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Thread: Indirect collapse of the wave function

  1. #1 Indirect collapse of the wave function 
    Super Moderator Quantime's Avatar
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    I was reading up on Quantum Non-locality last night and learned that by virtue of entanglement one can learn of a system without interacting with a system directly. I used the Schrodinger's cat analogy to explain this.

    Imagine that there are three systems:

    Cat A, Cat B, and Me; C

    Let us assume that cat A and cat B are entangled. Both cats are present deadalive. Let's now say that I as system C, interacts with system A and open the box to find that System A, namely cat A is dead. Knowing that the cats are entangled I can deduce that System B, namely cat B, is now alive. I have collapsed the wave function of System B as System C, without directly interacting with System B being myself System C. What concerns me of this is that System B is not aware of me, System C and has no awareness as to my state, but I do of it.

    Does this suggest that the uncertainty principle is violated between System B and C? By definition without observing that system I cannot determinately know for sure if the cat is dead or alive yet because I know system A is dead I know that system B is alive.

    I want to expand on this using Everett's many worlds interpretation and say that instead of the following possibilities:

    System A is Alive and System B is Dead.
    System A is Dead and System B is Dead.
    System B is Dead and System A is Alive.
    System A is Alive and System B is Alive.

    In a lineally interacting way with no entanglement I would theoretically only be able to see a split in the universe when interacting with with either box, in other words 4 possible probabilities as to the reality of each box with a universe for each box, but when they are entangled we have only two:

    System A is Alive and System B is Dead.
    System A is Dead and System B is Alive.

    This reduces the possible 'many worlds' when the systems are entangled. Does this suggest that Quantum Entanglement reduces the number of universes in the many worlds interpretation? Would this also not mean that there are NOT an infinite number of universes?

    What is current understanding from scientific institutions on this? Or have I just added something new here? Not quite sure!
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan.
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    mvb
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    I suspect that most working physicists subscribe to the "shut-up and calculate" philosophy about these kinds of situations. Life is much simpler that way.

    My take on what that philosophy means in practice is that it is always possible to describe a measurement in quantum mechanical terms alone. [My take only; I don't know how others feel but the following is plausible and works in many of the simpler situations.] That is, there is a QM operator O(x,t) representing the measurement process, and

    f(x,t) = O(x,t)i(x,t)

    If you are making two measurements, you simply multiply by operators representing each measurement. Then when everything you are interested in doing is finished, you calculate the probabilities of the results in the usual way. The key word is "everything". Only when you try to talk as if the intermediate state(s) are classical do you get into hassles. In particular, don't make part of the description classical and the remainder quantum-mechanical at the same time.

    In particular, I would argue that the world consists only of wave functions. Classical descriptions are only approximations, although in many cases they are extremely good approximations. If only the wave functions truly exist, there is no need to talk about worlds where different things happened to the same system with probabilities given by wave-function calculations. Wait until everything is done, and calculate the probability of those combinations of things you are interested in happen.

    These calculations will always be consistent with each other.
    Last edited by mvb; 01-29-2013 at 12:03 AM.
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    The uncertainty principle simply states that you cannot precisely "know" the state of two non-commuting observables at the same time, for example position and momentum or energy and time. It's a statement about the "observed" and not the relation between "observer" and "observed."
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    Quote Originally Posted by Quantime View Post
    Does this suggest that the uncertainty principle is violated between System B and C? By definition without observing that system I cannot determinately know for sure if the cat is dead or alive yet because I know system A is dead I know that system B is alive.
    No, the problem you describe is exactly the EPR Paradox.

    First of all, the uncertainty principle isn't violated. Our prepared entangled state has already a maximum uncertainty. This reduces after observation. We had a lot of pre-knowledge about the prepared state. There is no problem here at all. This is also not what the EPR Paradox is about. Nor has it much to do with the non-locality of (all) quantum physics.

    The 4 systems you described are not entangled. If all things in your system are distinguishable, you cannot make entanglement.

    A proper version would be that you have 2 Identical cats. And you wouldn't know which one is which. Lets call a dead cat, a capital cat (A,B), and an alive cat a small letter (a,b)
    Then your states are (from top to bottom):

    |a b >
    sqrt(1/2)(|a B > + |A b>)
    sqrt(1/2)(|a B > - |A b>)
    |A B>

    Only the two center states are entangled as the average of the whole system is a dead cat, but we don't know which cat is dead.

    Also the original schrodinger cat experiment was with one cat, as you only needed 1 cat, you already have two states, dead and alive.

