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Are Eigenstates of a Wavefunction Entangled?

  1. Nov 1, 2013 #1
    The way I understand it is when particles are entangled, when you measure one the entangled pair is instantly in a measured state. This question really goes to Copenhagen vs. MWI.

    If Eigenstates of the wave function are entangled, that seems to support MWI. If these Eigenstate are not entangled that could support Copenhagen.

    Here's a hypothetical. Say you have a wave function of the universe, if the Eigenstates are entangled then wouldn't each probable state exist? If Eigenstates are not entangled then you can have local universes with their own laws of physics made up of a combination of Eigenstates of the wave function of the universe and if these Eigenstates are not entangled, then every probable state wouldn't have to exist because on probable state is measured.

    Does this make any sense?
     
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  3. Nov 1, 2013 #2

    Simon Bridge

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    Welcome to PF;
    You appear to be mixing models here ...
    A state is represented by a state vector.
    A wavefunction is one way of writing a state vector.
    There are lots of ways.

    An eigenstate of an operator will have a state vector which is an eigenvector which may be represented as a wave-function or some other kind of vector. The wavefunction that corresponds to a single eigenvalue is an eigenfunction.

    Some eigenstates in a large closed system (i.e. the Universe) may be entangled and others may not be - the effect is on measurement, so the Universe would not know about the entanglement until some interaction has occurred which would reveal it. Not all states of the system need be occupied either. Technically it is the particles that are entangled, not the eigenstates. It is also possible to have particles in a superposition of states without being entangled.

    With any luck you can refine your question...
    http://web.utk.edu/~cnattras/Phys250Fall2012/modules/module%203/entangled_electrons.htm [Broken]
     
    Last edited by a moderator: May 6, 2017
  4. Nov 1, 2013 #3
    Thanks for the response Simon.

    Do you think this applies to Copenhagen or MWI in any way?

    I'm in unfamiliar territory but can the wave function be described as a flipping coin of all possible measurements. When a measurement occurs this flipping coin is on heads or tails and is known. I read about Hawking and the Wave Function of the Universe and I was wondering if there was such a thing could it be measured? Say you have a Wave Function of the Universe that can't be measured because there's nothing outside of the wave function of the universe to measure it, would that be like a constantly flipping coin and local universes could have different physical laws because local universes are a combination of probable states of this Wave Function of the Universe. Therefore the laws of physics we discover apply to our local space-time and are not universal to every brane or local universe.

    My forte is Philosophy but I'm fascinated by Quantum Mechanics. I wanted to make sure I was describing things in a way that's in line with scientific understanding. Also, thanks for the link.
     
  5. Nov 1, 2013 #4

    Simon Bridge

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    Erm - I don't think it is useful to think of a wavefunction as a constantly flipping coin.
    Some constructions behave like that - where the probabilities kinda "slosh" between states.

    You should realize that Hawkins "universe wavefunction" is a poetic metaphor, not physics.
    It's pretty and it sounds nice but don't go around thinking it means anything.
     
  6. Nov 2, 2013 #5

    meBigGuy

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    That is not exactly correct. Rather, one can say that in a simplistic entangled two particle system in which each particle will be measured, measuring 1 particle will give you information about what the other particle will give when measured. The measurements will always correlate. Measuring one does not "cause the other to be in a measured state" nor does it "cause the other to take the opposite state". All it does is tell you about what the other particle will report when measured, and the results will always correlate. Mushy but beautiful.

    It gets even weirder in that the first measurement will always give a random result and the second measurement will correlate. But if you don't know the results of the first measurement, the second will seem random anyway, so it could have been the first.
     
  7. Nov 2, 2013 #6
    Simon,

    Thanks for the response. Doesn't the universal wave function support M.W.I.? This is from Wikepedia:

    So, the universal wave function remains in a state of superposition while it's probable states Decohere into the local universes we see. If the universal wave function is fiction then doesn't that support Copenhagen?

    The way I understand it is strong support of M.W.I. is because it reduces the role of the observer. I remember reading somethlng like this in David Deutsch's book The Fabric of Reality. With Copenhagen it's just shut up and calculate and the observer causes the wave function to collapse and not just the appearance of collapse. Are the two mutually exclusive? Couldn't decoherence cause the appearance of the wave function collapse and the observers choice causes the appearance of the wave function collapse? Wouldn't this tie decoherence to consciousness a la Roger Penrose?

    meBigGuy,

    Thanks for clearing that up. I thought when you measured one particle it caused the other particle to take a measured state. Doesn't this mean observation plays a big role in QM and therefore the observers choice causes decoherence of the wave function?
     
    Last edited: Nov 2, 2013
  8. Nov 2, 2013 #7
    Hi matrix...

    There is a good but detailed discussion here on superposition and entanglement:

    Is Superposition widely Accepted?
    https://www.physicsforums.com/showthread.php?t=710188

    It takes a while to get the subtlies in perspective.....for example, a wave is never detected...the 'wavefunction' is an abstract model [often in Hilbet space not three dimensional physical space] ....what we measure, observe, are always point like particles, say photons.

