talk about this because everyone seems to have a different mental picture of what a wave or a particle is. I believe your question only becomes unambiguously and physically answerable after you give a precise definition of what constitutes a quantum wave theory in contrast to others. – ACuriousMind Aug 25 '14 at 21:06
  • @jigoings Thanks for that link, it is really what I think is correct. – Per Arve Aug 25 '14 at 21:24
  • @ACuriosMind Also when the electron hits a detector can be described as quantum process. The fact that we experience the electron to hit just one point, that is the wave function appears to collapse, is an effect of entanglement. Thus pure quantum wave physics. – Per Arve Aug 25 '14 at 21:25
  • @Danu Which experiment? – Per Arve Aug 25 '14 at 21:29
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    "The fact that we experience the electron to hit just one point, that is the wave function appears to collapse, is an effect of entanglement." I think you have misunderstood what entanglement means. Perhaps you had decoherence in mind? Even so the claim that you are then allowed to dismiss the particle-like properties of the electron misses the point. – dmckee --- ex-moderator kitten Aug 25 '14 at 23:49
  • @PerArve: I have no idea what "pure quantum wave physics" is. I was never taught about such an animal in university. My physics teacher in high school was more than competent to resolve this question once and for all using trivial logic. "What", he asked, "are electrons? Are they waves or particles? The answer should be obvious: they are neither. Both waves and particles are merely some simplifying but insufficient properties that arise from averaging about this new "neither"". – CuriousOne Aug 26 '14 at 02:44
  • @ACuriousMind got it right. I'll add that you can recover most of what we think of as 'particle' behaviour from wave theory if you really understand decoherence. You can't recover all of the particle behaviour though. – DanielSank Aug 26 '14 at 02:57

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Is there any phenomena where the wave description of electron (motion) is not applicable?

Let us touch base and have a look at this bubble chamber picture:

omega

This is one single elementary particle interaction, rare, because it is the creation of an omega particle, but it is one single instant.

There is nothing wavelike in this datum. The particles behave in the magnetic field exactly like charged classical particles are expected to behave and their momentum and mass can be measured or fitted to great accuracy.

This is a particle interaction. The point I want to make is that even though this is a reaction that can only be mathematically modeled statistically by quantum mechanics, there is absolutely no manifestation of the wave nature of elementary particles in this one instant.

We might have a single electron turning in the field . It is not interesting enough to be recorded for teaching purposes, but again it would not display any wave properties.

In conclusion, in the quantum mechanical framework, single events/instances can be described by classical trajectories and physics. It is when the statistics are accumulated that the wave behavior appears. The statistical distribution of such scatterings will be a probability distribution given by the quantum mechanical wave equations, and will display the wave nature of the underlying framework. The waves in quantum mechanics are probability waves . Many instances must be accumulated in a distribution to manifest the wave nature . In the double slit experiment with single electrons a single electron does not express any wave nature. One can calculate its trajectory classically after the fact. One cannot predict the trajectory unless the probability wave nature of the underlying framework is taken into account.

To summarize for individual measurements the wave nature may not appear at all or cannot be predictive of a trajectory. What the wave nature does is predict a statistical distribution for the particles under consideration. In the example above, a statistical distribution will give the crossection for producing omega- in kaon interactions, angular distributions etc , and these distributions can only be explained with the wave nature of quantum mechanical entities.

The reason for this question is really to find out if there are any situations were quantum wave theories fail.

The quantum wave theory is continually validated by all experiments. If there were a failure it would have meant a major disturbance in the physics community. Everything is consistent with the particle manifestation for individual events, probability wave distributions for statistical accumulations.

If not it seems that the Everett's multiworld analysis as described by Coleman, http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv works.

This last is not clear, seems to me a non sequitur .

anna v
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    You bring up an interesting example, at least historically. It was this kind of picture (though with fewer tracks, that made Bohr and Heisenberg to conclude that once the particle is being measured, it behaves like a classical particle. However, Bohr was mistaken when he concluded we that we cannot use quantum physics, also to describe what happens in the measurement process. This was what Coleman advocate in the video. E.g. the tracks in the pictures are fully explained by quantum wave theory and you don't NEED classical physics at all. But it might be convenient, that's another thing. – Per Arve Aug 27 '14 at 19:28
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The physics of particle mechanics is contained within quantum mechanics, so I don't know if it's correct to say that there is a place where the "wave description is not applicable." However, there are experiments where the wave description is not apparent.

