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What causes a particle to go into superposition?

  1. Dec 17, 2005 #1
    What causes a particle to go into superposition?

    Is it correct to say that it goes into superposition when it is unobserved?
     
  2. jcsd
  3. Dec 17, 2005 #2
    What do you mean by "go into superposition"? The particle will be in whatever state is dictated by its surrounding environment, if that environment does not force it into one particular eigenstate of the hamiltonian then it will be in a superposition of eigenstates.
     
  4. Dec 17, 2005 #3
    I have a question, suppose the environment does not force the electron (e-) into one particular eigenstate of the hamiltonian (as you say). What then would be the equation of the "superposition of eigenstates" for the (e-) that you refer to ? Thanks for helping me understand your concept of the (e-) superposition.
     
  5. Dec 17, 2005 #4
    First of all, I'd just like to point out that you're entirely correct in phrasing this as my "concept of the (e-) superposition," this discussion goes beyond the mathematics of the situation ("the particle is in such-and-such state") and delves into the much trickier question, "how did it get into that state?" Everything that follows is simply my personal interpretation of how the universe works.

    My QM professor was always careful to point out that the problems we typically do (in undergrad classes anyway) are somewhat contrived, we are told that the particle is measured to be in some particular eigenstate or superposition of eigenstates of some hamiltonian operator, and we then go about calculating expectation values for some particular observable or expand the state function in terms of the basis states of another hamiltonian operator or whatever the problem asks for. The question as to how the particle got into that state is left largely undiscussed.

    When I think of this, I think of it in terms of trying to put the particle into an eigenstate of position, although the situation is obviously much more complex for real world systems and observables. Suppose you have a particle which is in a perfectly isolated box, with the exception that you can inject EM waves in order to get an idea as to where the particle is. From optics, the accuracy to which you can determine the particle's position is related to the wavelength of the wave you use (I believe it's something like half a wavelength). So, if I put in an EM wave of such-and-such wavelength I can measure the particle's position to within roughly half that wavelength. I can then say that the particle's position state function is some Gaussian which is centered at such and such point with a width related to the half wavelength of the EM wave I used.

    We can generalize this to a particle which is sitting in some potential environment somewhere: it's subjected to various EM waves and potentials, the net effect of which is to box the particle down into some superposition of eigenstates.
     
  6. Dec 18, 2005 #5

    vanesch

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    "superposition" is a concept that only makes sense when you talk relative to a basis. "Is a vector in a vector space in superposition ?" doesn't mean much: if the vector is one of the basis vectors, then you'd be inclined to say no, if not, then you'd be inclined to say that it is a superposition of different basisvectors (weighted with the coordinates of the vector in that basis).

    So you can say: what causes a particle to go into superposition wrt the position basis, for instance.
    Then the answer is rather straightforward: in most cases, the unitary time evolution causes this ; simply because the position basis is not the eigenbasis of the hamiltonian.
    If you say: what causes a system to go into superposition wrt the hamiltonian eigenbasis, then the answer is that a strictly isolated system will NOT go into superposition wrt to the hamiltonian eigenbasis if it wasn't already so.

    What measurement does, will depend upon how you see measurement in quantum theory. If you take projections for real, then clearly, a measurement *removes* superposition wrt to the eigenbasis of the measurement operator ; if you take an MWI view, then measurement *entangles* the system state with the observer state ; however, the observer will experience only one of these terms, so we can now forget the other terms (although they are there) and consider we will only study what will happen to the term we experience (which comes down, of course, to use the projection in one way or another).

    What doesn't make sense, however, is to consider the superpositions wrt a basis of a system which interacts with its environment, limited to the system hilbert space. Because you now do not get the environment to get your system to go into a superposition ; you rather get your system to *entangle* with the environment states, in the bigger hilbert space of states of system+environment.
     
