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I won't debate on the wavefunction collapse

  1. Oct 5, 2007 #1
    I won't debate on the "wavefunction collapse" ...

    ... since this is just a lazy debate started from a misunderstanding.

    Clearly when a small system interacts with a measuring device, the wave function of the small system just loses any meaning.
    There is only one "larger" wavefunction for both systems together.
    Why then should we say it has "collapsed"?
    Well ok, I know we need this probability rule, but let's say it is a practical rule.
    This collapse question has been debated since every long now, in different flavours, but this debate has really been sterile.
     
    Last edited: Oct 5, 2007
  2. jcsd
  3. Oct 5, 2007 #2
    the collapse of the wavefunction is merely a demon hand-waved into existence who's purpose was only to ease the minds of some who were uncomfortable with the existence of parallel universes
     
  4. Oct 5, 2007 #3

    Hurkyl

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    When you seek the probability of something happening "given that this other event happened", that's essentially a collapse.

    There isn't really an observable difference between "the state of the universe collapsed onto the branch where that event happened" and "Since I remember that event happened, the future probabilities I see will be derived from that branch".

    In fact, you can go so far as to say that the choice of whether to collapse the wavefunction or to compute conditional probabilities is simply a matter of choice; it's unphysical, much like your choice of coordinate axes has no bearing on reality.
     
  5. Oct 5, 2007 #4

    nrqed

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    But, in my humble opinion, this is simply replacing one mystery with another mystery. How does this "interaction" occurs? What is the physical process behind it? When does it occur? Etc etc.

    saying that "hocus-pocus, the wavefunction of the particle becomes entangled with the the measurement device when we do the measurement" is as mysterious as saying "the wavefunction collapses".

    I am not saying I disagree with your point. I do agree that a formalism in which the collapse never occurs is more satisfying than the collapse approach. I am just pointing out that saying this opens up as many questions as it answers, IMHO.
     
  6. Oct 5, 2007 #5
    well, someone just needs to answer those questions then--that's all!:tongue2:
     
  7. Oct 5, 2007 #6
    does it not suffice to say that there should be a solution to the SE for the system containing the entire universe? in which case, both measurement apparatus and the system-to-be-measured would be described by this wavefunction, and hence there would be no collapse. the prospect of collapse enters the picture when we make the decomposition of system and bath. i believe this is what the OP is asking?
     
  8. Oct 5, 2007 #7

    Mentz114

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    The wave function is not physical and so cannot collapse. I know I don't have to remind people of this, but it seems some still think the wave function has a physical existence.
    Probability is not a physical quantity either, and probabilty amplitude even less so.

    Looking for physical meaning in the wave function is sterile, it cannot be otherwise.
     
  9. Oct 5, 2007 #8
    There is nothing mysterious in the wave function collapse. Any probability distribution is supposed to collapse upon observation. This is just a part of definition of the probability distribution (or wave function).

    Suppose you've closed your eyes and thrown a die on the table. Before you opened your eyes the state of the die is described by a probability distribution. The probability is 1/6 for each of the faces. When you open your eyes (make the observation) this probability distribution "collapses" and you get a single outcome.

    Now, how this classical collapse if different from the quantum collapse? The only difference is that in classical physics you can in principle know exactly all the details of the prepared state of the die and predict exactly which face will be up. For microscopic quantum systems you cannot make such a prediction even in principle.

    So, the main mystery of nature is not the collapse of the wave function, but the fact that micro-systems behave unpredictably, randomly. There is no way to predict which spot on the screen will be hit by the next electron passing through the slit. There is no way to predict when a given radioactive nucleus will decay. These events can be described only probabilistically. So, there is some element of indeterminism in nature. Nobody knows why it is there, and I suspect we will never know that. At least, quantum mechanics doesn't provide an answer. QM simply accepts this indeterminism as a fact and incorporates this fact in its mathematical structure. You may think that there can be a theory more fundamental than QM, which will deterministically explain all quantum probabilities. However, as far as I know there was zero progress along this line of thought for the last 80 years.

    Eugene.
     
