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B Hilbert Dynamics in choosing position in BM/MWI

  1. Feb 23, 2017 #1
    In General Relativity. Gravity is caused by curvature of spacetime.

    In MWI and Bohmian Mechanics.. the position observable and position preferred basis is chosen. There must be a non-zero energy or some kind of dynamics that would lock the particular Hilbert space vectors into those special bases. What is this dynamics caused akin to gravity caused by the curvature of spacetime or akin to the non-zero value of the Higgs Field in the vacuum. You can't just say the position is chosen as the preferred basis in Bohmian Mechanics without any consequence or dynamics.
     
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  3. Feb 23, 2017 #2

    bhobba

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    Last edited by a moderator: May 8, 2017
  4. Feb 23, 2017 #3
    But if the position observable and position preferred basis won't be selected as preferred in the environment, there won't even be any radial nature in particles in the environment. Imagine the vacuum of the Higgs. It's not zero but forced to choose a Vacuum Expectation Value. So in Hilbert Space (of environment), preferred basis of position is chosen ad hoc.. what is the corresponding dynamics causing it.. anyone?
     
    Last edited by a moderator: May 8, 2017
  5. Feb 23, 2017 #4

    bhobba

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    The basis is chosen in theory ie the position basis is implicit in the normal form of the Schrodinger equation. When expressed in that basis virtually all interactions turn out to be radial ie the V(x) in the Schrodinger equation. Its purely arbitrary what basis you chose to write your equations in - writing them in the position basis is whats usually done and you can easily see their radial nature.

    Thanks
    Bill
     
  6. Feb 23, 2017 #5
    Does this normal form of the Schrodinger also the one use by Bohmian, Copenhagen and Many Worlds? Which doesn't use it? If they all use it.. then why is there a distinction between Bohmian, Copenhagen and Many Worlds?
     
  7. Feb 23, 2017 #6

    bhobba

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    There is the QM formalism that all interpretations have. The usual form of Schrodinger's equation is part of that formalism.

    The diffference between interpretations hinges on things other than the formalism.

    1. Copenhagen has the idea the state is like the Baysian interpretation of probability.
    2. MW has the interpretation the state of the universe as very real, but when decoherence happens in the mixed state that results each outcome is a separate world. Everything simply evolves according to Schrodinger's equation. It uses the decision theory approach to probability
    3. BM uses any interpretation of probability - the particle has actual position and velocity at all times - you use probabilities because according to QM you cant know initial conditions with certainty ie you cant know both position and momentum at the same time.

    Interpretations are at least partially just arguments about of interpretations of probability:
    http://math.ucr.edu/home/baez/bayes.html
    'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'

    Thanks
    Bill
     
    Last edited: Feb 23, 2017
  8. Feb 23, 2017 #7
    Have you not heard about the problems of how to define preferred basis (like positions) in Many worlds? how do you connect this with what you mentioned above?
     
  9. Feb 23, 2017 #8

    bhobba

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    Yes.

    Many are BS, but some are legit eg the so called factorization problem. Decoherence explains it in all interpretations including many worlds with a few caveats such as the factorization issue I mentioned. IMHO much too much is made out of that and similar issues, but it is legit.

    You will find a discussion in the textbook I gave before - but it is not at the beginner level - unfortunately the questions you are asking are not answerable at the beginner level except in very broad terms.

    If you want to understand MW you must study its detail:
    https://www.amazon.com/Emergent-Multiverse-Quantum-according-Interpretation/dp/0198707541

    Unfortunately it is an advanced I level text - meaning upper undergraduate with at least a first proper course in QM.

    Thanks
    Bill
     
    Last edited by a moderator: May 8, 2017
  10. Feb 23, 2017 #9

    PeterDonis

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    Yes, but this is a classical theory, not a quantum theory. It is not relevant to the question you are asking in this thread.

    Yes, but that's true in any basis.
     
  11. Feb 23, 2017 #10
    But in Many Worlds how is the position basis chosen when the wave function "must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilitie"? are you saying the following is BS? Please comment this.

    https://arxiv.org/abs/quant-ph/0110148

    "This section identifies the core basis problem. The essential point is that if the universe has been evolving since the big bang in accordance with the Schrödinger equation, then it must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilities. Indeed, the planet Earth would not have a well-defined location, nor would the rivers and oceans, nor the cities built on their banks. Due to the uncertainty principle, each particle would have had a tendency to spread out. Thus various particles with various momenta would have been able to combine and condense in myriads of ways into bound structures, including measuring devices, whose centers, orientations, and fine details would necessarily be smeared out over continua of possibilities. The quantum state would be, to first order, a superposition of a continuum of slightly differing classical-type worlds with, in particular, each measuring device, and also each observing brain, smeared out over a continuum of locations, orientations, and detailed structures. But the normal rules for extracting well-defined probabilities from a quantum state require the specification, or singling out, of a discrete set (i.e., a denumerable set) of orthogonal subspaces, one for each of a set of alternative possible experientially distinguishable observations. But how can a particular discrete set of orthogonal subspaces be picked out from an amorphous continuum by the action of the Schrödinger equation alone?"
     