  7. Dec 18, 2005 #6
    Indeed, this is what QM measurement is all about...AND NOTHING ELSE !!!:uhh: yeah yeah, it is...:approve:

    mmmmm, i think this is a TD thinghy...:wink:

    regards
    marlon
     
  8. Dec 18, 2005 #7

    vanesch

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    The day we will know about non-unitary physical process, maybe, this projection will obtain a physical meaning as a shortcut to something real :biggrin:
     
  9. Dec 18, 2005 #8
    :rofl:

    Beats looking for multi universa, no ?

    marlon
     
  10. Dec 18, 2005 #9

    vanesch

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    I really don't know.

    Unitary QM incorporates of course many worlds if you extend the validity of it to the level of objects on the scale of a human body. Although there are some, most researchers stick to strict unitarity (and hence to no projection and hence to many worlds), and today we don't have any other working theory, so we better, at least temporarily, come to terms with strict unitarity, no ?
     
  11. Dec 18, 2005 #10
    :uhh:
    I am sorry but i have no idea what this means. "the scale of a human body"...C'mon man...what is that about ?



    No most researchers stick to the "original" interpretation of QM, ie the fact that measurement breaks superposition and all other info is GONE. It did not get entangled or... what ever...

    This is also the vision i have on this.

    The only thing that bothers me is where do we make the distinction between QM and Newtonian physics ? At what distance scale ?

    But ofcourse, the fact that this border is not "clear" or known, does NOT imply that there is something wrong with the underlying formalism...

    regards
    marlon

    EDIT : you know, Vanesch, i have really read some of the links to papers you provided on the measurement problem. We have had some small discussions on this before. But i still really do not understand what all the fuzz is about. Even this Bell-thing is not clear to me. I understand what it is about but i do not get the content of this theorem. Even in college, it seemed very superfluous to me. Perhaps it is me; but i feel like i am missing out on something here. I use QM almost every day for my ab initio simulations. I look at QM from a very pragmatic point of view. The QM formalism works because i can calculate physical quantities with it, that are ofcourse correct. So, i am happy...That is all for me.
     
