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What causes wavefunction collapse?

  1. Aug 29, 2011 #1
    I've always been confused about something -- I'd love for someone to clear up my ignorance.

    I understand that the position of a particle can be modeled as a wavefunction (a probability distribution, to my understanding) where we can describe the position as fundamentally random, but it takes on a value at a frequency in accordance to the distribution once it interacts with something.

    My question: What does it mean for it to "interact?"

    When two particles collide into each other to take on their "real" states, how does it know when this occurs? In my mind I am viewing it as two clouds of probability heading towards each other. Technically, the clouds are always intersecting because the wavefunction distributes itself across all space and time, right?

    Even if I am wrong on that point, my question is what is actually happening here when probability clouds collide. What is the mechanism that describes the actual collapse of the wavefunction from probability clouds to real states? Do they just have to take on the same values at the same time, where this becomes more and more likely as the clouds intersect more intimately?

    Sorry if I am not making much sense.
     
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  3. Aug 29, 2011 #2
    I think the simple answer is that no one TRULY knows.

    Roger Penrose has some interesting ideas on wave function collapse. Basically, he feels it is ultimately related to gravity and an explanation for WF collapse will have to be included in any theory that succesfully combines QM with GR.

    A google will probably provide more info.
     
  4. Aug 29, 2011 #3
    So not only is the real state of the collapse random, but the actual act of the collapse of the wavefunction itself is random?
     
  5. Aug 29, 2011 #4
    Granted I am very new to this stuff, and probably don't have nearly the amount of knowledge on the subject as some here, I'll try and help. What you're asking is basically an answer to something called the quantum measurement problem. There are a lot of differing ideas on it, of course, but nothing concrete that is agreed upon by 99% of the scientific community. Basically, when a scientist "looks at" (measures) a particle, it changes from its wavefunction form of limbo into the particles we know and love today -- physical things with exact locations, velocities, spins, etc.

    I would start by not calling these things probability clouds. I'd stick with two probability waves (since they are waves, after all -- there are just a lot of them, everywhere). From my reading, wavefunctions interact all of the time -- it's how they discovered wavefunctions exist in the first place! When viewed correctly, interacting wavefunctions create interference patterns, and can thus be observed. The wavefunction doesn't, however, immediately collapse because of this interaction between multiple wavefunctions. It collapses (if wavefunctions even collapse at all) because of . . . well, nobody really knows. We don't even know if a wavefunction even collapses! There are theories, however.

    One approach is to abandon the view that that wavefunctions are objective features of quantum reality; instead, they're just an embodiment of what we know about reality. In other words, we don't know where the particle is yet, so we come up with probabilities. Once we gain the knowledge of where the particle is through measuring it, the wavefunction "collapses" and we gain knowledge.

    Another, far cooler idea, is the Many Worlds interpretation. If you've ever watched the last season of LOST, you'll have an idea of what it is. Every probability of a particle being here, there, or over yonder in a wavefunction is realized -- the wavefunction never collapses. It's just realized in different parallel universes.

    Another thought is that particles do actually have an exact location and spin, etc., at any one time, just like Einstein thought they should. The wavefunction is not separate from the particle, but is instead included with the particle. So when you find the particle, that's exactly where it was previously, too. Quantum uncertainty comes into play in this interpretation.

    There are others, of course, too, but there's a big one that seems to be gaining traction called decoherence. You might want to look some info on it up, since I won't go into much detail here, since, honestly, I can't -- it's confusing! Basically, if I understand it right, the environment is always interacting with wavefunctions, and nudges a wavefunction in one direction or another, giving the particles their classical appearances -- basically how we interact with our environment on our larger scale of everyday life. For instance, photons are always bouncing and hitting things, "blurring" their wavefunctions, and forcing them to appear here or there. No wavefunction collapse occurs, but wavefunctions "blur."

    I hope this helps. I am sure I got some of it wrong, and others can go in depth with it far more than I can.
     
  6. Aug 29, 2011 #5

    kith

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    Not every interaction is a measurement. There is no collapse in your example. After the collision, you just have two new clouds. The cloud collapses to a point only if a position measurement is performed.

    Having understood this, your new question will probably be "what interactions are measurements then?". In the mainstream interpretation of QM (Copenhagen), this question is not fully answered. Measurement takes place, when you're using a classical measurement apparatus to interact with your quantum system. For example, if you use a photo plate to detect photons.

    This is unsatisfactory, since a fundamental theory should also be applicable to the process of measurement itself. This means it should be possible to describe the measurement apparatus quantum mechanically as well, which is quite difficult.

    In principle, it should be possible to explain the collapse by so-called decoherence. In this framework, a measurement devices constitutes a large environment for the system of interest. Interactions with this environments on a very short timescale can then be approximated by an instantaneous collapse of the corresponding wavefunction. However, this view is not compatible with the mainstream interpretation of QM.

