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Collapsing Wave Function

  1. Apr 21, 2009 #1
    I have a question on collapsing wave functions. Suppose one observes the wave function of an electron. The wave function should collapse, but would it collapse instantaneously? If so, wouldn't this violate relativity?
     
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  3. Apr 21, 2009 #2

    Fredrik

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    There's no way to use wavefunction collapse to send a message faster than light, so there's no violation of relativity.
     
  4. Apr 21, 2009 #3
    So it is instantaneous or not? If not, does it occur at the speed of light?
     
    Last edited: Apr 22, 2009
  5. Apr 21, 2009 #4

    DrChinese

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    That's a great question. The answer is definitely, maybe.

    Assuming that wave function collapse involves a physical mechanism (which it is not entirely clear that it does): the lower limit on the speed of collapse has been experimentally pegged to be about 10,000 times the speed of light (4 orders of magnitude greater than c). See Testing Spooky Action at a Distance.

    - However, this is interpretation dependent. Some interpretations, specifically Many Worlds, do not require any FTL action.

    - In addition, even in interpretations in which there are FTL influences (such as Bohmian/dBB/Pilot Wave): Relativity is not thrown out the window.

    - Also, there are time symmetric interpretations which fully support relativity and still provide answers to apparent FTL collapse.

    So the upshot is: there is a lot of ground to cover in this one question. :smile:
     
  6. Apr 22, 2009 #5
    It's like a throw of dice. Before the throw, it's probability. after the throw, the wavefunction collapse and the result is certain. Would this violate relativity?
    This is just Bohr's version of quantum mechanics. Einstein and Schrodinger refused to accept this baloney.
     
  7. Apr 22, 2009 #6
    Max Tegmark ridiculing Wavefunction Collapse:

    "Electron obeys the Schrodinger Equation, except when it doesn't".

    Wavefunction collapse is related to the "Measurement Problem" in physics.

    It can by no means be used to undermine one of the most successful and bulletproof theories in science, such as special relativity.

    The opposite is quite possible though!

    Collapse "justification" is not even wrong.
     
  8. Apr 23, 2009 #7

    Fra

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    There are probably a few threads on this already but I think most of the objection on Bohr's interpretation is created out of a realist mindset, that refuse to see this in the context of science.

    I hold Bohr's spirit that

    "It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature"

    very high.

    Einstein may have been a genious, but I in despite of what he did, I think he was inhibited by his apparent realist mindset.

    On this issue, and in the context of a scientific method, if I have to choose which attitude is "baloney", it certinly wouldn't be Bohr's :wink:

    The conclusion here is that no matter what "nature is", ALL a real observer can EVER know about this, must be acuqired by means of interactions ~ questioning ~ measurements. So you never get closer to reality than your own perspective. Anything beyond that is IMHO at least, a naive realist ideal that doesn't match the standards of a good theory of science and measurement.

    Bohr, apparently understood that this is how nature works at the deepest level. The wavefunction is not just applied to human observers. It is really how parts of the material physical world interact with each others. This also means that "the wave function of an electron" is not an objective entity, that anyone can "measure". The wavefunction represents a sort of relative information. And the differing information two sub-systems have on their common environment, would typically result in an interaction. So this subjectivity, is not a PROBLEM, it's apparently a key to how the world world, and relates to why we have physical interactions.

    Why isn't the universe already at equilibrium?

    In this view, the collapse of the wavefunction is a localised to the observers. And a collapsing wavefunction (over say entire universe), obviously doesn't mean that the universe itself collapses. It just means that the observers INCOMPLETE, and UNAVOIDALY BIASED image of this mysterious reality, is UPDATED.

    I really don't see why this is so hard to accept.

    I posted this before, but I think the easiest analogy of this, is to think of quantum mechanics as a game, where each observer is a player. And all players want to control, predict and get on top of other players, to preserve themselves. In this game, the action of these players are determined but the observers knowledge, of the other players. Even the rules of the game are open. One player nevers know what the others REALLY know. The only way to learn is to take risks. They make a guess, and test it by acting as per it. The feedback they get is either constructive or descructive. So the emergent "opinon" has evolved simply because it preserves the observer itself. What is "real" beyond that is irrelevant.

    Cheers to Bohr ;-)

    /Fredrik
     
  9. Apr 24, 2009 #8
    Do you believe the moon is Not there if nobody is looking at it?

    >>Einstein's ironic statement was "Does the moon disappear when I'm not looking at it?" This was stated in order to show the absurdity of the Copenhagen Interpretation of Quantum Mechanics, which states that there are no particles in the universe until scientists perform experiments; i.e. the experiments themselves 'create' reality ahead of them, creating an illusion that scientists are exploring a reality that is independent of their mental existance.
     
  10. Apr 25, 2009 #9
    The moon is not exactly where we think it is - ever. We cannot know with infinite accuracy so in fact it does behave with some uncertainty.