  12. Feb 24, 2017 #11

    bhobba

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    Partially BS, partially the factorization problem.

    You have started a B level thread for at least an I level issue.

    The answer of how that basis is singled out is as I told you before. Its detail can be found in the standard reference I gave.

    The reference you gave is at least I level, probably A level - it cant be discussed at the B level.

    You just have to take the word of the experts here - the solution is well known.

    If not then you have 2 options:

    1. Learn the technicalities yourself and study the references I gave.

    2. Get Dr Stapp to come and argue his case here.

    The other thing I need to mention is the modern version of MW you will find in Wallace is based on the idea of history which clarifies many (but not all) issues. I suspect Stapp has not gone into its detail. The thing is this, MW is basically Consistent Histories without the Many Worlds. You prove one wrong - down goes the other. Consistent Histories is basically the modern version of Copenhagen that fixes a blemish it has. In Copenhagen QM is a theory about observations that appear in an assumed commonsense classical world. How such a world emerges from a theory that assumes it in the first place is an issue. Consistent Histories and other modern interpretations based on decoherence fixes that - not entirely - some issues still remain, but most think they are nothing to really worry about.

    You will find the state of play here (it's a B level reference):
    https://www.amazon.com/Understanding-Quantum-Mechanics-Roland-Omnès/dp/0691004358

    BTW Stapp, while a legit scientist and researcher, is well known to hold views outside the mainstream.

    Thanks
    Bill.
     
    Last edited by a moderator: May 8, 2017
  13. Feb 24, 2017 #12

    Demystifier

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    In MWI, the preferred basis problem is much more serious than in other interpretations
    https://www.physicsforums.com/threads/many-worlds-proved-inconsistent.767809/

    For instance, in BM one can pick the position as a preferred observable simply because it leads to results which agree with observations. In principle one can do that even in MWI, but this breaks the spirit of MWI.
     
  14. Feb 24, 2017 #13

    bhobba

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    Its the legit Factorization problem I mentioned before.

    Its worse in MW because it does not explicitly assume the existence of structure like other interpretations do.

    I have never however seen exactly why the same issue doesn't occur in Decoherent Histories which as far as I can see doesn't either.

    If you read Walllace's book its all based on Histories - not structure.

    Thanks
    Bill
     
  15. Feb 24, 2017 #14

    Demystifier

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    Good point!
     
  16. Feb 24, 2017 #15

    bhobba

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    Yes. If you read the book Understanding QM, which basically elucidates decoherent histories, I gave the link to (it's at the beginner level) it points out a number of key theorems are missing. The factorization problem is one of them. We need theorems to elucidate exactly what happens with different factorizations - if so under what conditions - its a minefield that needs more work.

    I don't think at this stage it can be used to rule out MW, Decoherent Histories etc, but more work is required.

    Thanks
    Bill
     
  17. Feb 24, 2017 #16

    Demystifier

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    You mean Omnes, not Wallace, right?
     
  18. Feb 24, 2017 #17

    bhobba

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    Yes - sorry for not being clear.

    Although Wallace gives the modern version of MW it is not at the B level and not suitable for the OP.

    Thanks
    Bill
     
  19. Feb 24, 2017 #18

    bhobba

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    Just to show the OP this emergence of a classical world is NOT universally accepted as not possible (in fact I am pretty sure most scientists are like me and think saying it must be like that is BS) see:
    http://rsta.royalsocietypublishing.org/content/370/1975/4566

    Is the above right? Who knows - we need a lot more work here which is why articles like Stapp annoy the bejesus out of me and confuse beginners unnecessarily IMHO.

    Thanks
    Bill
     
  20. Mar 10, 2017 #19

    Hi Mr. Hobba. I finally received this book "Understanding Quantum Mechanics" by Roland Omnes that you recommended. But I couldn't find the topic about Factorization (which was why I bought it). Can you please review your book when you have time and please share what pages are they in. Also I tried to find the pages where it says key theorems are missing. I couldn't find them either. I think you mistaken it for another book?
     
  21. Mar 10, 2017 #20

    bhobba

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    Sorry. I can see how my wording would indicate he did mention the factorization problem. He doesn't - but does mention other unresolved issues eg see page 206. My recollection is that is not the only one either but I would have to go through the book to find them.

    But the factorization problem has a number of papers about it eg:
    https://arxiv.org/abs/1210.8447

    However the link I gave above makes some conjectures on how structure can emerge.

    Right now that's where it stands - we don't know.

    But you have not wasted your money on that book - ts very good and at what I would call the B level.

    Thanks
    Bill
     
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