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Is the wave function real or abstract statistics?

  1. Nov 10, 2013 #1
    Is the wave function describing reality or does it describe the observers uncertainty about the system? I say that it's real but I would like to hear any comments or evidence that suggest the wave function isn't a description that has a one to one correspondence with a underlying reality.

    It's like a function that describes a car driving 50 miles an hour for 1 mile. You can predict where the car will be at a half a mile or 3 quarters of a mile. The function describes the underlying reality of the car traveling for 1 mile at 50 MPH.

    With a quantum system, we can't predict where the particle will be but we can assign probabilities to where the particle might be. The wave function describes an underlying reality where the particle is in a pure quantum state and goes through both slits at the same time to a mixed state where we assign probabilities and the particle has went through one slit or the other and the observer just doesn't know which slit.

    So why is the function for the car traveling 50 MPH for 1 mile real and the function for the pure or mixed state of the wave function abstract? In other words, when there's a one to one correspondence, how can it be abstract?

    Here's an article from phys.org:

    So this is really the crux of the debate. Is randomness inherent in nature or is their some hidden variable or new physics that will do away with this inherent randomness. It goes back to Einstein.

    So I see think there's a universal wave function in a pure state and when these pure states decohere into mixed states then local universes emerge. So it's like the wave function is the UN and everything from photons, atoms, rocks, trees and human beings are measuring devices that represent the wave function in these local environments.

    A measuring device like the human brain or a photon can store bits and measure it's environment. So we can reduce classical Shanon entropy to zero. When this occurs we have a now moment for example, turning over a playing card that's face down. I think this speaks to a Quantum mind but that's a topic for another thread.

    I wanted to hear the evidence that the wave function doesn't correspond to an underlying reality that's inherently random and it's just an abstract description of the observers uncertainty. How can we build quantum computers if superposition isn't an objective reality of the system's wave function?
     
    Last edited: Nov 10, 2013
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  3. Nov 10, 2013 #2

    atyy

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    The paper by Colbeck and Renner you cite is http://arxiv.org/abs/1111.6597 . Two interesting papers they cite are Pusey, Barrett and Rudolph's http://arxiv.org/abs/1111.3328 and Harrigan and Spekken's http://arxiv.org/abs/0706.2661v1 .

    Colbeck and Renner state that their result assumes "freedom of choice for measurement settings", while the PBR paper conclusion can be avoided if one of its assumptions is removed as Lewis, Jennings, Barrett and Rudolph show in http://arxiv.org/abs/1201.6554 .

    Matt Leifer wrote an informative essay on these issues which was published in "Quantum Times" http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/ .
     
    Last edited: Nov 10, 2013
  4. Nov 11, 2013 #3

    bhobba

    Staff: Mentor

    If you think that then you need to read Ballentine - Quantum Mechanics - A Modern Development.

    It may be real, but doesn't have to be. IMHO its more like probabilities which most would not say is real in any usual sense.

    Here is the skinny. Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. This is the first axiom of the treatment in Ballentine foundational axiom of QM, and heuristically why its reasonable.

    Next we have this wonderful theorem called Gleasons theorem which, basically, follows from the above axiom:
    http://kof.physto.se/theses/helena-master.pdf [Broken]

    This is the second axioms in Ballentine's treatment.

    This means a state is simply a mathematical requirement to allow us to calculate expected values in QM. It may or may not be real - there is no way to tell. But its very similar to the role probabilities play in probability theory, and like I said, most would not say they are real.