  10. Oct 5, 2007 #9

    dlgoff

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    "These events can be described only probabilistically. So, there is some element of indeterminism in nature."
    How does decoherence fit in? Isn't there something to pointer states; that shows a little determinism?
     
  11. Oct 5, 2007 #10
    As far as I understand, decoherence is the result of interaction between quantum system and its environment. I don't know much about this subject. Perhaps others can shed more light on it. I would prefer to discuss isolated quantum systems, where quantum effects can be seen in their pure form. An electron passing through a single or double slit is a good example of such a system. An unstable nucleus is another good example.

    Eugene.
     
  12. Oct 5, 2007 #11

    strangerep

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    Decoherence is a word for how quantum indeterminacy (superposition of states)
    becomes classical indeterminacy (not knowing which way the dice fell until you
    open your eyes). It is thought to occur via interaction of a system with its environment.

    In math terms, this means getting rid of any off-diagonal terms in the density
    matrix of the system. There were some papers by Ford et al a few years ago that
    showed (for simple examples) how powerful this effect could be. Even the miniscule
    gravitational interactions between a system and its environment could cause
    decoherence very quickly.

    BTW, the distinction between quantum and classical indeterminacy described above
    heuristically is the essence of what is expressed quantitatively by Bell's inequalities.

    - strangerep.
     
  13. Oct 6, 2007 #12

    Mentz114

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    meopemuk :
    Well said. It's pretty obvious we can never know our initial conditions in any setup because the quantum phase is admitted to be unobservable and beyound our influence.
    It is this which makes me believe that wave functions have no actual existence.
     
  14. Oct 6, 2007 #13
    I think the problem is that most think that when you open your eyes, there's a banana laying there, instead of a die.
     
  15. Oct 6, 2007 #14
    I don't agree that the prediction problem is the key difference.

    With a classical dice, the reality is that the dice has some particular side up after the throw, and the probabilities arise from our lack of knowledge. If we have not seen the dice after the throw, from our point of view there is 1/6 probability for each face, because we don't know it better.

    In quantum mechanics the reality is that a system has complex amplitudes to be in different states. The amplitudes are not only our tool to describe the system, but the amplitudes are the objective reality.

    That is a big difference.

    As consequence of this difference, also the nature of the collapse is fundamentally different too.
     
    Last edited: Oct 6, 2007
  16. Oct 6, 2007 #15
    So you have understood that there is no collapse, but instead the wave function looses its meaning, and there is a larger wave function that describes the system, and the probability rule comes out of this.

    And now you are confused, that why are so many folks still wondering what the collapse is? Why can't they see that this debate arises from misunderstandings?

    That's life, man.
     
  17. Oct 6, 2007 #16

    vanesch

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    This is in fact nothing of a mystery. The interaction between the observer and the observed is entirely defined by "standard" physics, which can in principle be written down in a hamiltonian. The entanglement then follows from the simple application of Schroedinger's equation to the overall observer-observed system. Although for a genuine observer (say, a human body and so on) this is untractable, for toy systems this is easy to do. In fact, even von Neumann did that already in his monumental 1932 work (mathematical foundations of quantum mechanics) where he introduces the "pre-measurement interaction" which is nothing else but the normal physical interaction between the measurement apparatus and the system, and out of it comes that each "measured state" ends up entangled with a distinct "pointer state" of the apparatus. This really follows from standard Schroedinger evolution.
    The point is now, that we now end up with an overall wavefunction which says:
    "particle was in state |a> and pointer is "1" " plus "particle was in state |b> and pointer is "2" " in the sense:
    ( |a> + |b> ) |0> evolves into (|a> |1> + |b> |2> )

    This is normal unitary evolution.
    The mystery is not here. It is what is expected. The mystery resides in the fact that we don't see ourselves in a superposed state, where we see "one world" where the particle was in state a and the pointer was 1 and at the same time see another world where the particle was in state b and the pointer was in state 2.

