the wavefunction

Discussion in 'Physics & Math' started by Lucas, Jan 31, 2004.

  1. errandir Registered Senior Member

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    These are two different interpretations: I believe Copenhagen and Bohm-deBroglie, respectively. There are good arguements for both, and there are aspects of both that make one wonder.




    Does this analogy have anything to say about the interference of a particle with itself?
     
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  3. Neurocomp2003 Registered Senior Member

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    thank you...cuz a friend of mine always repeats the phrase "is everywhere" when we discuss related issues(like outta the textbook). And its rather confusing because physicists always like to coin their own phrases. And this one in particular in all my AP and QM courses. So if its everywhere then you should be able to measure it at different places at a single time.
    This all goes back to his description of an experiment where it goes through many Electric field devices and the result is that you do not know which final plate it will hit.
     
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  5. Crisp Gone 4ever Registered Senior Member

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    This is not entirely correct. You cannot get an interference result from the dice (i.e. you cannot get 3.5 as a result because the 1 and 6 interfered). The electron really is "everywhere" (not localised) because otherwise you cannot explain how electrons can form two-slit diffraction patterns.
    [Edit: Euuhmmm.. bad example of interference]

    You are in a sense correct in saying that it is not "anywhere": the position is not determined before the/a measurement, in which case the wavefunction (and hence the electron) collapses to one give point. Each outcome has a certain possibility and that "might be anywhere" indeed. But at the same time, the physical properties of the system you are measuring change if you perform the measurement.

    I know this sounds incredible, but that is what the theory says... whether it is correct or not is a totally different issue ofcourse. In fact we know that it is not entirely correct: using this you get problems like "a watched radioactive isotope never decays". The solution lies in not seeing the measurement as such a intrusive event, but as something which preserves the non-locality in a small way (e.g. Krauss measurements). But I have to admit I am not entirely into measurement theory.

    So I guess the right answer was a superposition of what you and Neurocomp said

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    Bye!

    Crisp
     
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  7. Neurocomp2003 Registered Senior Member

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    i'm sure you can explain the 2 slit diffraction pattern as a particle interaction.
     
  8. Crisp Gone 4ever Registered Senior Member

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    Please, by all means do this and go collect your Nobel prize in Sweden

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    Bye!

    Crisp
     
  9. Neurocomp2003 Registered Senior Member

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    just to clarify that the 2 slit diffraction pattern is the grated patterns you seen...the higher th Hz the thinner/more the lines right?
     
  10. Crisp Gone 4ever Registered Senior Member

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    Ehr well yes... but I am not refering to the number of lines you see, but rather to the pattern of a bright one in the middle, and then a void, another line which is less bright, another black line, ...

    I have absolutely no idea how you are going to explain that using only the corpuscelar character of particles.

    Bye!

    Crisp
     
  11. ryans Come to see me about a dog hey Registered Senior Member

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    995
    Neurocomp
    If you are not happy with the explanation given utilising Schrodinger's equation, you may wish to utilise Feynman's path integral approach, as it stems from a well known principle in classical mechanics, namely the principle of least action. A warning though, this method is mathematically more intense than the convention, quantum mechanical textbook treatment of the problem.
     
  12. lethe Registered Senior Member

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    also, it is mathematically ill-defined
     
  13. ryans Come to see me about a dog hey Registered Senior Member

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    Yes, but us physicists aren't usually too fussed on the pedantics of mathematicans. The validity of the Dirac delta function is still being argued.
     
  14. lethe Registered Senior Member

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    no it s not. the Dirac delta is a perfectly valid functional, even mathematicians will tell you the same.
     
  15. Neurocomp2003 Registered Senior Member

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    i'm fine with mathematics...its the physical descriptions that i have trouble wiht because physicists and their unique ways.

    As for the dark light patterns, it all depends on the interaction of light.
    Its commonly stated that light interaction is a superposition which confuses the heck outta me.

    Because light is a duality but superposition treats light interaction as going from 2 waves/particles to 1particles/1wave but how can 2 particles just turn into one?

    My particle description of diffraction patterns stems from a grid pattern of bouncing balls that in a system bounce off each other to form a unique pattern(like that jezzball windows game)...in this case the diffraction dark/light bands. But of course this assumes that light particles can bounce off each other upon interaction but of course this is not what physics states.