    In the end, most confusing questions about QM reduce to the question 'which interpretation of QM is the right one?' and there's still no consensus about it's answer in the physicists community.
     
    Last edited: Aug 29, 2011
  7. Aug 29, 2011 #6
    In my mind, interaction and measurement are pretty much the same thing, since I consider a measurement an act of interaction.
     
  8. Aug 29, 2011 #7

    K^2

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    And you're wrong. Measurement and interaction are two different things in Copenhagen Interpretation. Otherwise, superposition would not exist at all. There is always some kind of interaction.

    This is why I like MWI. That sort of question doesn't enter. There is no collapse in MWI, and that's that. Of course, there are other questions there.
     
  9. Aug 29, 2011 #8
    There's always some kind of interaction due to the fact that wavefunctions extend through all time and space, correct?

    Can you give an example if interaction versus measurement? I guess I don't understand because all sorts of processes happen without us measuring them. Things take on real values.
     
  10. Aug 29, 2011 #9

    K^2

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    A spin-1/2 particle is placed in magnetic field. That spin will precess due to the interaction with the magnetic field, yet its wave function will not collapse, because you are not measuring the actual spin.
     
  11. Aug 29, 2011 #10
    That is my question though -- when we say the spin will precess due to its interaction with the field, how are we saying that the wavefunction hasn't collapsed yet? I may be incorrectly assuming that a wavefunction collapse means you change a particle from a state of uncertainty to a state of real confirmation. So for the field to cause the precession in the first place, it needs to somehow interact with the particle.

    Or, are you saying that the field affects only certain properties, and these properties are affected along the particle's entire wave function -- but we don't actually know its position until we measure it directly?
     
  12. Aug 29, 2011 #11

    K^2

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    Suppose, the spin is initially in the sate |chi>=a|up>+b|down>, and is placed in a magnetic field along x. To within constants, the state at time t is Exp(iHt)|chi>, and H~=Sx. Or when expanded:

    [tex]\chi(t)=\left(\begin{array}{cc}cos(\omega t)&sin(\omega t)\\sin(\omega t)&cos(\omega t)\end{array}\right)\left(\begin{array}{c}a\\b\end{array}\right)[/tex]

    So |chi>(t)=(a cos(wt) + b sin(wt))|up> + (b cos(wt) + a sin(wt))|down>

    Notice that at any given moment, the spin is still in superposition.
     
  13. Aug 29, 2011 #12
    I am not familiar with the terminology, but I am assuming that a and b are properties of spin, and the omega-t stuff is the interaction of the magnetic field. The end result is a combination of the two. This corresponds, though, to what I was calling "properties being affected along the particle's entire wave function" (is this inaccurate to say?). Would it be accurate to say that the particle is in many places at once and the field is affecting ALL of those "possible particles"?

    What, then, would it look like if we measured it? How would this act of measuring be any different from a field interaction?
     
  14. Aug 29, 2011 #13

    K^2

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    This is a point-particle. Its total wave function is given by [itex]\chi(t)\phi(x,t)[/itex]. Phi is what gives the spatial distribution. The parameters a and b are just fraction of wave function corresponding to spin up and spin down respectively.

    In measurement, the wave function collapses to eigen states of the measurement operator. Suppose, you measure spin along z of the particle in initial state |chi> above. The eigen vectors of Sz are |up> and |down> vectors from above. So after measurement, with probability a² the state will be just |up> and with probability b² it will be just |down>
     
  15. Aug 29, 2011 #14
    I think I need a bit more education on the basics, because I am having a hard time understanding those kinds of explanations when I am not familiar with the terminology.

    You say "measure spin along z of the particle in some initial state" -- what does it mean to physically measure a "spin"? How is a "measurement" in itself not an interaction with a physical entity?
     
  16. Aug 29, 2011 #15

    DrChinese

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    You are going to find yourself in the land of semantics pretty quickly here. Spin measurements are usually performed without scattering or absorption. You have also field effects to consider, and those of course should be considered physical. But there are no particles touching other particles in the normal sense of the words.
     
  17. Aug 29, 2011 #16
    An 'interaction' between two particles can be modelled for example by writing out schroedinger equation for a system of two particles and adding an extra term V(r1,r2) to the hamiltonian, which represents potential energy of particle interaction. Before the interaction, the WF for a system is a product of WFs of individual particles. After the interaction, in general, the WF of a system is no longer separable, the particles are said to be entangled. The same applies when more complex systems interact with each other. As long as you keep track of the details, there is no collapse.