    Further in that vein, nowadays its often thought of as just a novel version of probability theory - there basically being just two reasonable models applicable to physical systems. Check out:
    http://arxiv.org/abs/quant-ph/0101012
    http://arxiv.org/abs/0911.0695

    That would probably be the most recent view - QM is basically a probability model - there are many of those and the study of such is a modern development - but for modelling physical systems some very reasonable assumptions leads to basically two - bog standard probability theory you learnt about at school and QM - but what distinguishes QM is it allows entanglement, which would seem the rock bottom, basic, essential weirdness of QM.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  5. Nov 11, 2013 #4
    Thanks for the response bhobba,

    I think ensemble interpretations are another form of shut up and calculate. This is because they make an argument that we should exclude individual measurement's that have a one to one correspondence with the wave function and just look at these things in the context of an ensemble of probabilities and ignore the one to one correspondence between the wave function and individual particles. The two things don't have to be mutually exclusive.

    This is from Wikepedia:

    This is the ball game.

    When you have one to one correspondence between a single photon and the description of it's wave function, then the wave function is describing reality. That doesn't exclude that this single measurement can't be looked at in the context of an ensemble.

    Let's look at a slot machine in a Casino. By itself, one spin of the slot machine can't tell the Casino owner how an ensemble of spins will be in his favor statistically speaking but that one spin being "real" is important to the ensemble of spins.

    I think the crux of the matter goes back to my original post. People don't like what QM says or shows in experiments, so these things can't be "real." God doesn't play dice so to speak.

    Look at an uranium atom in it's ground state. When the single atom is subjected to external forces it moves in a way that is predicted by it's wave function. There's a one to one correspondence between a single atom and it's wave function.

    Why does an ensemble interpretation exclude the "reality" of a single photon with one to one correspondence with it's wave function in order to say we can only look at it as an ensemble of particles. In other words, shut up and calculate.

    This is from Wikipedia:

    Again, even though we wave a one to one correspondence between the wave function and the system, we're supposed to look a way and only see the statistical interpretation of an ensemble and ignore the one to one correspondence between a single photon and it's wave function.

    Here's a paper from nature titled Direct measurement of the quantum wavefunction.

    http://www.nature.com/nature/journal/v474/n7350/full/nature10120.html

    How can there be a direct measurement of something that's not real? Isolation of a single particle and it's wave function being real doesn't exclude a statistical interpretation of the data over an ensemble of particles. In fact, you have to include the single photon as being real in order to look at the wave function of an ensemble of photons which are in accordance with the predictions of Quantum Theory.

    So if I create a stream of photons with identical wave functions there shouldn't be a one to one correspondence with the wave function if the ensemble theory is correct. Why should the wave function of a single photon be in a one to one correspondence with the description of the wave function according to QM if the wave function of a single photon isn't real?
     
    Last edited by a moderator: May 6, 2017
  6. Nov 11, 2013 #5
    But is it a direct measurement? Those experiments rely on the notion of weak measurement. A criticism raised against a weak measurement is that it says little about the properties of an individual system. Demystifier discusses this issue here:
    Weak measurements in quantum mechanics and 2.6 children in an American family
    https://www.physicsforums.com/blog.php?b=1226 [Broken]
     
    Last edited by a moderator: May 6, 2017
  7. Nov 11, 2013 #6
    Bohm2,

    Thanks for the response. I think it's apples & oranges when it comes to the comparison you cited.

    It's basically saying the wave function doesn't correspond to classical reality so it isn't real. There isn't a one to one correspondence between 2.6 children and the formula that says there's 2.6 children in an American family. So of course you can say that nf=Nc/Nf is just statistical because it doesn't correspond to a physical reality.

    This isn't the case with the wave function. There's a one to one correspondents to the system's wave function. You can't say because the wave function doesn't correspond to a classical underlying reality that it isn't real. What you can say is that there's a one to one correspondents with the quantum system's wave function therefore the quantum system's wave function represent an underlying reality.

    What you're basically saying in an ensemble approach is that a quantum reality isn't real because it doesn't correspond to the classical world we experience.

    Experiment after experiment has thrown a monkey wrench into this view because there's a one to one correspondents with the wave function and the way the system behaves.