The beginning paragraphs of this page give a very short historical account of wave & particle behaviors of particles. Here's a quick example:

Certainly the early experiments on the properties of electrons did not suggest that any unusual behaviour was to be expected. Everything pointed to the electron being a particle of very small mass. The trajectory of the electron can be followed in a device such as a Wilson cloud chamber. Similarly, a beam of electrons generated by passing a current between two electrodes in a glass tube from which the air has been partially evacuated will cast the shadow of an obstacle placed in the path of the beam. Finally, the particle nature of the electron was further evidenced by the determination of its mass and charge.

Those three examples suggest particle-like behavior. But keep in mind that quantum mechanics, and its inherent wave-like nature, is capable of accounting for the observations.

I haven't read the entire page I linked to, but some of the wording I saw is very carefully thought-out (which is a good thing!), so it might be good to read through. For example, it states:

a number of experiments were performed which could be interpreted by classical mechanics only if it was assumed that electrons possessed a wave motion...

This statement reminded me that you may want to search these forums for discussions about the dichotomy between particle-like and wave-like behavior. It's the opinion of many that the distinction isn't so black and white as one might expect.

BMS
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  • Well, I hoped that if there is a case for the old fashion particle wave duality someone here would know about it. I have read a few quantum mechanics textbooks. I don't remember having seen anything that we nowadays can't describe with the equations of Schrödinger and company. – Per Arve Aug 25 '14 at 20:19
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Probably only the collapse of the electron wave function, which occurs point-like in experiments. That means, electrons make point-like response on photographic plates, CRT screens and in other instruments, both in spatial and temporal sense. No wave description of this process has been built (yet).

Maybe also that several electrons make a many-particle wave function in higher dimensions, rather that just add up like classical waves. But this can be disputed.

firtree
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  • That there is a collapse of the wave function is very much disputed, see Coleman's video that I added in last edit. – Per Arve Aug 25 '14 at 20:36
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    You can take the word "collapse" as "what happens in experiments when the particle interacts with some macroobject". – firtree Aug 25 '14 at 20:38
  • What is it in "what happens in experiments when the particle interacts with some macro object" that we could not describe with quantum mechanics. I very much believe that the researchers of surface physics quite well describe the situation of an electron hitting a surface, with quantum mechanics. – Per Arve Aug 25 '14 at 20:43
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    Alas, they do not yet. And I don't want to discuss your (or my) beliefs, I just intend to answer the question. Some clarification added to the answer body. – firtree Aug 25 '14 at 20:46
  • Do you say there are no quantum description of electron hitting a semiconductor surface? – Per Arve Aug 25 '14 at 20:54
  • There exists such a description, but it does not answer all questions. Some are answered and some are not. And I mean "wave-like descritpion", because the collapse postulate answers the rest (in probabilistic manner). – firtree Aug 25 '14 at 20:58
  • I and many others don't believe that the wave collapse postulate was a mistake. That is very much what this discussion is about. – Per Arve Aug 25 '14 at 21:08
  • Mistake in the last comment: I and many others believe that the wave collapse was a mistake. – Per Arve Aug 25 '14 at 21:32
  • Again: I don't want to discuss your beliefs. There is an experimental fact and I informed you about it. It is independent of any postulates and theories, and cannot be the matter of discussion. – firtree Aug 26 '14 at 00:48
  • If you know some experimental fact, be more detailed about it. I have studied the physics of a few detectors, and all of them have quantal descriptions. The collapse of the wave function is not needed to understand the measurement process. – Per Arve Aug 27 '14 at 19:51
  • Probably you are confusing the "quantum description in general sense" and the "quantum description without collapse, even implicit". For example, a photoemulsion is a well-known kind of detector. The interaction of the electron with the silver halide crystal is well described, but which crystal have the chance to interact remains the matter of collapse. The electron's wave function may fall onto the entire photographic plate, but only one crystal will get exposed. Do you know the quantum description of this choice? – firtree Aug 27 '14 at 20:43
  • If you look at the video I have linked, you can learn that the fact that we see one particular part of the emulsion being hit is an effect of entanglement, which is a well understood quantum effect. Thus there is no reason to believe that the wave function collapses. – Per Arve Aug 28 '14 at 00:07
  • This is not yet a rigorous theory, just mostly ideas and handwaving. Real scientific results are not in videos, they are in papers with lots of formulas and strict reasoning. If something is presented in videos but not in accompanying papers, then it is not a result yet, but only a personal belief. I'm telling you about the current status of theory in physics, not the personal Coleman's opinion. – firtree Aug 28 '14 at 11:10
  • There are loads of papers about this. I'll come back later with more arguments and references. I referred to the video because I recently found it on this site and it is quite pedagogic to my mind. – Per Arve Aug 28 '14 at 15:03
  • Please add references to the top post then. – firtree Aug 28 '14 at 15:06