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Proof of correctness of MWI

  1. Apr 12, 2009 #1
    This is similar to an argument made by David Deutsch. The argument appeals to artificial intelligence that can be implemented by a quantum computer. So, the first part of the argument is that however the brain works, it is ultimtely formally describable using a finite number of bits. Therefore it can be implemented by a computer and thus also by a quantum computer.


    The different branches of the observer correspond to the different projections of the quantum computer in the |0>, |1> basis of the qubits. Suppose that this observer measures the state of a qubit in the |0>, |1> basis. Let's call this qubit a "spin" to avoid confusion with the qubits that are part of the observer.

    Then what we can achieve is the following.

    1) We start with the spin in state |0>, then we rotate it to
    1/sqrt(2) [|0> + |1>]


    2) The observer then does a measurement in the |0>, |1> basis, which causes a qubit (that was initiallized to |0>) of his memory to be entangled with the state of the spin. This is performed using the controlled NOT gate. Also another qubit of his memory that was initialized to |0> is flipped to |1>. That qubit detects that a measurement has taken place (but not the result of the measurement).


    3) The observer then applies the controlled NOT gate again, reversing the measurement. Then he flips another qubit that was initialized to |0> to |1>, which records the fact that the memory qubit that registered the spin has been erased.


    4) At this stage the spin is back in the state 1/sqrt(2) [|0> + |1>]. The observer can verify this by applying the inverse rotation that he appied to the spin at the start, rotating it back to the state |0>. A measurement of the spin by the observer (or some other observer) will yield zero with 100% probability.


    Now, the fact that the observer knows that he measured the spin in the |0>, |1> basis when it was rotated to 1/sqrt(2) [|0> + |1>] means that in the CI interpretation, the spin's state should have collapsed to either |0> or |1>. Only one of the branches really exists. Then, applying the inverse rotation won't bring the spin back to the state |0>, instead it will be a mixed state of

    1/sqrt(2) [|0> + |1>]

    and

    1/sqrt(2) [|0> - |1>]

    Measuring the spin again in the |0>, |1> basis must thus yield a 50% probability of finding it to be |0>.

    So, the CI interpretation makes a different prediction than the MWI. Moreover, since the spin can be measured by an external observer, the CI interpretation predicts non-unitary time evolution for an isolated system that can be verified by an external observer.
     
  2. jcsd
  3. Apr 12, 2009 #2

    Hurkyl

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    The obvious CI rebuttal would seem to be
    Sure, you can call it a measurement, but that doesn't mean it actually is one. In fact, it's reversibility is proof that it isn't.​

    I can also envision CI proponents making the additional claim
    Observers and measuring devices aren't within the domain of validity of QM, so your toy example doesn't really say anything about them.​
     
  4. Apr 12, 2009 #3
    But how does the CI proponent explain the fact that he himself can have a memory of having measured the wavefunction of a spin that verifiably hasn't collapsed in the basis he measured it?
     
  5. Apr 12, 2009 #4

    Hurkyl

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    He wouldn't; he would accuse you of asking a loaded question. He has not agreed with your hypothesis that your experiment constitutes (what CI calls) a measurement.
     
  6. Apr 12, 2009 #5

    alxm

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    Why do you think 'artificial intelligence', human memory, simulations thereof, computer simulations, or quantum computers would be the least bit relevant here? I think you're just obfuscating the issue to an extent where you've managed to confuse yourself.

    They're called 'interpretations' for a reason; they're not scientific theories because they're not testable. The MWI in particular is untestable by definition since a universe external to our own can never be proven or disproven. You might as well say 'God did it.' (which is popular, but not a scientific theory either).
     
  7. Apr 12, 2009 #6
    Will the CI proponent say that a perfectly isolated quantum computer will always under a unitary time evolution?
     
  8. Apr 12, 2009 #7

    The MWI does not postulate "many worlds", it merely postulates unitary time evolution ("many worlds" is how we can visualize the unitary tme evolution, but it is not a priori assumed). The CI postulates non unitary time evolution associated with the interaction of humans with physical systems.

    So, this is a clear difference that can in principle be measured.
     
  9. Apr 12, 2009 #8

    Hurkyl

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    The untestability is not for the reason you think -- it's simply a matter of practicality. CI predicts that "measurements" cannot be reversed. MWI predicts that all interactions can be reversed. (Including those interactions CI would call a "measurement") In principle, this divergence could be tested -- the only reason it has not is that the experiment would be far too difficult to engineer.

    The toy example of using a CNOT gate as a "measuring device" is an experiment that is not too difficult to engineer -- and I'm pretty sure it has been done, conclusively demonstrating that it does not invoke a collapse.

    Of course, that does not disprove CI -- CI is somewhat vague about what is and is not a "measurement", and all this experiment would prove is that a CNOT gate is not one.

    And, of course, such an experiment would do nothing to distinguish between MWI and other decoherence-based interpretations.

    :confused:
     
  10. Apr 12, 2009 #9

    Fra

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    I'd prefer to not mix the two different views.

    - The collapse is the inside view, it is what the observer sees.
    - A second observer, observing observer 1 + the environment does would for sure describe it differently.

    Another opinion on the consistency of different observers descprition of "reality", Dmitry67 alsed a good question here, which relates to this indirectly:
    "The role of false info in the Copenhagen Int. "
    --https://www.physicsforums.com/showthread.php?p=2129766

    I'm not a strict CI, but I think I am closer to CI than some others here. My view is more than interpretations, it suggest a reformulation of QM, where QM is emergent. But the collapse isn't the problem.

    /Fredrik
     
  11. Apr 12, 2009 #10
    true MWI'ers are denialists, claim their interpretation is a representation of a realist interpretation, howver it really breaks down easy.
    It can't deal with probability, so all our observations really contradicticts MWI at this point.
    No preferred frame.
    all these problems, it's a retarde dinterpretation.