    From the above there is an important change to be noted. There are 2 entangled states, the symmetric and the anti-symmetric. But let's not go there now.
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    Senior Member merumario's Avatar
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    no one knows why quantum physic should voilate principle of locality.bohr while arguing with einstein said that this cannot be used for communication.although this is still unresolved it worth more attention,to me i stand for einstein saying quantum theory is not complete and that the wave function is more than superpositions of a particle.
    Bodies attract each other at near distances,the convergence is inevitable. A fundamental,subtle spirit which lies hide in all gross bodies.(Newtonian gravity)
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    Quote Originally Posted by Quantime View Post
    I was reading up on Quantum Non-locality last night and learned that by virtue of entanglement one can learn of a system without interacting with a system directly. I used the Schrodinger's cat analogy to explain this.

    Imagine that there are three systems:
    Chapter 5 @ 6:30 explains entanglement and how it can be manipulated (if at all).

    NOVA | The Fabric of the Cosmos
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    Quote Originally Posted by merumario View Post
    no one knows why quantum physic should voilate principle of locality.bohr while arguing with einstein said that this cannot be used for communication.although this is still unresolved it worth more attention,to me i stand for einstein saying quantum theory is not complete and that the wave function is more than superpositions of a particle.
    Actually, it is very much the question how non-local quantum physics is. Factually seen, it doesn't violate 4D local causality at all.
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    Senior Member merumario's Avatar
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    Kerling am afraid it voilates the principle of causality.
    Bodies attract each other at near distances,the convergence is inevitable. A fundamental,subtle spirit which lies hide in all gross bodies.(Newtonian gravity)
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    Senior Member merumario's Avatar
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    Kerling am afraid it voilates the principle of causality. Although the cause can be trace back to the first particle observed,the effect ought to be definite in that enviroment only.
    Bodies attract each other at near distances,the convergence is inevitable. A fundamental,subtle spirit which lies hide in all gross bodies.(Newtonian gravity)
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    Quote Originally Posted by merumario View Post
    Kerling am afraid it voilates the principle of causality. Although the cause can be trace back to the first particle observed,the effect ought to be definite in that enviroment only.
    Haha, don't be silly. Of course it doesn't. Quantum mechanics, and especially the Copenhagen interpretation is very causal. Why would it not be, we have never seen any experiment that violates causality. Logical causality and 4D locality. Just because actual causality doesn't live up to your demand of fixed past, and notions of a separate time and spatial dimensions. Doesn't mean that it doesn't exist.
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    mvb
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    As far as I have seen -- and I would love to see more if it exists -- the causality and locality proofs on quantum mechanics apply only to the determination of the wave function using Schroedinger's equation. If you believe in a real collapse of the wavefunction caused by a measurement, and don't specify exactly how this collapse occurs, it seems to me that you have lost causality. After all, with a given wavefunction, the particle can show up in many locations with various probabilities. It's further progress, with a new, localized wave-function that is not, in practice at least, determined by Schroedinger's equation, is causal from then on. However, there will be differences in behavior depending on where the particle was found to be. These are not, in the wavefunction-collapse idea, determined by the Schroedinger equation, so they are not known to be causal. Since the mechanism of the "collapse" is not specified exactly in terms of the wave-function, there is no way to tell if it is causal.
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    Quote Originally Posted by mvb View Post
    As far as I have seen -- and I would love to see more if it exists -- the causality and locality proofs on quantum mechanics apply only to the determination of the wave function using Schroedinger's equation.
    Ehm, no try wikipedia. for instance the bell-inequalities. Or the delayed choice experiment. Or the Aharonov Bohm experiment.

    If you believe in a real collapse of the wavefunction caused by a measurement, and don't specify exactly how this collapse occurs, it seems to me that you have lost causality.
    No you don't. You don't need to explain how the collapse has come to be, but why.
    Just because you don't know how you have become pregnant. Doesn't mean that you have been conceived by god.

    After all, with a given wavefunction, the particle can show up in many locations with various probabilities. It's further progress, with a new, localized wave-function that is not, in practice at least, determined by Schroedinger's equation, is causal from then on.
    Actually it doesn't have to be. Causality only has use to exist between observation. It's evolution in between is not of our concern. After all, we cannot violate causality which we cannot observe. (I cannot break laws that are invisible for the world)

    However, there will be differences in behavior depending on where the particle was found to be. These are not, in the wavefunction-collapse idea, determined by the Schroedinger equation, so they are not known to be causal.
    once a particle is found to be somewhere, its wavefunction is decayed, and it will be in that state. The wavefunction collaps, is quite literally the discontinuous evolutions of the Schrödinger wave function. That is actually what it is.