    Apparently they fire lasers at the moon every few seconds which updates our approxiamtion of where it is right now, meaning where its likely to be at x time from now.
     
  11. Apr 25, 2009 #10

    I rather think of it as we, or our shared reality, defines our environment - not necessarily creates it. Think about it; we can only sense the environment around us with the sensory organs we have evolved. So our view on this reality is biased from the start, and we are limited to some extent.

    To me it makes sense for nature to only provide a tangible reality for what is absolutely necessary. Think of it like shared services.
     
  12. Apr 25, 2009 #11

    Fra

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    This must be put in a proper context to be worth discussing. Ie. what is the operational difference in wether the answer is yes or wether it's no? Ie. what difference does it make?

    IMO, the proper context of this knowledge, is that of an action.

    - A human observer, bases his actions upon his beliefes. So his actions are indifferent to wether what his best beliefs is fact or fiction. However, once action is taken, there will be a backreaction from the environment, and here is DOES make a difference. This can be interpreted as forces, or interactions, that works to evolve the observer, and his knowledge.

    - A physical observer (subsystem of the universe), acts as per his subjective knowledge of it's environment. IE. a systems interaction properties, is determined by the systems "belief" or "illusion" of it's environment. Similarly however, once you take into account teh backreaction to these actions, a sort of contradiction appears in the form of interactions, again, working to deform the observers information state of it's environment.

    So, to the immediate question, what "instant" difference does it make wether the moon REALLY is out there, or if everybody shares the same illusion? The obvious answer is NO.

    Now, this does however not mean that this illusion is static - it is not! Due to the infinite regress outline above. But this infinite regress is IMO nothing by ordinary dynamical interactions.

    Think of a poker game. The immediate behaviour and strategy of your opponents, are independent of what cards you REALLY have. He will form his strategy, in compliance with his belief. So you can modify and control a REAL GAME, and REAL ACTIONS, simply by trying to make your opponents think you have some particular cards.

    The story is very similar in physical interactions IMO. The poker game analogy is something everyone can understand. IT is also the case that the opponents beeing aware if that he is in fact only guessing, he also ACTS upon the risks. His actions is different from a random action of a set of possible certiain opinons. His actions is formed as if he somehow holds all opinions at once (weighted)

    /Fredrik
     
  13. Apr 25, 2009 #12
    I hold it very low. One thing is to think that some research direction will not give, in observables future, some results. This is a decision every scientist has to make for himself: What is the direction of research which has the greatest chances to give some new insights. At Bohr's time, it was a quite reasonable choice to think that it is not yet the time to think about how nature is, let's better care about what we can say about nature.

    It is a completely different thing to exclude the alternatives from science. That is simply the totalitarian spirit of that time.

    This is positivistic theory of science, which has been refuted by Popper long ago. Realism is, instead, the true method of science. We propose theories, as hypotheses how nature really works. From these hypotheses, we derive what can be observed, and compare these derivations with observation. Even if this does not help, if there are different realistic theories able to preserve the phenomena, we have criteria for comparison (simplicity, beauty, explanatory power, internal consistency) which allow to reject some if not most of the alternatives even without support from observation.

    An important point is that one has to do the scientific theoretical work to find out if there are some possibilities to test some ideas of how nature works really do not have observable consequences. Once Bohr's position forbids such research as not being part of physics it should be rejected as preventing future progress of science in this domain.
     
  14. Apr 25, 2009 #13

    apeiron

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    It is perhaps better to treat truth and control, realism and pragmatism, as two ends of a spectrum for modelling.

    I see it as the difference between science as philosophy and science as technology.

    The natural desire of a modeller is in fact for local control. An animal just wants to anticipate its world in a way that maximises its control over its surroundings. A thermostat needs to know very little indeed to act as a controlling mechanism.

    So modelling is very pragmatic in most examples of systems that model. But we humans dream of seeing the global view, the big picture, even if that knowledge does not seem practical - we cannot apply the learning to change things.

    So rather than get hung up on positivism vs realism, philosophy vs technology, or any of the other many divides, you can instead see that it is all about the common act of modelling. The observer relation. Semiotics. And then that it is possible to be an observer at many different scales.

    You can be a highly located observer (which is the natural kind - the useful pragmatic position we would take to live in our worlds). Or you can dream of rising up to some global scale observer status - to see the whole of nature, to stand outside the very universe to see its start and end.

    That breaking of natural scale has been also useful. In imagining things from "unnatural" scales - much larger, much smaller - we have been able to apply some of that perspective. We have technology of the very small and very large.

    And we can, as I say, imagine taking a completely general or global view. But it does become less applied knowledge, less testable knowledge, and so things get controversial.

    Anyway, start with a theory of modelling, a theory of observers, then consider how scale affects things. Humans have a natural physical scale of observation. We want to "unnaturally" extend it. We have to understand that this is what we are doing so as not to get confused about "truth vs control".