    Like I said, it's shut up and calculate just wrapped in a slightly different package. We will just ignore the wave function as representing any underlying reality because it doesn't have a one to one correspondence with the classical world. Why should the wave function have a one to one correspondence with the classical world when it's describing the wave function of a quantum system?
     
  8. Nov 11, 2013 #7

    Cthugha

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    To get what they mean by a direct measurement, you need to know how measurements of the state of a light field are usually done. The information you have in the wavefunction is equivalent to that contained in the density matrix or the Wigner function of the state. The latter is a quasiprobability distribution in two quadratures of the light field which cannot be measured simultaneously due to uncertainty. However, one can measure the projection of the whole function along a slice at some angle through the function. The typical strategy then relies on taking a set of those slices at different angles. Afterwards, one has to reconstruct the Wigner function or density matrix that is most likely to give all the measured slices. So you start out by guessing some function and then run an iterative procedure that converges towards the state that has the maximum likelihood of reproducing the results. The procedure is quite similar to what happens when tomography is done in a hospital - this is why that procedure is called quantum state tomography. It is obviously a very indirect technique as you use maximum likelihood reconstruction. Lundeen's technique is more direct because it gets along without that reconstruction thing. It is still a measurement on an ensemble of identically prepared single photons. See the introduction of the paper for details:
    "In contrast, we introduce a method to measure Ψ of an ensemble directly. By ‘direct’ we mean that the method is free from complicated sets of measurements and computations"

    Direct does not mean that you can do the measurement on a single photon realization.


    Let me mention that your wiki quote is somewhat taken out of context. This part is explicitly about "Early proponents of statistical approaches regarded quantum mechanics as an approximation to a classical theory." which is not what the actual ensemble approach is about.

    When people talk about the wave function of a single photon they mean a single photon state. They never talk about just one realization. The wave function of a single realization is not really defined or of interest in standard qm. You can interpret the wavefunction in a realistic way, but there is nothing urging one to do so. There is also nothing urging us to do it in a different way.
     
  9. Nov 11, 2013 #8

    bhobba

    Staff: Mentor

    Individual measurements that have a one to one correspondence with the wave function?

    I have zero idea what you mean by that.

    Your query was why can the wavefunction (ie state) be considered not real.

    I gave arguments from the modern viewpoint where its simply a device to calculate expected values, like probabilities is in probability theory. In that view, just like probabilities, its not real in any usual sense, simply a theoretical device to aid in calculations.

    Indeed general considerations single out probability theory and QM as the only two possibilities in modelling physical systems - but QM is special - it allows entanglement, which modern research shows is quite likely the real rock bottom essence and weirdness of QM.

    Check out:
    http://theoreticalminimum.com/courses/quantum-entanglement/2006/fall
    'The old Copenhagen interpretation of quantum mechanics associated with Niels Bohr is giving way to a more profound interpretation based on the idea of quantum entanglement. Entanglement not only replaces the obsolete notion of the collapse of the wave function but it is also the basis for Bell's famous theorem, the new paradigm of quantum computing, and finally the widely discussed "many-worlds" interpretation of quantum mechanics originated by Everett.'

    Thanks
    Bill
     
  10. Nov 11, 2013 #9
    Cthuga,

    Thanks for your response.

    It's still a direct measurement of a photon's wave function. This is the point. The system behaves in a way that's described by the wave function. So even in a stream of identically prepared photons, the system and the wave function still behaves in a way that's predicted by quantum theory.

    It's like my Casino example. One spin of the slot machine has to be real in order to give you a statistical picture of an ensemble of spins.

    How can the system be in a probable state that's not an underlying reality? The wave function has to be an underlying reality that describes the probable states of the system.

    I can say that I will be in the Bahamas next week. There's a slim chance that this will occur because I have no plans to go to the Bahamas next week but it's only a probable state because of the underlying reality of the Bahamas or getting in an airplane.

    I couldn't say I'm going to planet Lexar next week which is 20,000 light years away. This isn't a probable state because there isn't any underlying reality of the planet Lexar or of me traveling to a planet 20,000 light years away.