    Can anyone explain to me how light behaves upon interaction with a surface?
    it reflects back off right(with of course a change in certain ppts)?

    Its also funny that we can study so much about light(massless and assumed the fastest particle there is) but yet we have trouble detecting neutrinos/microwave bkgd/gravitons.
     
  16. ryans Come to see me about a dog hey Registered Senior Member

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    Yes, o.k. you are correct, but I still see it being flung around in ways which seem contrary to its definition as a distribution. It is often believed that it may be treated as a function.
     
  17. ryans Come to see me about a dog hey Registered Senior Member

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    Say Lethe, have you dealt with Airy functions before. They have come up as being the solutionfor a particular problem I am working on, and am now trying to satisfy the boundary condtions, hopefully obtaining quantised energy levels (i.e. analogous to say the particle in a box). They are defined in terms of Bessel functions, which are not in general periodic, but as in the harmonic oscillator case, have discrete eigenvalues.

    This is slightly off topic, but since it relates to a solution of the S.E., I will not start a new post.
     
  18. lethe Registered Senior Member

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    it's times like those that you will wish you hadn't dismissed us mathematicians so callously, when you physicists find yourselves getting into trouble for treating the Dirac delta like a function. you need a mathematician to tell you exactly when and where you are entitled to take this privilege.
     
  19. Dinosaur Rational Skeptic Valued Senior Member

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    A maddening aspect of discussions of quantum theory is that it never seems possible to stick with one issue at a time. You get questions like the following.
    • What does the dice throw analogy have to say about the interference of a particle with itself.
    A particle does not interfere with itself. Interference is a wave property. When you talk about interference, you are talking about apparatus set up to detect wave properties. The dice throw analogy applies to particle position probabilities, and is not applicable to wave phenomena.

    This thread started with a question about the reality of the wave function. It has digressed into other issues, including wave/particle duality. At some deep level all aspects of quantum theory might very well be interrelated. Until we discover such relations (if any exist), it is best to stick with one aspect of Quantum theory at a time.

    It is my belief that the jargon used by quantum theory experts misleads amateurs. (I include myself with the amateurs) The term collapse of the wave function seems to me to be misleading jargon.
    • The wave function is a mathematical equation which provides probabilities relating to the possible positions of a particle. The dice throw analogy to the wave function is a table of probabilities indicating the frequency of 12 possible totals resulting from one throw of a pair of dice.
    • When a measurement is made, a particle is discovered at some position, and the experts say that the wave function has collapsed. This implies (to some amateurs) that the wave function is a physical object or process. Statisticians do not say the probability table has collapsed when the dice are tossed and you get a particular total. They say a six was rolled instead of some other total.
    • I think the experts use the jargon to indicate that until a measurement is made, there is some process occurring which cannot be modeled by the motion of a classical particle, but when a position measurement is made, you can model what has happened using a classical particle model.
    A book I read some time ago, said that it helps if you view photons (and other quantum entities) as particles when they depart and/or arrive, but view them as waves when they are traveling.

    The above is not directly related to the wave/particle duality issue. That is another confusing can of worms. Until modern technology allowed experiments using one photon or electron at a time, the wave/particle duality issue was not as confusing as it is today. When many particles went though the apparatus concurrently, you could imagine that the particles interfered with each other, although the experts insisted that something more subtle was occurring. The experts proved to be correct.

    Imagine the two slit experiment being run twice. for each experiment, one photon (or electron) is sent through the apparatus at a time and photographic film is used to record the results.
    • For one experiment, both slits are open at all times.
    • For the other experiment, one slit or the other is closed.
    • When both silts are open, an interference pattern develops on the film (alternating bright and dark lines).
    • When the slits are opened alternately, the expected particle pattern develops on the film (two patterns each with a bright central line).
    The really confusing aspect of this experiment becomes apparent when the experiment is run hundreds of times to create a series of films showing how the patterns build up.
    • The two-slit interference pattern builds up one pixel at a time, strongly suggesting that each particle went through a slit and arrived at a position on the film with no interference occurring (This surely makes sense, a particle cannot interfere with itself).
    • The problem is that the pattern being created as more particles are sent through is an interference pattern.
    • When only one slit is open at a time, the particle pattern is slowly developed.
    The Schrodinger wave equations describe probabilities which predict the results of the above experiments. The experts trusted the equations before the experiments could be done with single particles.