    Interaction causing WF collapse are called 'observation' or 'measurement'. They involve quantum system interacting with macroscopic 'observer' (aka 'detector' or 'measurement apparatus'). Macroscopic is understood as having very large (many orders of magnitude) number of degrees of freedom. Clearly we would have a bit of a problem writing out schroedinger equation for it, never mind solving it, so whatever is going on there is shrouded in mystery. Nevertheless, we find that after such interaction the WF of the particle collapses into an eigenstate of a certain projection operator called 'observable', which is specific to the observer. At the same time the macroscopic state of the observer changes according to the eigenvalue associated with the new state of particle's WF. The interesting part here is while schroedinger evolution is linear, the collapse isn't. So at some point somehow the superposition is destroyed and only one eigenstate is chosen seemingly at random with probability proportional to the square of magnitude. Exactly how, when and why this happens is subject to interpretation.
     
  18. Aug 29, 2011 #17
    This is an incredibley helpful post for me in my early research into the problem, thanks!

    It is becoming quite a struggle to categorise the different interpretations, would you mind telling me if the bolded section is referring to Bohr's epistemological interpretation? As compared to the Copenhagen interpretation (of which Bohr was instrumental) which appears to be a different concept.

    Also, what is the underlined idea(s) referred to as? Thanks!
     
  19. Aug 30, 2011 #18
    I don't think that the implication of interaction from measurement [itex](M\implies I)[/itex] is under question (although maybe some here do), but rather the other direction, that interaction implies measurement, [itex](I\implies M)[/itex], these are two different things, you need both for equality.

    I seem to agree with K^2 here, but I have some question about the interactions.

    How would a silver atoms electromagnetic interaction not cause collapse, but the interaction of the silver atom with the florescent screen would cause collapse? Especially since, at the fundamental level, the interaction with the florescent screen is really an interaction with the atoms in the screen, which is really an electromagnetic interaction also!

    But, it's also true that the E&M interaction is not solely responsible for the interaction of the silver atom and the screen, the anti-symmetric nature of the wave-functions also plays a role. If this is your rebuttal then I'm even more fascinated, and have to think more on it... :smile:
     
    Last edited: Aug 30, 2011
  20. Aug 30, 2011 #19

    K^2

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    That would definitely help. There are a lot of things you can't learn efficiently by just asking questions. Sometimes you need to sit down and listen to a good lecture or read a book.

    Measurements are a type of interaction, always. But there are interactions that collapse the state and interactions that do not. In Copenhagen Interpretation, it's not always clear which is which, and that's why more and more physicist switch over to Many Worlds Interpretation. It is more clear on what does and what does not constitute a measurement. You can try reading Wikipedia article on MWI and see if it helps you answer a few of the questions.

    Keep in mind that Copenhagen and MWI are equivalent in terms of their prediction. One of these is not better than the other, and you really should understand both to have the better understanding of QM overall.
    Because when you get right down to it, collapse doesn't happen when film gets exposed. Collapse happens when you use film for measurement. Again, what constitutes measurement is iffy in Copenhagen. MWI tells you exactly when the apparent collapse should happen.

    The Quantum Eraser experiment demonstrates this pretty well. There, the measurement is made, and is then discarded, which prevents the collapse that would have happened due to the measurement. Again, makes little sense in Copenhagen, but perfect sense in MWI.
     
  21. Aug 30, 2011 #20

    Fra

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    I'm as biased as anyone else but they way I see it, those interactions that don't collapse the state, are those that either are already implicit in the expected evolution (ie. hamiltonian, interaction terms etc), or that doesn't even couple at all to the system.

    This is why the unitary evolution of the schrödinger equation is best thought of as an "expected evolution". When the information on which the prior expectations are based are suddenly changed so does the new expectations.

    The whole point with updating to NEW information, is that it isn't previously expected. If it was, it would not be new.

    In this picture, there is no problem of the collapse at all. The information update is a basic mechanism of how rational inference works. To think you can do away with an information update is irrational if you have this view. It's instead the key to learning.

    Instead the problem is another one: to explain the de facto objectivity we all agree upon when it seems at deepest level all we have are observer dependent expectations.

    But in that conceptual picture the idea is that interaction between observers, causes an evolution to take place in a way that not all observers (views) are equally preferred at equilibrium (although they are all possible). So at equilibirum we recover de factor objectivity, simply because those that don't comply are destabilised.

    Compare with biology. You can easily picture countless perfectly "consistent" life forms, that we nevertheless don't see in nature? Why? They just don't have a place in the current state of the ecosystem and evolution.

    So any two systems that are interacting and communicating, tend to negotiate and reach agreements, and if they don't, they will destroy each other. Similar mechanism could explain objectivity of laws of physics, in such a weird apparently solipsist picture I outlined. It's really like Van der Waals / Casimir like effect that takes place in "theory space".

    /Fredrik
     
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