    A mix between Bohm and some ensemble view is more likely.
     
  12. Apr 12, 2009 #11
    Regarding 1,
    http://en.wikipedia.org/wiki/Many-worlds_interpretation
    Regarding 2, in case if you like Bohm
    http://en.wikipedia.org/wiki/Bohm_interpretation#Isomorphism_to_the_many_worlds_interpretation
     
  13. Apr 12, 2009 #12
    First off I got to laugh at you for citing randomly written wikipedia pages obviously biased...

    Anyways, yes Deutsch prestented what HE claimed was a proof, which has been thoroughly critized and disproved.
    (don't believe the hype).


    Also Deutsch's desperate attempts at claiming BM is MWI in denial has been disproved too:
    http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.0810v2.pdf

    In this paper by Antony Valentini, David Deutsch's claims are raped, there's also a counter argument against MWI.

    Sorry your wasting your time..


    Currently there exist no MWI that can arrive at the born rule:

    http://arxiv.org/abs/0808.2415

    Hilary Putnam, David Z Albert and other's have also written a lot of good work on this.


    Not to mention this is far from the biggest cirticism of MWI.


    What makes MWI so appealing to you personally?
     
    Last edited: Apr 12, 2009
  14. Apr 12, 2009 #13
    MWI is deterministic. The wavefunction of the universe satisfies the equation:


    H|psi> = 0 (1)


    The question is then what the meaning of |psi> is and how one gets to the Born rule. In my opinion people are making things far too difficult for themselves. One can intepret |psi> exactly as on would interpret the eigenvector of a row to row transfer matrix of a lattice model, e.g. the 2d Ising model.


    There is absolutely no ambiguity here and the Born rule is what you would expect if |psi> is analogous to an eigenvector of a transfer matrix.


    You are saying that a mix between Bohm and some ensemble view is more likely. But then, people are tackling important problems in theoretical physics using Eq. (1) (e.g. Black hole evaporation), while your favorite Bohm theory has yet to be properly formulated to be able to deal with quantum field theory.
     
  15. Apr 12, 2009 #14
    It looks like the annihilation operator has been applied to |QMessiah>.:biggrin:
     
  16. Apr 16, 2009 #15

    Fredrik

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    I didn't fully understand the argument in #1, but I'm not posting to ask about that. I just wanted to say that I wouldn't consider a process that entangles the eigenstates of a qubit with the eigenstates of another qubit a "measurement". To me a "measurement" is a process that entangles the states of the system with macroscopically distinguishable states of a system that (at least in the particular experiment we're considering) can be treated as classical. For example if someone bets $1000 that the result of a measurement will be|0>, the time evolution of the qubit-gambler system is (approximately, and ignoring normalization factors)

    (|0>+|1>)|:shy:> → |0>|:smile:>+|1>|:frown:>

    We can "measure" this system just by looking at the gambler's face. I'm not assuming a collapse here. I'm assuming that there are other terms on the right, but I expect them to be extremely small because of decoherence, so there's no point in including them.

    Unfortunatley, I don't have an exact definition of what it means for a system to be effectively classical, and I don't think anyone else does either. I suspect that it just isn't possible to define the concept in a way that draws a sharp line between systems that are effectively classical and systems that are not. And I believe that this means that it isn't possible to draw a sharp line between the two situations "a measurement has been performed" and "a measurement hasn't been performed". I find that both confusing and disturbing.
     
  17. Apr 16, 2009 #16

    Hurkyl

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    So, in your opinion, it's only a matter of scale. That's fine -- the point of the original argument is an attempt to refute the hypothesis that a measurement is a fundamentally different physical process, rather than quantum mechanics operating at large scales.



    I thought it was rather clear in decoherence-based interpretations of QM -- a system is 'effectively classical'* if and only if its (relative) state is approximately a purely mixed state.

    You don't want there to be a sharp line. (At least, it's a bad thing if you want macroscopic behavior to be the by-product of quantum mechanics applied to a huge number of particles) You simply want "obviously nonclassical" and "obviously classical" to be widely separated.

    * I don't think that's a technical term
     
  18. Apr 16, 2009 #17
    MWI in relation to Decoherence can be testable, and is routinely tested. People have seen interference patterns on double-slit experiments where instead of photons they used C_60 molecules which are like huge planets compared to a single photon. Decoherence theory survived many of these experiments, and is well on track to be falsified further in the future.

    There is going to be an adopted "interpretation" in the future, and treating them on equal footing because the current day scientific community hasn't adopted one is a big scientific sin.

    And preaching people to stop thinking about the interpretations and telling them to "shut up and calculate" is an even bigger sin!

    Copenhagen, with its kitsch wavefunction "collapse" assumption is SURELY going to be replaced.

    Although we may not get to see it.
     
  19. Apr 16, 2009 #18

    Hurkyl

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    Sure -- and these experiments support MWI in favor of non-quantum theories. But they have nothing to say regarding whether MWI should be favored over CI. (or Bohm, or RQM, or ...)
     
  20. Apr 16, 2009 #19
    I don't know anything about any non-quantum theory being clashed with a quantum interpretation. That doesn't make sense to me. Can you provide some examples or references?


    And No. They do say MWI should be favored over CI. MWI does not need wavefunction collapse --- which is an ugly artifice added to the theory by hand.

    Similarly Decoherence theories try to explain the classicality emergence and they favor MWI because of its lucid approach.

    What says Occam?

    The simpler the better.
     
  21. Apr 16, 2009 #20

    Hurkyl

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    What prediction of CI was violated by these experiments? If you cannot give a satisfactory answer to that, then you're wrong.
     
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