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Momentum Basis Dynamics

  1. Dec 17, 2015 #1
    Can you describe or how does one visualize a decoherence branch where the position basis is not preferred (copenhangen, bohmian) but momentum basis (as say one of the Everett).

    Or if a world has position basis disallowed (suppressed for sake of discussion) and it's all momentum basis.. would there be physical objects, would there be form or would we have blobs of momentum only (and how does one visualize this).

    I have spent 3 days reading about decoherence in dozens of papers suggested by Hobba and company and this is what I need to know at this point. Thank you.
     
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  3. Dec 18, 2015 #2

    bhobba

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    The position basis is nearly always singled out - there is a general argument based on radial interactions ie interactions without a preferred direction. It is independent of interpretation. In cases (usually experimentally contrived) where you measure energy or momentum the setup singles out a different basis. There is nothing else to it - no visualisation etc etc. Its simply the 'observational' setup.

    Thanks
    Bill
     
  4. Dec 18, 2015 #3
    You are saying that in Many worlds, there will be no branches without position basis?

    Remember there are branches where the cat is dead and alive plus 1/2 dead and alive plus 1/4 dead and 1/8 alive as the superposition can be decomposed in any combination. So I was wondering if there was combination where there is no position basis selection but only momentum basis.
     
  5. Dec 18, 2015 #4

    bhobba

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    Of course not. Why you would think that has me beat.

    That's false. The cat is never in superposition - end of story. Its in a mixed state which is different to a superposition:
    http://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf

    Here is what's happening in Schroedinger's cat. Decoherence occurs at the particle detector so you get a mixed state of particle detected or particle not detected. Everything is common-sense classical from that point on. You can go the whole hog and think of the cat and the other paraphernalia as entangled with the detector and hence also in a mixed state of dead or alive. But there is no need for that - simply say the observation occurred at the particle detector and everything is sweet.

    Thanks
    Bill
     
  6. Dec 18, 2015 #5
    I'm aware of what you were describing. I was inquiring whether any of the mixed state of many worlds can occur without any position basis. Remember in the beginning it's all Hilbert space.. all decompositions or combinations occur.. resulting in many kinds of mixed state.. there should be one where there is no position basis..
     
  7. Dec 18, 2015 #6

    bhobba

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    Of course it can. All that's happening in MW is you interpret the parts of the mixed state after decoherene as different worlds. If you have a momentum observation then the mixed state is in the momentum basis.

    One of the things that decoherence solves is the preferred basis problem - it singles out the basis of the resultant mixed state.

    The measurement problem has three parts:
    1. Why we generally don't see interference effects. Decoherence solves that easily.
    2. The preferred basis problem ie why is say a position basis singled out. Decoherence solves that - but with more work. It turns out that most of the time a position basis is singled out - but most of the time is not all of the time - sometimes its momentum, or energy, or something else.
    3. Why we get any outcomes at all. Technically how does an improper mixed state become a proper one. Most interpretations stand powerless before that - but MW doesn't have that issue - its trivial. Each part of the mixed state is a separate world.

    Thanks
    Bill
     
  8. Dec 19, 2015 #7
    The law of physics (like constants of nature) is the same in all branches of the many worlds? I thought they could differ. What is the principle or theorem that disallow or allow it?
     
  9. Dec 19, 2015 #8

    Nugatory

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    MWI says that if I start with a wave function that is a superposition of A and B, I'll end up with two worlds. In one of the them the Copenhagen crowd will be saying that the superposed wave function collapsed to A; in the other they'll be saying that it collapsed to B. If the laws of physics could be different between the branches, then in at least one of the branches we'd be seeing them changing across the observation that led to the collapse or split - and that's contrary to our experience.
     
  10. Dec 19, 2015 #9

    bhobba

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    Just think about what's going on.

    Instead of one part of the mixed state being the one that occurs they all occur but in separate worlds. Since any outcome keeps the same laws of physics obviously each world has the same laws.

    Thanks
    Bill
     
  11. Dec 19, 2015 #10
    Ok. Thank you. I think my level of question is in this context. In Bohmian mechanics, position is the preferred basis. What if there was a Bohmian Mechanics where momentum (instead of the position) is the preferred basis or hidden variable. Then what will happen to position of objects? Or what would a world with BM that has position vs momentum preferred (as hidden variable) differ? I think this is my question.
     
  12. Dec 19, 2015 #11

    bhobba

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    Since BM has been cooked up to be equivalent to standard QM its exactly the same. You can get position basis, momentum basis etc etc - there is none preferred.

