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How fast does the wave function decollapse ?

  1. Apr 3, 2006 #1
    how fast does the wave function "decollapse"?

    as you know the wave function (indeterminacy) may collapse due to a measurement. However, after a measurement it returns after a while to its initial state of indetermincy. (I don't know what to call this transition back to indetermincy; is there a commonly used term for this?)

    My question is. Have there been any investigations of the average time it takes after a "collapse" for a wave function to return to its initial state of indeterminacy. Can anyone point to a site with information about this?
     
  2. jcsd
  3. Apr 3, 2006 #2

    Galileo

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    After the measurement the state simply evolves according to the Schrodinger equation. There's no sudden 'decollapsing' transition.
     
  4. Apr 3, 2006 #3
    Wavefunction collapse in the formalism is instantaneous. See for yourself what kinds of contradictions you could create if it were otherwise.

    (of course, the wavefunction is not an actual physical entity, so when it collapses nonlocally you can't start talking about SR violations - because there is nothing moving that violates SR!)
     
  5. Apr 3, 2006 #4
    Oops I misread the question! What you call decollapsing is merely the unitary evolution according to Schrodinger. (repeating Galileo)
     
  6. Apr 4, 2006 #5

    Hurkyl

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    It doesn't have to decollapse -- it already is in a state of "indeterminacy". Remember that an eigenstate of position contains absolutely no information whatsoever about momentum! So when you measure position, then momentum could be absolutely anything, with equal probability!


    I do have caveats, though:

    (1) Actually, it doesn't make too much sense to speak about probability in this particular case, but that's okay because:
    (2) You can't actually measure position exactly anyways.

    And
    (3) All of this only applies in a "collapse" picture: in other pictures, a measurement simply gets you and your measuring device entangled with whatever you're measuring.


    Incidentally, no matter what your wavefunction is, there are always observables for which there is absolute certainty about its value.
     
  7. Apr 4, 2006 #6
    ok

    ok, well let's take an example. Let's say we measure the z compenent of the spin of the electron. The remaining compenents (x, y) will be indeterminate (the reason is of course the quantum indeterminacy pertaining to non-commuting operators). Now, I then wonder. If, UNPERTURBED, will the electron stay in this state forever? Will the z component be determinate and the remaining components stay indeterminate forever? I somewhat naively thought that the electron might eventually somehow go back to a full indeterminacy with regard to all spatial components.

    Do we know the answer to this experimentally?
     
  8. Apr 4, 2006 #7

    reilly

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    Here's where the "knowledge interpretation" scores big-time. That is, the collapse takes place in one's mind -- as new knowledge replaces older knowledge; uncertainty -> certainty. This approach does not distinguish between classical and quantum situations; it's just a common sense approach to probability, as used in practice. (Just to be clear, the content of quantum probabilities and classical ones are, generally, quite different.) The time interval of a collapse is the time it takes the brain to process the signals, and convert probabilities to a certainty -- probably on the order of milliseconds, an estimate that can be sharpened by going to the neurophysiology literature

    Regards,
    Reilly Atkinson
     
  9. Apr 4, 2006 #8

    ZapperZ

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    But if that is true, then you are implying that the time resolution of what we can deciper or understand is of the same order of magnitude, i.e. milliseconds. Obviously, this is clearly not correct.

    Zz.
     
  10. Apr 4, 2006 #9

    eep

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    Isn't this the correct answer?
     
  11. Apr 4, 2006 #10

    Galileo

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    Why, yes it is eep! Thank you :biggrin:

    Put two Stern-Gerlach apparatuses in series which both measure the z-component of the spin. Let one beam (say the one corresponding to spin-up) go through the second apparatus. Then there is no splitting of the beam at the second apparatus (all spins are up). The time interval between the first and second measurements is of no importance as long as you don't perturb the system (no B-field).
     
  12. Apr 4, 2006 #11

    reilly

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    Not at all -- unless you know someone who can perceive microseconds. Surely you must know that to measure very small time intervals, we must use some type of instrumentation. The collapse, as I view it, happens when the person reads the meter. (Now, of course, we may make surmises or conjectures about what happens to the system during or after measurement. That's a different ballgame -- Mandel and Wolf (...Quantum Optics) do this in exhausting detail for photoelectric detectors.) (But there is a mystery: given the slow speed of neural signals, how can a batter hit a 95 mph fast ball? How can a concert pianist play trills as fast as they do? )

    Regards,
    Reilly Atkinson
     
  13. Apr 4, 2006 #12

    ZapperZ

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    My RF pulse has a pulse width of the order of 100 ps. The electron bunch that I create has a length of roughtly 10 ps. I have a 15 GHz oscilloscope from Tektronix that can sample a 14 GHz signal. And I haven't even touched the time resolution that we require in some of these high energy particle detectors.

    Unless you are accusing me of being a liar, and unless you think that the ONLY means of an observation is to look at a measurement only with our own eyes, then I would say that we have a significantly better time resolution than milliseconds.

    Zz.
     
  14. Apr 4, 2006 #13

    Hurkyl

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    Well, there's a problem with this interpretation: it doesn't explain the consistency of observation.

    E.G.

    Suppose I look at something and a collapse takes place in my mind.
    Suppose you look at it too, and a collapse takes place in your mind.

    When we compare notes, we will always have seen the same thing -- how do our minds know to collapse in the same way?


    Similarly, if I look at it, and then I look at it again, my second observation is consistent with my first. How does my mind know to collapse the second time in the same way as it did the first time?
     