    So this never happens:
    that is, an abstract wavefunction does not 'become' universes.....it only represents abstractly those observations we are able to make. QM says nothing about characteristics between measurements.

    Are you familiar with Fourier Decomposition? It illustrates how one wavefunction can be equivalently represnted by others....A simple example is the old trig identity: Sin2x = 2SinxCosx.....In this example, the sin [wavefunction] of a function is the same as the product of a sin and cos as shown. Which represents the 'wave'??....both sides of the equation.
     
  9. Nov 2, 2013 #8
    Yes I think you are correct in this. It is the state of the observer that actually determines what is actually measured. Consider spin, which is always found to be parallel along the axis measured. I like to think the observer determines the line of sight.
     
  10. Nov 2, 2013 #9
    Naty1,

    Thanks for the response. I wasn't saying the wave function becomes local universes but the probable states of the wave function decohere and become the local universes we see and experience and some of these universes may even have different laws of physics based on the combination of probable states that decohere from the universal wave function.

    I think the debate between the wave function being abstract or real is interesting. I remember reading a paper that said the wave function was real. This is from phys.org:

    Here's the abstract:

    The way I understand it is the wave function is inherent with characteristics like spin and momentum and they become measured states after these probable states decohere from a coherent wave function that's in superposition. So these characteristics aren't "real" but "inherent" prior to measurement and the wave function describes a superposition of inherent states that decohere and become a mixture of inherent states that appear real to local observers.

    Jilang,

    Thanks for your response. If the observer determines the line of sight, wouldn't that tie observation to decoherence? I think a fascinating and emerging field of study is Quantum Biology. If classical systems can incorporate quantum effects I think that would be pretty huge. There looking at things like migration of birds, a sense of smell, photosynthesis and more. I would think evolution would give a huge advantage to a species that could incorporate quantum effects like superposition and entanglement when it comes to consciousness a la the quantum mind and Roger Penrose.
     
  11. Nov 2, 2013 #10
    It is.
    In the following discussion a number of people here, I think everybody in the discussion, disagree. There is a lot that might interest you.

    Shape of the Wave of a Photon
    https://www.physicsforums.com/showthread.php?t=715821

    Of course this remains an open issue in quantum mechanics, so if you find it interesting the above thread would provide a lot of good perspectives likely contrary to the three physicists you cite.


    Wikipedia says this:

    On the side of the three physicists, the Schrodinger wave equation IS deterministic. On the other hand, I posted in the above thread:

    [Are real numbers 'real; are complex numbers 'real'....or merely representations?]

    I think it was Born who guessed at such an approach....
    In any case, suppose I described to you the evolution in time of a car trip...say it is traveling at a 55mph going north on highway #287 in NJ...between two designated cities. So you can find where it is at any time by calculation. Is such a function 'real' [an awful word to use in physics] ore merely informational??
     
  12. Nov 2, 2013 #11

    Simon Bridge

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    I think there is a reason the question is an open one. If it were that easy, it would be settled by now.

    The best we can do is point you at the various positions different people hold and help out with some of the concepts ... philosophy and QM overlap quite a bit. Subjects that tended to be pure philosophy like "what is the nature of reality?" turn out to have a physical bearing.

    An example - a measurement of spin always finds a spin along the axis determined by the equipment. (See Stern Gerlach experiment.) This is because the particle has no sense of up and down before it enters the equipment. Philosophically, the concept of "up" does not exist outside the equipment.

    A simpler example: the concept of movement, changing position, for a particle all by itself in free space, is meaningless. Since it is alone and the space "free", there is nothing to distinguish one position from another - so everywhere is the same place ... when you crunch the numbers, the position wavefunction of such a particle is uniform 1 everywhere. When we do quantum mechanics, the particles are either confined (so the space is not free) or they are coming from an interaction and on their way to another one (so they are not alone). That can make their wavefunctions quite complicated.

    But people will argue with that - and that's as close to philosophy as I'll get without a double-whiskey :)
     
  13. Nov 2, 2013 #12

    meBigGuy

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    All you can really say is that when you measure a particle it will show one of the expected values with probablities as predicted. No one know why. It is the basis of QM. You can go on to call it collapse, world splitting, or whatever, but that becomes religion.

    Personally I like the "decoherence causes appearance of collapse" approach.
    http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf
     
  14. Nov 3, 2013 #13
    Yes, observation would cause decoherence, but to my mind so would any other non reversible process (e.g a particle making a record on a photographic plate). My understanding is that the Schroedinger Equation describes evolution of the state which is inherently time reversible, so once a non reversible event occurs the solutions cease to be valid and you have to start it all over again from a new t=0.
     