    Oh, and on the initial question. Of course collapse violates relativity. One is a model that preserves locality, the other dichotomises into the local and non-local. But both are just models. Useful for different tasks. They apply best at quite different scales of observation. And yes, it would be nice to have an uber-theory that applies smoothly across all scales of observation.
     
  15. Apr 25, 2009 #14

    Fra

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    The objection you raise seems to be a common objection to the CI-spirit from certain people who seeks realism. IMHO at least, this is a misconception. The implication you suggest, is not the case for me.

    The fact that an observer do not KNOW with certaintny, does NOT imply that I can not LEARN. These are two different things and the first does not imply the latter.

    So, the attitude that we can only speak about we know about nature, definitely in my mind, does not in any way inhibit science. It does not exclude any possibilities.

    But I should add that my view is not a plain CI-interpretation. I think QM is - rather than as Einstein thought, "incomplete" - only emergent. But this emergence, can still be seen in the Bohr spirit, because what an observer can say about nature, is not static. His ability is evolving, and in particular depends on his complexity.

    Reading some of your other posts, I'm not too surprised that I strongly disagree with your view here.

    I also think that Karl Popper's description of the scientific method is too simple. I do not share Poppers reasoning at all. His idea is better than nothing, but he ignores the importance of the effiency of hypothesis generation, by trivializing it into psychology of scientists. And his attempt to avoid induction fails. Popper is a classic, but he is not from my perspective not one of the deep thinkers. His reasoning largely overlooks the difficult parts - but this is a separate discussion, I wont go into details here.

    Also, about your idea of simplicity and beauty. You have a poitn about simplicity as discriminator, but that really isn't hte problem. The problem is that there is no objective measure of simplicity. You can probably make anything simple, by constructing a custom measure.

    To me simplicity is closely related to speculation. A simple "theory" is a one which contains a minimum of speculation. To stick to what we know, and not adapt to realist constructs are to me simple, beucase it does away with the redundant baggage.

    /Fredrik
     
  16. Apr 25, 2009 #15

    apeiron

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    It would be possible to take an information theoretic approach here (as Norretranders in his pop sci book, The User Illustion, argued).

    Simplicity involves a reduction in the information required to specify a particular theory or law.

    E=MC^2 excites people because it is compact enough to fit on a t-shirt. It is simple in an information theoretic sense.

    This is of course why we want to go generally from philosophy (much waffling) to mathematics (abrupt equations).

    Modelling involves a reduction of information. Of course, models often end up too simple to apply to more than small (particular scale) applications.

    But the general point is that modelling theory (the modern stuff post popper, positivism, etc - so Rosen, Pattee, those kind of modern era guys) can operationalise the notion of simplicity.
     
  17. Apr 26, 2009 #16

    Fra

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    Apeiron, like I concluded in previous posts. As an overall view, we are in close agreement. I agree with your sentiment.

    I haven't explained my personal modelling because it's not mature enough, but indeed there are possible information theoretic and operational definitions of simplicity. But these things contain many complications. The information theory we need, is different that the what I call background dependent information theory in the tradition of shannon etc. This is a technical challange. We need a relational information theory, that emphasises the inside view, without relying on a birds view. I see that this is possible, but apart from philosophers, the realisation of this into mathematical models are yet absent. This is the challange.

    To just get in the ballpark of what I have in mind, the most obvious more detailed notions of simplicity is the idea of maximum entropy principles - for states, minimum action as in minimum information divergence - for transitions. These constructs are depending on abstractions and measures. Microstates and entropy measures. Differential microstates and action measures. I see these mathematical measures, as represented by the physicalk observer. And as the observer evolves, due to backreation from the environemnt, these mathematical measures also evolve. This is why we don't necessarily NEED UNIVERSAL measure of information. Universal measures usually implies external bird views. And then we step outside of science, because there are not outside observers.

    The mathematisation of evolving LAW, can be thougt of as evolving mathematical systems, whose evolution map out a flow - this flow is identified with the flow of TIME. But this flow can only be described from the inside. The flow itself is not objective. The COMPLEXITY of the mathematical strucutres, puts a bound to what possible phenomenologies that are possible. The different interactions here between mathematical systems, can possibly be idenfited with physical interactions and the fundamental forces.

    This contains alot of self reference, which makes this very complicated. I have not myself yet seen anyone having published a paper which realises these ideas. That's why it's hard to give references. There are a number of people which I mentioned before, which are partly sniffing this direction, but none which yet IMO has a grip on the full picture.

    About my own work, it's yet very much in progress. And before I would think of publishing anything it would have to reach at least a minimum of maturity, and I have long way to go. I am aware enough to see that a radical suggestion would have to be exceptionally clear to be able to convince others to accept it. Fuzzy discussion is what we have meanwhile.

    /Fredrik
     
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