    However it also resolves the outcomes issue trivially since the particle has position, momentum energy etc at all times.

    Thanks
    Bill
     
  13. Dec 19, 2015 #12
    I guess my confusion can be traced to this odd thing called Factorization. You always said whenever this is mentioned. there is hot debate.. but note you only have debate about this with Ruth Kastner in the archives.. not with others. So since she doesn't participate anymore, there will be no debates.. especially with newbies or even experts who may not be familiar with it. For us newbies.. we just want a clear treatise on it. Do you have other references of the basic about Factorization besides the ones already shared in this room? Because it seems that Many worlds alone can't create any outcome. You have to add hidden variable to it to get the Factorization. This means Many worlds must have Bohmian Mechanics in combination for it to work to produce any outcome. Or Quantum Darwinism to produce it.. but then Quantum Darwinism still need a classical hidden variable to produce any Factorization since Quantum Darwinism is purely Hilbert Space. You can't argue that the quantum fluctuations being random can give quantum Darwinism factorization.. it seems a separate problem. I think Scientific American or other sci magazines must present this clearly to the public.
     
  14. Dec 19, 2015 #13

    bhobba

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    I seem to remember it with others eg Quantumental.

    Forget about it. Its a fringe issue and seems to worry philosophy types more than mathematicians like myself. Do you really think how you divide a system for analysis is a critical thing? I dont, and it seems rather obvious to me. But everyone's different.

    Thanks
    Bill
     
  15. Dec 19, 2015 #14
    In a few words that summarize the main idea. What is the connection of Factorization to Preferred Basis. Is it right the choice of Factorization can affect the Preferred basis?
     
  16. Dec 19, 2015 #15

    bhobba

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    None. Factorisation is simply the idea how you decompose a system gives different results. Its always decomposed in the obvious way - what does the observing, what is being observed, and maybe the environment. Those that harp on about factorisation think if you decompose it differently you get a different result.

    Thanks
    Bill
     
  17. Dec 21, 2015 #16
    I have been reading one of Tegmark paper mentioned in your past conversations with others and I came across this line "Finally, out of all the possible factorizations of Hilbert space, why is the particular factorization corresponding to classical space so special? Why do we observers perceive ourselves are fairly local in real space as opposed to Fourier space, say, which according to the formalism of quantum field theory corresponds to an equally valid Hilbert space factorization?"

    I'd like to know about Fourier space, is it a legal mixed state? Tegmark asked why we were in classical space and not in Fourier space, was he talking about after decoherence? This means Fourier space is not a superposition but a legal mixed state, is this about right? Thank you.
     
  18. Dec 21, 2015 #17

    bhobba

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    Who knows what Tegmark means - I find him particularly opaque and to be blunt, sometimes downright silly (eg his writings on quantum suicide)

    His fellow MIT professor is more my style:
    http://www.scottaaronson.com/democritus/lec9.html

    But my reaction to the above is if you do a Fourier transform on a wave-function you go from position space to momentum space. The reason position space is more useful is the position basis is usually singled out rather than momentum.

    Thanks
    Bill
     
  19. Dec 21, 2015 #18
    The paper is in message 163 in this thread you also participated https://www.physicsforums.com/threads/why-does-nothing-happen-in-mwi.822848/page-2

    We won't discuss Tegmark stuff but just the meaning of Fourier Space or the general meaning of classically being singled out by decoherence.. Specifically I'd like to know example of mixed state that is not classical.. can you cite any?
     
  20. Dec 21, 2015 #19

    bhobba

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    First explain what you mean by a mixed state that is not classical. Classical in the sense of mixed states I would take to mean the absence of interference terms so classical probability applies.

    Thanks
    Bill
     
  21. Dec 21, 2015 #20
    Based on Mentor Peterdonis own words in message #33:

    "The problem, according to Schwindt, is that the MWI doesn't have any states other than "the pure state of the entire universe". For example, when you say "cats decohere", you are assuming that there are "cats" picked out somewhere as identifiable quantum states. But if all we have is the pure state of the universe, there are no "cats"--or humans, or anything else. So you don't even have the structure needed to talk about "decoherence" at all."

    So by mixed state that is not classical. Maybe cat-dog combination factorization? So instead of a cat or dog.. we have half cat and half dog as legal mixed state (that is unclassical).. why don't we have them after decoherence is the question. So do you agree that half cat and half dog is unclassical mixed state?
     
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