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Interpretations of Quantum Mechanics

  1. Jul 18, 2014 #1
    Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase). It can be unknowable (the future)...but it shouldn't be random in any way.

    Edit: basically I'm looking for a hard determinism type of QM interpretation.
     
  2. jcsd
  3. Jul 18, 2014 #2
    I don't believe so.

    The closest I've encountered is Bohm Mechanics.
     
  4. Jul 18, 2014 #3

    jedishrfu

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  5. Jul 18, 2014 #4
  6. Jul 18, 2014 #5
    Not necessarily. There is some question surrounding whether its evidence for Bohm Mechanics or not.
     
  7. Jul 18, 2014 #6

    bhobba

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    Sure eg as another poster said BM and its probably not the only one.

    The real issue with QM is not this or that issue such as being probabilistic, non local or whatever. Its that we have all these different interpretations that fixes up any issue that may annoy you such as lack of determinism, but we don't have one that fixes them all.

    The issue with BM is its explicitly non local (that personally doesn't worry me - but others find such quite troubling) and you have this unobservable pilot wave - which does. Its far too much like the aether hypothesis in SR for my liking. One of the lessons of modern physics is to not introduce ad hoc hypothesis whose only purpose is to have the world conform to a pre-conceived bias in how it operates - which was Einstein's issue that caused Bohr to comment - Einstein - Stop telling God to do. The joke is on both of them though because it turns out they were both wrong - but that is another story. Do a post about it if you are interested - its way off topic in answering this so doesn't belong in this thread, but is an interesting issue.

    But if you discuss the aether hypothesis with genuine physicists that believe in it (not kooks - which leaves only a few - it really is a backwater idea these days) you find they have a slightly different take - ie we live in a world of broken symmetries and this breaks symmetry at a very fundamental level.

    No right or wrong here.

    Thanks
    Bill
     
  8. Jul 18, 2014 #7

    Nugatory

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    Google for "superdeterminism" and "block universe". They won't be exactly what you're looking for, but they'll give you a pretty good sense of what it might mean to set the the future "in stone". Be aware that neither one can be refuted by experiment, so although they're interesting to contemplate there's not a lot of solid physics content here.
     
  9. Jul 18, 2014 #8
    Technically the wavefunction evolution is deterministic in Many Worlds, so this is kind of like the future being "set in stone". This doesn't help us know our own subjective future, though, since we never know what branch of the wavefunction we are in/will experience.
     
  10. Jul 18, 2014 #9
    You can say any interpretation of QM is deterministic in the sense that it follows the fundamental Schrodinger equation, which only deterministically predicts probabilities for certain events to occur.
     
  11. Jul 18, 2014 #10
    Well not really. If wavefunction collapse "really happens" in a non-deterministic way, then that is a fundamentally non-deterministic part of the evolution of the universe. This never happens in many-worlds; there is only schrodinger, and no other kind of evolution. From the initial conditions of the multiverse you can predict the full history of the full multiverse. You can't do that if there is a fundamentally non-deterministic step somewhere. You can instead only predict the full possibility-space. But in many-worlds, those are not just possibilities, they are reality.
     
  12. Jul 18, 2014 #11
    If there was actually collapse of the wave function, then QM would need modification to allow that.
     
  13. Jul 18, 2014 #12
    Why? It already has projection operators.
     
  14. Jul 19, 2014 #13

    bhobba

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    No it wouldn't. You simply postulate that's what happens. Any theory has unexplained things.

    Exactly. Its interpreting it that's the issue. There are all sorts of ways of doing that. A modern one is consistent histories. A history is a sequence of projection operators. In that interpretation QM is the stochastic theory of histories - there isn't collapse. Some say its MW without the worlds.