    The wave function has to be real because it's an underlying reality of all probable states of the system. Like I said earlier, there's a one to one correspondence between the wave function and the system.

    So you can see the wave function as a pool table. The pool table describes all the states the pool ball can be in. So you couldn't say, 8 ball in the pocket 3 inches away from the corner pocket. This is because this isn't a probable state described by the underlying reality of the pool table.

    So the wave function has to be real because there's a one to one correspondence between the wave function and the quantum system. The wave function represents an underlying reality of all probable states of the system. How can the system be in a probable state that isn't first a "real" possibility?

    I can't take a trip to Middle Earth to visit the Hobbits because there's no underlying reality to make this a probable state. I can say that I'm flying out to Vegas to visit my cousins because there's an underlying reality of my cousins living in Vegas so it is a probable state.

    The wave function describes the probable states the system can be in just like the pool table describes the probable states the pool balls can be in.
     
  11. Nov 11, 2013 #10

    bhobba

    Staff: Mentor

    If the state is like probabilities your question is how can there be a direct measurement of probabilities?

    Just like probabilities there is no way a single observation can determine a systems state - its encoded in the Born rule.

    If we observe a state with an apparatus that gives 0 if its not in that state and 1 if it is then the quantum formalism tells us that since states can be a superposition of those two outcomes it may be in a state that sometimes gives 0 and sometimes 1. To determine it is in that state you need to carry out the observation a sufficiently large number of times for the null result to be below your level of confidence - you can never be sure - all you can do is simply make the chances of being wrong arbitrarily small ie is zero for all practical purposes.

    Just to be 100% clear - there is no way - zero - zilch - nada (it's not a subtle point I am trying to make) a state can be determined except in a statistical sense - just like there is no way to determine probabilities except to an arbitrarily small confidence level. The quantum formalism is unequivocal on this point - you cant determine a systems state exactly.

    Thanks
    Bill
     
    Last edited: Nov 11, 2013
  12. Nov 11, 2013 #11

    bhobba

    Staff: Mentor

    I may be missing something.

    Please describe to me the direct measurement of a SINGLE photons wave function.

    Because if you can, you have contradicted the quantum formalism.

    I am not talking about the bulk wavelength etc of a beam of photons - that can be measured - I am talking about the state of a single photon.

    Thanks
    Bill
     
    Last edited: Nov 11, 2013
  13. Nov 11, 2013 #12

    bhobba

    Staff: Mentor

    Indeed you cant.

    If you could then you contradict QM's basic postulates - particularly the Born rule.

    I have tried to explain this as carefully and unambiguously as I can in a previous post from the basic postulates of QM.

    Thanks
    Bill
     
  14. Nov 11, 2013 #13

    Cthugha

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    Ok, nobody denies that.

    I do not get your comparison.

    Hmm, you might be confusing terminology here. If the wave function just describes the probable states of the system, it is assumed to be not a real entity. In this sense it is rather a statistical entity that tells us in which state we might find the system and what the probabilities may be. If you consider the wave function as a realistic entity, you express that the wave function is more than that and applies directly to every single realization of an ensemble. In this case the wave function does not represent the probable states of the system, but a system that actually indeed is in all of these probable states with some weights given by the wave function.

    This has nothing to do with what is meant by the wave function being considered real or not. Nobody doubts that the probable states are there. Assuming that the wave function is real means, that they are all realized - not only probable - within each realization of a single experimental run.

    Well, to stick with your pool table setting, the pool ball actually and literally IS in all the pockets (and everywhere on the table) simultaneously when you consider the wave function as real. It actually is in all of these pockets and "collapses" to one of the pockets as soon as you take a look. A non-realistic wave function approach instead just considers the wave function as describing all the probable states the ball could be in.
     