    Since the mechanism of the "collapse" is not specified exactly in terms of the wave-function, there is no way to tell if it is causal.
    A collapse, requires a measurement. A measurement is either causal or not. In reality this boils down to: A recorded measurement or an unrecorded measurement. Unrecorded measurements do not discontinuate the wave function. And recorded do. Making a record is a causal action. Even if you didn't know, finding the record will be a causal act. If you do not find the measurement then the wave-function isn't discontinuated. There are quite some neat experiments that prove this. It's interpretation how the wavefunctions collapse gives rise to the infamous measurement problem.
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  13. #13  
    mvb
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    Quote Originally Posted by Kerling View Post
    Ehm, no try wikipedia. for instance the bell-inequalities. Or the delayed choice experiment. Or the Aharonov Bohm experiment.
    The Bell inequalities apply specifically to the wave function formalism. It is difficult to see how they could be proved for wave-function collapse without some expression for how the collapse occurs. You can do it, for instance, for observing the position of a particle through its interaction with a photon. That calculation is done with wave functions and there is no collapse to classical values. The delayed choice experiment can be analyzed with perfectly conventional wave mechanics. You do not need an intermediate collapse, although it is helpful to think that way when you are getting a qualitative feel for what is going on. I haven't seen the analysis with the Aharonov-Bohm experiment, but I don't see why it would be different.

    Quote Originally Posted by Kerling View Post
    If you believe in a real collapse of the wavefunction caused by a measurement, and don't specify exactly how this collapse occurs, it seems to me that you have lost causality.
    No you don't. You don't need to explain how the collapse has come to be, but why.
    Just because you don't know how you have become pregnant. Doesn't mean that you have been conceived by god.
    Physics normally tells you how things happen. Abandoning the need for this knowledge means abandoning physics. This is a philosophical statement, but we are really discussing a philosophical issue. You prefer "collapse of the wavefunction" and I prefer "shut up and calculate." It seems clear that we will simply have to agree to disagree.
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    Senior Member merumario's Avatar
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    You agree to disagree but never get the problem solved. Bell's theorem had more application in explaining EPR PARADOX.
    Bodies attract each other at near distances,the convergence is inevitable. A fundamental,subtle spirit which lies hide in all gross bodies.(Newtonian gravity)
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    Quote Originally Posted by mvb View Post
    The Bell inequalities apply specifically to the wave function formalism. It is difficult to see how they could be proved for wave-function collapse without some expression for how the collapse occurs.
    There is several formalisms that deal with things differently, but in the end, whether I use the Heisenberg picture or second quantization alls formalisms have some sort of a schrodinger wave equation. There is no formalism that doesn't have the measurement problem, and hence no formalism that is devoid of the collapse. The quantum interpretations resolve why and how the collapse in fact occurs.

    You can do it, for instance, for observing the position of a particle through its interaction with a photon. That calculation is done with wave functions and there is no collapse to classical values.
    Observing the position of a particle by a single photon is not quite as simple. First of you are troubled by the uncertainty principle of both your photon and your particle. Then at observation you determine it to be at a position. Even in calculating this observable discontinuates your schrodinger equation.

    The delayed choice experiment can be analyzed with perfectly conventional wave mechanics.You do not need an intermediate collapse, although it is helpful to think that way when you are getting a qualitative feel for what is going on.
    ... Have you even read the delayed choice experiment?!? There is no intermediate collapse. The whole idea of the experiment is to probe the dependence of evolution of the system by the act of measurement. Really the whole idea of the experiment is to collapse between a wave an a particle. You cannot describe it by conventional wave mechanics without introducing infinite Fourier transforms. (which is mathematically the same as to non-wave mechanics). I seriously doubt you know where you are talking about.

    Physics normally tells you how things happen. Abandoning the need for this knowledge means abandoning physics. This is a philosophical statement, but we are really discussing a philosophical issue. You prefer "collapse of the wavefunction" and I prefer "shut up and calculate." It seems clear that we will simply have to agree to disagree.
    No, Physics explains what we observe. The words 'how things happen' implies determinism, and implies realism. That is 2 philosophical notions you cannot super-impose upon the whole of physics, as they are as you say a philisophical interpretation.

    But the measurement problem isn't a philosophical issue. It is a physical issue, which has different philosophical resolves. But you cannot just refute the collapse as being a philosophical debate. It is observed, over and over again, and hence a physical reality.
    In the age of information, ignorance is a choice.
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