  15. Apr 5, 2006 #14

    reilly

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    Hurkyl
    OK. In fact, the neural collapse occurs, whether or not it has anything to do with QM. And, it seems to me, that since the collapse is real, that it is a great, Occam driven alternative interpretation of QM. This collapse occurs for classical phenomena as well. The only problem is whether this knowledge interpretation fits QM, which seems virtually self evident to me. Again the neural collapse is a real physical, measureable phenomena. Why not use it?

    Hurkyl says:
    Well, there's a problem with this interpretation: it doesn't explain the consistency of observation.

    What does?

    And, people can and do disagree. Of course, the assumption of some kind of objective reality helps explain the consistency of "natural phenomena".
    As Wigner wrote, why does human language, mathematics in particular, work at all?. For him it was a great mystery. Same deal with the consistency -- who really knows? (If you fancy Hume, you would say, nobody knows, which i'm inclined to do.)

    Zapper-- I think we may have miscommunicated; your veracity is not in question. I'm simply saying that any deficiencies in direct perception of time intervals, can be corrected by measuring devices. And I apologize for any mistakes in logic or language .


    A measurement, for me, is not a measurement until I know about it. And when I learn about it, I'll have a neural collapse -- from one knowledge state to another. Guaranteed.
    Regards,
    Reilly Atkinson
     
  16. Apr 5, 2006 #15

    Hurkyl

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    In fact?!?! That's an awfully bold statement!

    Except for the fact that it doesn't tell us anything about the interpretational issues with QM. :tongue: It doesn't address questions such as:

    ::: Is nature fundamentally uncertain? Or are there variables hidden from us that determine things?
    ::: What physically happens to the physical system when a measurement occurs?
    ::: Does QM apply to the macroscopic world?
    ::: Is nature local?
    ::: Are we humans in superpositions of states?


    You only address the last of these points, and I'm not even sure your interpretation answers it! Moreover, your interpretation introduces new unanswered questions, such as the consistency of neural collapse.


    Quantum mechanics does.

    In formulations where the collapse is taken to be physical, it's trivially easy to derive consistency: if I measure something, the physical system itself collapses into a state consistent with that measurement. Future measurements will automatically be consistent with what I measured!

    In MWI-style interpretations, consistency is almost as easy -- it's just a superposition of all the possible things that could happen in the previous approach.

    I presume other interpetations, such as Bohmian, can also derive consistency, but I don't know much about those.


    I don't see how this is relevant.


    Well, then there's a problem. It is possible for measurements that you don't know about to have an effect on what you see.

    For example, in the basic two-slit experiment, there are places on the screen that the particle cannot strike.

    But if we put a detector into the experiment that can tell through which slit the particle travels, then it suddenly becomes possible for your particle to strike the previously forbidden zones.

    So whether or not you want to call it a measurement if you haven't seen the results, it is still important to consider what they do.
     
  17. Apr 5, 2006 #16

    ZapperZ

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    But "you" are not built into the QM formulation. The operators that represent the type of observable that you get does not depend on you making that observation, the same way that I don't have to be in the lab for my fast scope to measure the pulse width of the electron bunches. In the same vein, the uncertainty principle has nothing to do with the accuracy of your measurement.

    So "you" are not part of the QM formulation beyond the choice of the type of observable that is to be measured.

    Zz.
     
  18. Apr 5, 2006 #17

    reilly

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    Of course I'm not in my quantum reality. So what's the problem? In fact, with the knowledge interpretation, there's no real problem incorporating the observer into the problem -- provided that I assume that a particle, atom, molecule, nucleus can only be in one place at one time-- when I measure, and that's major part of the measurement problem -- why only one result from most measurements.? (It is, of course, possible to relax that notion with the use of fuzzy logic, which allows a considerable amount of cognitive dissonance.)

    As I've said before, my strong belief is that if there is a solution to the "measurement problem", it will come primarily from neurophysiology of human perception and the processing thereof.


    If I don't know what's on the scope, I don't know. Someone else may know, but unless they communicate with me, I don't know.

    Regards,
    Reilly Atkinson
     
  19. Apr 5, 2006 #18

    ZapperZ

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    I don't have "one result" at any given time. I can make a measurement that implicates a superposition of an observable in several different states simultaneously. That's the whole premise of the Schrodinger Cat-type experiments that I've mentioned several times. I can make a measurement of a non-commuting observable to detect the superposition without doing any "collapsing" of the other observable. How else would you explain the presence of bonding-antibonding bonds seen in chemistry, and the superpostion of the supercurrents in the Stony Brook/Delft experiments?

    Again, coming back to this time-resolution thing. The fact that in many high energy experiments, we have very fast electronics that often do the vetoeing for us, implies that the time scale for such an event is WAY shorter (by orders of magnitude) than any neurological time scale that can be easily fooled by a simple movie reel at a movie theater. Why such an "observation" is an integral part of your QM, I have no clue.

    Zz.
     
  20. Apr 6, 2006 #19
    reilly,

    just because you can't physically observe, with your eyes, some pair of events that occur within [itex]10^{-15}\mbox{s}[/itex] of each other doesn't mean that they cannot be recorded and observe these with your eyes at your leisure.
     
  21. Apr 6, 2006 #20

    reilly

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    Exactly. You have made my point. Thanks.
    Regards,
    Reilly

    (More later re superposition for ZapperZ. But, as a trailer, as I've said before, The Schrodinger Cat is not a quantum problem -- it could be triggered by the 10th homerun in major league ball, hit after the cat is imprisoned, it could be triggered if one of my kids goes to Japan, and so forth. The issue could have been brought up 200 years ago.)
     
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