  15. Nov 11, 2013 #14

    bhobba

    Staff: Mentor

    There is a 1-1 correspondence between probabilities and the sides of a coin in the sense you can conceptually attach them to a side and consider them a vector - but that doesn't make probabilities any more than a calculation device.

    The same with a quantum state.

    Thanks
    Bill
     
  16. Nov 11, 2013 #15
    bhobba,

    Thanks for the response.

    I was talking about the weak measurements carried out in the experiment I listed above. My point was, the system still behaves in a way Quantum Theory predicts. If an ensemble interpretation is correct, why don't we find huge deviations at these levels?

    Here's an interesting paper:

    Is a system's wave function in one-to-one correspondence with its elements of reality?

    http://arxiv.org/abs/1111.6597

    So how can you say the wave function of a photon isn't real when the wave function has been measured? In the experiment I listed above they did weak measurements on a stream of photons and both real and imaginary components of the wave function appear directly in the measuring apparatus. It says:

    Here's more from Lundeen Lab:

    http://www.photonicquantum.info/Research.html

    This goes to my point of one to one correspondence.

    There's a one to one correspondence when a pitcher pitches in the strike zone. When he pitches outside of the strike zone then he's no longer in correlation with getting a strike.

    In every experiment, the wave function has been in a one to one correlation with the quantum system. Is there any evidence that the wave function and the system is uncorrelated? If the wave function isn't real, why do we see this one to one correspondence? Where's the deviation if it's all abstract statistics?
     
  17. Nov 11, 2013 #16

    bhobba

    Staff: Mentor

    Scratching head.

    The ensemble interpretation fully conforms to the quantum formalism. If a system still behaves in the way Quantum Theory predicts then that can't be used as evidence against it.

    Thinking otherwise is simply, utterly, and outright SILLY.

    Can I ask you exactly where you have learnt QM from? For example can you state the Born rule? Not the basic version, but the proper one developed by Von-Neumann.

    Thanks
    Bill
     
    Last edited: Nov 11, 2013
  18. Nov 11, 2013 #17

    bhobba

    Staff: Mentor

    Your logic is erroneous - and obviously and trivially so.

    In every experiment the probabilities assigned to the sides of a coin is in 1-1 correlation with the outcomes. That does not make probabilities real.

    Thanks
    Bill
     
  19. Nov 11, 2013 #18

    bhobba

    Staff: Mentor

    Yea - know that one - its been debunked:
    http://arxiv.org/pdf/1302.1635v1.pdf

    The point is, as myself and Cthugha have tried, obviously unsuccessfully, to explain is it hasn't been measured.

    If you could measure it in a single observation, and not in a statistical sense, you have violated the basic postulates of QM.

    That's why I have asked where you have learnt QM from, because this is utterly foundational and basic to QM. It follows from the Born rule.

    What you are talking about are WEAK measurements, which does exactly what I said could be done - does it in a statistical sense - not in a single measurement. In the same way you can measure probabilities in a statistical sense - but that doesn't make them real either.

    Thanks
    Bill
     
    Last edited: Nov 11, 2013
  20. Nov 11, 2013 #19
    cthugha,

    Thanks for the response. You said:

    This is true in part.

    The pool balls can't be in a state that isn't described by the pool table. In the book Hyperspace, Dr. Kaku was talking about Hawkings Wave Function of the universe. Here's what he said:

    The point here is, system can only be in a state that's an underlying reality described by the wave function. The wave function couldn't be spread out to planet Lexar 20,0000 light years away because it's not an underlying reality. How can the quantum system be in a probable state that isn't an underlying reality that's described by the wave function?

    How can the quantum system be in a probable state that isn't first a "real" possibility?
     
  21. Nov 11, 2013 #20

    bhobba

    Staff: Mentor

    It isn't a direct measurement, and it only can be measured in a statistical weak sense - a point the OP doesn't seem to get.

    Probabilities can be measured that way to - but that doesn't make them real either.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
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