  15. Nov 3, 2013 #14
    Simon's post #11 offers some intriguing insights:

    Simon:
    This illustrates why it is said quantum systems [say, particles] are in a mix [a superposition] of all states and the probabilities differ along different axis. Quantum superposition is a fundamental principle of quantum mechanics which says a physical system exists partly in all its theoretically possible states simultaneously; only one of the possible configurations is observable at a time. Another perspective is that QM doesn't tell us about particle characteristics between interactions, only when they are localized, at detection via measurement...say as a dot on a screen.

    Simon:
    I have seen arguments the evolution description in time, say via the Schrodinger wave equation, does not describe a single particle but an ensemble of similarly prepared particles.
    Simon's post illustrates why....'everywhere is the same place' for just one particle.... And according to Vanhees of these forums, the mathematical evolution description of a single photon is especially problematic....he has posted, I think analogously, the description of a single photon evolution is undefined. I suspect Simon's post also illustrates that.

    Add to all this that real numbers, complex numbers, and imaginary numbers play essential roles in QM, each defining a different class of particles, and you begin to see why interpretational differences have persisted.
     
    Last edited: Nov 3, 2013
  16. Nov 3, 2013 #15
    I don't think that is quite right. The Schroedinger equation does tell you how the various probabilities of the characteristics evolve until they are localised.
     
  17. Nov 3, 2013 #16
    I agree......but then again I don't. [How's that for a 'cat like' statement! LOL]
    Is any single statement about QM 'right'??
    I don't disagree with your comment.

    Since we can't measure nor observe quantum waves, only their quanta, the disagreements among experts [exclude me from that category] will persist.
     
  18. Nov 3, 2013 #17
    Naty1,

    Thanks for the response. First the paper I mentioned above is called "On the reality of the quantum state" and you can download a free PDF on arXiv. It attempts to show why the wave function being abstract isn't compatible with Quantum Theory.

    I tend to agree with decoherence and the wave function being real. I think your example of the car trip illustrates my point. This is what Wikipedia says about Copenhagen:
    Why doesn't QM yield a description of objective reality?

    I think the answer is, when you look at QM it's counterintuitive to the classical world we experience. People saw things like superposition, entanglement and non locality and said, wait a minute, these things can't describe an objective reality. So you have hidden variables and the EPR Paradox.

    What if QM is the true reality and the classical universe emerged from decoherence? What if everything is quantum?

    I don't think you can look at it from the perspective of classical physics and say, the wave function has to be abstract because QM is counterintuitive.

    So when you look at the car trip, the function yields a description of an objective local reality which is the car trip itself. So why isn't the wave function a description of the universal objective reality which includes things like superposition, entanglement and non locality?

    Schrodinger's equation describes the evolution of the wave function just like your function describes the evolution of the car trip. Why would the underlying wave be any less "real" than the car trip?

    The main objection I see to the underlying wave being "real" is that it's too weird to be real and it can't describe an underlying reality just the uncertainty or lack of knowledge of the observer.

    How can this be when Schrodinger's equation describes a wave function that evolves in a deterministic way without observation? It has never been observed because observation disturbs superposition but that doesn't make it any less "real." We haven't observed entropy or gravity either but the equations involved with entropy and gravity gives us a description of reality that we can see. Just like Schrodinger's equation. We see it in experiment after experiment and how successful QM has been in areas like technology.

    Wikipedia says this:

    So the universal wave function would remain in a state of superposition while it's observables decohere into the local universes we experience. So the universal wave function could never be measured only it's observables when they decohere. Schrodinger's equation tells us why we can't measure this superposition but that doesn't make it any less "real." Why would the system's wave function evolve in a deterministic way without observation if it's just an abstract mathematical tool that doesn't describe an underlying reality?
     
  19. Nov 3, 2013 #18
    Whilst I agree that the wavefunction is not abstract I would disagree that it gives a deterministic evolution of the system. It gives a probabilistic one. It can tell you how the probabilities vary over time and that is all. I like to think of it as defining a random walk in state space.
     
  20. Nov 4, 2013 #19
    Jilang,

    Thanks for the response. I didn't say that it gives a deterministic evolution of the system. I said it gives a deterministic evolution of the system's wave function. This is from Wikipedia:

    So if you look at the car trip example from above, you can describe a trip on the highway in a deterministic way. What the function couldn't describe is if a drunk driver came onto the highway and caused a 3 car accident that you were involved in.

    So the question becomes, why does measurement disturb the evolution of the wave function in a non deterministic way? I think both Copenhagen and M.W.I. can be correct. The wave function can represent a lack of knowledge about the system because you're only measuring an observable of the wave function that has decohered from the wave function.

    So it's like a box that you open but you can only see what's on one side of the box. There will always be a level of uncertainty because you can only measure one side of the box and not the entire box. So you can measure an observable of the wave function but not the wave function itself.
     
  21. Nov 4, 2013 #20
    Yes you are right, sorry I misread that!
     
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