    The "standard" way is to say that the OVERALL state somehow collapsed into |a>|1> or into |b> |2> according to a probability rule.
    The MWI way is to say that "we" are just one of the observer states, randomly picked amongst the different existing ones.
    So the question is whether it is "we" who "collapsed" (or dedoubled?), or "nature".
    If the concept of a "we" is just limited to classically-looking states, and a previous "we" (classical) state evolves into a superposition, then this amounts to saying that the single "we" became multiple "we's". And we're one of them. This kind of stuff always leads to strange phrases because language and grammar hasn't integrated such a concept (in the same way as it would be difficult to do some grammar in 2-dimensional time...)

    No, really not. This is given by the physics of the measurement-system interaction.

    The "hokus pokus" resides in the "why don't we see this superposition".
     
  18. Oct 6, 2007 #17

    vanesch

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    This is a standard view on the issue (mainly Copenhagen's doctrine). Now, it is all fine and well to say that the wavefunction is NOT a description of "reality". Fine. So comes the next question: then WHAT IS a description of reality ?

    Bohr "answered" this question by saying that one shouldn't ask that question, but I find that a bit cheap. Of course, "reality" is philosophically always a matter of hypothesis, for you can do without, in a strong form of solipsism. But my answer to this issue is: if you haven't gotten any better than to tell me that I *shouldn't* talk about reality, but that we have a formalism that "pretends to describe reality but doesn't", then I find it still better to take as a (preliminary ?) hypothesis of ontology that that formalism IS describing reality, rather than telling me that I shouldn't make any hypothesis about reality. After all, making hypotheses about reality (even when wrong) has always helped us move on. Saying that one shouldn't make hypotheses about reality to avoid weird conclusions amounts to me to nothing else but mysticism. But we should stay modest, and recon that it is not because with what we know and found out TODAY about physics, and with our ability today to make ontological guesses, that these must be graved in stone for ever.
    Nevertheless, as of today, if we want to make a guess about reality on the quantum level, the best thing IMO to do is to give some status of ontology to the wavefunction. In the same way as we give some status of ontology to the banana on the table, just because that corresponds to our theoretical construct that our brain set up as a function of the sensations that we have (sight, feeling, taste,....).
    In other words, it seems to me that it is a good ontological guess (hypothesis) to take for real the best formal description that we have. We're not obliged to, but at least, it shouldn't be forbidden (what Bohr wanted us to believe).
    It's always better to have a strange reality, than no reality at all IMO.
     
  19. Oct 6, 2007 #18

    nrqed

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    Very interesting points (yoru posts are always extremely informative and thought provoking).

    The important point (that you also made) is, in my opinion, to keep in mind that what we use as ontology is not set in stone. All of physics is based on mapping observations to some mathematical framework 9with an ontology attached to it) and to map back the framework to observations. (Or, in some cases, to try to get the framework directly without any experimental input to map from, using arguments of elegance, unfication power, etc).

    The only danger is to start believeing so much in the mathematical framework and ontology assigned to it as to stop "thinking outside the box". The notion of absolute time is a good example. It became so part of the fundamental way of thinking of physicists that the ontology became set in stone, at least for the vast majority of physicists (philosophers were more open-minded :-) )

    The wavefunction concept is even more deeply abstract than time so that if it has used to build an ontology of the quantum world, it must be done with caution.

    I think that you agree with this. My main point i sthat it is nfortunately not emphasized enough to studentsof the field.


    Aside: In the end, the only measurements that are ever made are measurements of relative position between different objects, with time being a parameter specifying a rate at which relative position between certain "things" is updated. I always have wondered if a full theory should not simply use these data as the fundamental ingredients of the theory and nothing else.
     
  20. Oct 6, 2007 #19
    I think it is dangerous to pretend that we know what happens to the system "in reality", i.e., while we are not watching. This is a sure way to logical paradoxes. The whole point of complex amplitudes in quantum mechanics is to refuse any statements about "reality" and concentrate only on (probabilities) of measurable outcomes of experiments.

    Eugene.
     
  21. Oct 6, 2007 #20

    Hurkyl

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    I never found that mysterious: if wee see one state, we cannot see the other state!
     
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