    Last edited: Dec 18, 2005
  12. Dec 19, 2005 #11

    vanesch

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    Well, the first question is: do you think that the principles of quantum theory apply universally, or not ?
    I mean:
    when you have a system of, say 5 electrons and 5 protons, does quantum theory apply to it or not ?
    When you have a system of 200 electrons and 200 nucleae, does quantum theory apply to it or not ?
    When 20000 particles ? When 10^6 particles ? When 10^10 particles ?
    When 10^25 particles ? When 10^80 particles ?
    The "scale of the human body" is simply the number of particles that are concerned in your average human body. Does quantum theory apply to that system or not ?
    By the above phrase "does QM apply", I mean: can we construct the Hilbert space of the system with all its considered degrees of freedom.
    I would guess that most people would say "yes", right ? Only, most people would think that quantum theory somehow reduces to Newtonian physics in a very good approximation ; just like special relativity does. This is unfortunately not true. Quantum theory does NEVER reduce to classical physics. The only thing that MWI tries to do, is to explain why *an observer* gets *the impression* of a classical world. I know that in elementary QM courses, one goes quickly over the issue with Ehrenfest's theorem. But Ehrenfest's theorem does NOT show that QM reduces to classical physics ; because it ASSUMES already a transition to classical physics by using expectation values.
    Of course you can also be of the opinion that quantum theory as we know it today, is a limiting case for "small" systems, and that newtonian physics is another limiting case for large systems. I do consider that possibility ; but one thing is sure: we haven't gotten a clue then, what that theory is. And it would, in any case, have serious consequences.
    Let's be clear: I also stick to that "view" to do practical calculations of course. But it should be clear that it is a totally undefined procedure which violates locality and which has no grounds in any physical process, every physical process we know off being described by a unitary time evolution operator which cannot implement it. I think most people who have given it any thought realize that there is something highly fishy in this view.
    Well, as you know, the distance scale is at least 50 km if we accept the Vienna experiments. An entangled pair of photons 50 km apart still shows entanglement, so this is a system of 50 km diameter that needs to be described by quantum theory.
    It is entirely possible that QM and classical physics are two limiting cases of a yet unknown theory and that collapse occurs "for real". But the implications this would have are quite drastic, in that it would certainly imply non-local actions (with all the consequences for relativity).
    Yes, I think you're missing something then. If you're not struck by Bell's theorem, I think you're missing something. I would say that it is one of the most shocking results you could ever think of.
    That's an attitude that many people have. But to me, it is a very strange view. It looks a bit like chemistry when people still thought that you needed a "living force" to work with organic compounds. They considered their chemistry not "universal": certain things obeyed the laws of chemistry as they knew it, and other things, well, were the result of "living force". With the same atoms. But that didn't mean they could not do their anorganic chemistry well in the lab.
    To me it sounds strange that you have a certain theory that you apply to well-choosen things, and in the middle of the game, you change the *fundamental* rules: you switch to classical physics. And not in the sense that you can now allow yourself to do so because it is a good approximation, but it is a *totally different* theory with incompatible axioms.
    This is not the same as, say, switching from GR to Newtonian gravity, because we know that Newtonian gravity is an approximation to GR for weak fields. So when you do Newtonian gravity you can think of it as a numerical appoximation while you're in fact still doing GR.
    Another example is geography: you know that the earth is round, but when looking at the map of your city, you don't mind using a flat map. That's simply because it is a good approximation. But switching to Newtonian physics (not even relativistic physics because that's impossible) from QM is NOT an approximation. At no point Newtonian physics is a limiting case of QM.
    The reason why you cannot use classical relativistic physics when switching from QM to classical, is that you need to project your state *at a certain time* (the time of the measurement). When your quantum system has a certain spatial spread (in other words, if it contains more than one particle), then it is not clear *what reference frame to use* to do the projection in.
    Now, the only way to avoid that difficulty is to avoid projection all the way. But you see that if you're going to invent a theory in which there *IS* such a collapse, you're going to have to negociate extremely well with relativity!

    To put it differently, let's go back to the end of the 19th century. Imagine the "UV catastrophe": when you apply the well-founded statistical idea of equidistribution of energies to modes of the classical EM field, you get of course the UV-divergent spectrum for black body radiation. Now, some people might consider that a fundamental problem and others might say: well, in the case of the EM field, simply apply the well-working Planck curve for black body radiation, what's the problem ?
    The problem is of course that you switch rules halfway the game! Suddenly, statistical physics doesn't apply "in the same way" to the EM field as it does to gas molecules.
     
    Last edited: Dec 19, 2005
  13. Dec 22, 2005 #12

    reilly

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    vanesch writes:
    I would guess that most people would say "yes", right ? Only, most people would think that quantum theory somehow reduces to Newtonian physics in a very good approximation ; just like special relativity does. This is unfortunately not true. Quantum theory does NEVER reduce to classical physics. The only thing that MWI tries to do, is to explain why *an observer* gets *the impression* of a classical world. I know that in elementary QM courses, one goes quickly over the issue with Ehrenfest's theorem. But Ehrenfest's theorem does NOT show that QM reduces to classical physics ; because it ASSUMES already a transition to classical physics by using expectation values.
    .....................
    You are suggesting that expectation values are not appropriate for classical physics?


    Of course, QM -> CM under appropriate circumstances. That's, among other things, what our brain does, at least for vision. Remember that vision is fundamentally a quantum phenomena, triggered by molecular photodissociation. Our brain does a lot of averaging, both spatially and temporally, and therby transforms quantum generated currents into what we see, which, of course, is mostly classical.

    You don't like the WKB method?


    And, how can both quantum and classical computations yield identical results for the Rutherford cross section given your assertion?
    Regards,
    Reilly Atkinson
     
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