    The above is mind boggling enough for photons. For electrons, it is even more incomprehensible. Photons seem a bit ephemeral and when you think of them as light rays instead of particles, the two slit experiment is only some what mind boggling. Electrons are catalogued (erroneously I suppose) in my mind as little charged particles, perhaps like tiny ball bearings too small to be seen. My intuition insists that electrons cannot act the way the experiments say they do. Intellectually, I can accept the notion that my intuition is wrong, but intellectual acceptance does not provide any model for me to visualize.

    BTW: As posted previously, I consider the wave function to be ink on paper with mathematical significance. The reality it describes or models is something else.
     
  20. lethe Registered Senior Member

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    sure it does. a particle is also a wave, after all.

    not me. i talk about interference even in the absence of measuring apparatus.

    eh? you think only position measurements are probabilistic? energy measurements are also probabilistic, and energy eigenstates are much more "wavelike" than position eigenstates, so it is not accurate to pretend that the probabilistic nature of quantum mechanics is restricted to "particlelike" states.

    perhaps it does, but i think it elucidates matters for the experts.

    is it you that i already had this debate about? i guess i won't get into it again, but collapse is a very accurate description of a very mysterious phenomenon. if you think it is just mystifying jargon, that is not accurate. the phenomenon is itself not understood. hence the need for a phrase to describe it.
     
  21. ryans Come to see me about a dog hey Registered Senior Member

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    It can be very misleading, especially when talking about things like quantum entanglement with people not familiar with the lingo. For example, Mac put up a thing a while ago saying something like the spin state of say a electron does not collapse when it is incident on a metal sheet, which fruther propogates a phonon, which then emits another electron. He failed to realise however that any measurement of any of the properties of the metal foil would collapse the wavefunction, and thus we will know the spin of the electron, and thus another electron it was "entangled" with, is no longer connected to this electron. Typical Mac.
     
  22. metacristi Registered Senior Member

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    92

    In the vast majority of variants of the Copenhagen Interpretation the wavefunction is considered to be a mere mathematical 'tool' (the superposition of states is not something which exist in reality).When the wavefunction 'collapse' nothing physical happen.At least this is the acception of Heisenberg and Bohr,they merely assesed that it is futile to ask about the state of the particle between measurements.But as far as I know there are people who call themselves copenhagenists who believe that the superposition of states is something real.In this acception when the wavefunction 'collapse' the universe suffers a sudden change.Philosophically speaking this acception is not tenable,indeed why we do not see things as a superposition of states?Why should the universe suffer such a sudden change?

    Anyway the vast majority of serious copenhagenists avoid this interpretation not on philosophical reasons but on practical ones.Namely the necessity of full coherence with Special Relativity (no preferential frame allowed).Indeed the standard copenhagenist response to Einstein Podolsky Rosen paradox underline the fact that 'spooky' correlations at distance are real (as predicted by QM) but we should label these connections 'nonclassical' instead of 'nonlocal' (this in spite of the lack of a real explanation for the statistical correlations observed within the Copenhagen Interpretation).In other words they assume there is no instantaneous influence at distance (the 'c' limit cannot be crossed) implicitly meaning that entangled particles cannot be seen as really being the same 'object' (which would imply that the wavefunction is real,stretched in space,the collapse involving some instantaneous influence).When the wavefunction 'collapse' no instantaneous influence is involved.The experimental verification that Bell's inequalities are violated (Aspect 1982),which confirmed also the existence of those nonclassical correlations,only strengthened this interpretation of the wavefunction.As a matter of fact many copenhagenists find very unhappy that von Neumann's 'invented' the expression 'wavefunction collapse' for,in their opinion,it created a lot of confusion.

    Still the best philosophical interpretation of the current state of affairs is that no one really knows whether the strange correlations at distance involve an instantaneous action at distance (as some other interpretation of QM explain the observed correlations) or not...I'm afraid the implicit 'explanation' given by the usual copenhagenist approach is not really an explanation.That's why many still search...
     
    Last edited: Feb 4, 2004

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