    Thanks
    Bill
     
  15. Jul 19, 2014 #14
    According to QM there is only the Schrodinger equation evolution, correct?
     
  16. Jul 19, 2014 #15

    atyy

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    The question that diffrrent QM interpretations try to answer is not determinism versus randomnes. The question is whether a realistic theory can underlie QM, in contrast to the operational viewpoint of Copenhagen in which a measurement device is a fundamental object required in defining the theory.
     
    Last edited: Jul 19, 2014
  17. Jul 19, 2014 #16

    atyy

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    Wolchover's article is misleading. The analogy between the fluid experiments and quantum mechanics is so weak that the fluid experiments are not able to lend support to the pilot wave theory. Also, the pilot wave theory needs no support from such experiments. It is already a leading approach, and consensus acknowledges it as a correct solution to the measurement problem for non-relativistic quantum mechanics.
     
  18. Jul 19, 2014 #17

    Matterwave

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    Usually that the wave function evolves according to the Schrodinger equation is only one of the postulates of QM. The other postulates include that the observables are represented by Hermitean operators and that measurements of such observables yield eigenvalues of such operators in statistical accordance with the probabilities described by the wave function (the Born rule). It is this latter postulate that I think Bhobba was referring to in his previous post.
     
  19. Jul 19, 2014 #18

    RUTA

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    Last edited: Jul 19, 2014
  20. Jul 19, 2014 #19

    bhobba

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    No.

    Here is the basic axiom:

    An observation/measurement with possible outcomes i = 1, 2, 3 ..... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

    One then applies Gleason's theorem to prove a formula for that probability known as the Born rule, which is there exists a positive operator P of unit trace such that the probability of Ei is Trace (PEi). By definition P is called the state of the system.

    This has recently been discussed in a thread where I posted my proof of this important result (claiming no credit - I came up with it by picking the eyes out of a number of different proofs):
    https://www.physicsforums.com/showthread.php?t=758125

    These are the two axioms of QM the development of which you will find in Ballentine. But because of the beautiful Gleason's theorem its only one key axiom.

    Schrodinger's equation is simply a requirement from symmetry - again the detail can be found in Chapter 3 of Ballentine.

    Indeed, in both Classical Mechanics and Quantum Mechanics, and even Quantum Field theory, the dynamics is determined by symmetry. This is the amazing change in paradigm that came about when the great mathematician Emily Noether proved her profound and beautiful theorem:
    http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

    To understand it better I actually suggest a book on Classical Mechanics - Mechanics by Lev Landau:
    https://www.amazon.com/Mechanics-Third-Edition-Theoretical-Physics/dp/0750628960

    Whenever I link to that I cant resist posting the following:
    'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages.'

    'The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.'

    But back to the original question - no that is not what QM says - that the outcomes are probabilistic is built right into its foundations. Schroedinger's equation, rather than being at odds with it, depends on it.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  21. Jul 19, 2014 #20

    bhobba

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    Schroedinger's equation actually follows from symmetry so in a sense its not really a separate axiom but rather a requirement of the Principle Of Relativity (POR). Of course you have simply replaced one axiom with another, but most consider the POR to be more fundamental than things you can derive from it like Schroedinger's equation because its applicable to many different areas of physics. The POR is actually a meta law - a law about laws. Schroedinger's equation is simply an instance of that law. The strange, and very beautiful thing, is that meta law often implies the law in particular instances eg here Schroedinger's equation is implied by QM's foundational axioms (or in my case axiom) and the POR - specifically that the probabilities are frame independent. Its crazy when you think about it - but in science fact is often stranger than fiction.

    What I am trying to get across is that the FORMALISM of QM doesn't have collapse as part of its foundations. Its simply assigning a probability to the outcome of an observation that has been mapped to the mathematical objects of the theory - in my treatment POVM's. The state is simply a mathematical requirement from that mapping. Its not usually presented that way except in highly mathematical treatments such as Geometry of Quantum Theory by Varadarajan:
    https://www.amazon.com/Geometry-Quantum-Theory-V-S-Varadarajan/dp/0387493859

    But its still true.

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