The Knowable and The Unknowable in quantum mechanics

Discussion in 'Physics & Math' started by lethe, Nov 12, 2002.

  1. lethe Registered Senior Member

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    first of all, it is not the momentum that goes to infinity, but rather the uncertainty in the momentum.

    so if you make an exact measurement of the position, you cannot say anything about the momentum. it is completely unknown, and could have any value.

    energy conservation and momentum conservation still apply, so the particle doesn t get energy for free. i will necessarily have to impart some energy to the particle to make this kind off measurement. i don t know how much energy i might have to impart, but it might be a lot. it could be arbitrarily large.
     
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  3. overdoze human Registered Senior Member

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    Well, then we agree. In practice, nobody has access to arbitrarily large amounts of energy. Therefore in practice the uncertainty principle puts limits on precision.

    But now, I find it most interesting where this particular line of questioning landed us. It seems we're discussing the theoretically possible vs. the practically feasible. This is quite analogous to discussions concerning detection of hidden variables. Thus, I'm told we can't know and therefore they don't exist. Well, I can take that same argument and turn it around to claim that since we can't know the perfectly exact position of anything (it would take more than the entire energy of the universe), then nothing ever has an exact position (same for momentum.) Therefore, it doesn't make sense to discuss conservation of energy, since such conservation requires exact mutual cancellations which are impossible. Now, I happen to dislike this conclusion, so I would claim that exact positions, momenta, etc. in fact do exist, despite the fact that we can't determine them experimentally.
     
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  5. lethe Registered Senior Member

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    Yes. nothing ever has an exact postion. they are waves, afterall.

    i don t see any reason we can t know with arbitrarily high precision...


    didn t follow that last bit about mutual cancellation?
     
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  7. aseedrain Registered Senior Member

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    **edited** - needs to re-think question.
     
    Last edited: Nov 25, 2002
  8. chroot Crackpot killer Registered Senior Member

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    No, lethe, time and energy are non-commuting observables.

    delta-E * delta-t <~ h-bar

    - Warren
     
  9. James R Just this guy, you know? Staff Member

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    <i>...because quantum systems are very small, we only observe their quantum natures when we have carefully prepared experiments in the lab.</i>

    Not quite. In fact, all chemistry depends on the quantum natures of atoms. Atoms wouldn't bond into molecules and substances wouldn't combine the way they do without quantum mechanics.

    On another point, everyday applications of quantum mechanics are all around us. Does anybody own a CD player? It has a laser in it which could not work if quantum mechanics didn't exist. Its design is based on our knowledge of quantum physics.
     
  10. aseedrain Registered Senior Member

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    99
    I had posted this question in another thread but it was a bit off-topic there. So I'll ask it here:

    What happened during the initial moments after Big Bang when the universe was a quantum system for it to transform to its subsequent state? Was there a collaspe of wavefunction? If so, what caused the collaspe?

    Thanks.
     
  11. lethe Registered Senior Member

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    2,009
    firstly, time is not an "observable quantity", in the sense that it is not a hermitian operator in hilbert space, and hence it makes no sense to say time doesn t commute with energy. and the law about time and energy uncertainty is actually a completely different relationship from the regular uncertainty principle, at least in a nonrelativistic quantum mechanical treatment.

    however, that is just a matter of terminology. all i meant is that the heisenberg uncertainty principle is unrelated to, say, the law of conservation of energy. the uncertainty in energy is independent of the kinematic constraints implied by other conservation laws. that is all i meant by that statement.
     
  12. chroot Crackpot killer Registered Senior Member

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    This is all very true. Sometimes I lose sight of the fact that there is no T-hat.

    - Warren
     
  13. Paul W. Dixon Registered Senior Member

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    Extended Tensor as Quantum

    Extended Tensor as Quantum

    The g(mu)(nu) of the generalized theory of relativity would be substituted into the wave theoretic equations of Schrodinger in this postulation and thus provide a term which symbolizes both time and space vectors. This four dimensional construct would be a wave-like function in the densely energetic field of energy now thought to provide for some 9/10ths of the mass of the universe. It would have a solition like existence in this field.

    This would be an extended tensor of a wavelike configuration extending infintely far in all directions. Such a postulation would account for diffraction patterns whose existence demonstrates the wave-like nature of elementary particles. Questions concerning both momentum and location would be of a complex nature but yet definable within the complex patterns of wave interactions. In this manner and way, those observations at the quantum level would be returned to the realm of physics and not be answered approximately via statistical mechanics as in now currently the case. The various paradoxes and diffculties so well illustrated in the denken experiment of Schrodinger's cat would then no longer obtain. This is what both Heisenberg and Einstein hoped to find in that a deterministic physics would then be found.

    Wishing everyone a most Joyous Holiday Season!!!

    Yours sincerely,

    Paul W. Dixon, Ph.D.
     
    Last edited: Nov 30, 2002
  14. alisson Registered Member

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    5
    i've just read most of these posts, and have realized that i will never have the comprehension of even one of you ameteur physics enthisiasts, much less someone spending 20,000 a year trying to understand it. what a waste...and what a sad 2 a.m. this has been.
     
  15. James R Just this guy, you know? Staff Member

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    Who are you calling an amateur, alisson?

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    (Welcome to sciforums, by the way.)
     
  16. chroot Crackpot killer Registered Senior Member

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    2,350
    Re: Extended Tensor as Quantum

    Paul,

    Exactly how would you insert the Riemann tensor into Schroedinger's equation:

    H-op * phi = E * phi

    Are you attempting to make the Riemann tensor a state function? In what way does this make sense, either mathematically or conceptually?

    I know it's pointless, since you're a nutcase... but I'm curious as to the mechanisms that lead you to say the dumb shit you say.

    - Warren
     
  17. lethe Registered Senior Member

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    i would say that there probably haven t been any external measurements of the universe (who would do the measuring?), so the wavefunction of the universe would be uncollapsed still.

    remember though that the universe is made up of a product of all the wavefunctions of all its consituent particles, and that their individual wavefunctions can at one time or another collapse.
     
  18. 1119 Registered Senior Member

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    Collapse on its own or upon interactions with other wavefunctions?
     
  19. lethe Registered Senior Member

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    2,009
    interaction with others. in other words, measurement.
     
  20. Paul W. Dixon Registered Senior Member

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    EXTENDED TENSOR AS QUANTUM

    EXTENDED TENSOR AS QUANTUM

    May it, therefore, be conjectured that the g(mu(nu) (extended tensor in Riemannian noneuclidean geometry) may be substituted into the basic equations of quantum mechanics of Schrodinger without contradiction. In this manner and way, all of the aforetmentioned results will obtain which is then cited here as part of the historical record.

    It may be suggested that the fiber bundle exposition found in differential topology may be used to express the world lines in 4-space for an appropriate quantal description.

    Please discuss this conjecture with a University Faculty Member whose work encompasses both differential topology as well as an interst in modern physics.

    Wishing all and everyone,

    A VERY MERRY CHRISTMAS!!!

    Yours sincerely,

    Paul W. Dixon, Ph.D.
     
    Last edited: Dec 6, 2002
  21. chroot Crackpot killer Registered Senior Member

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    2,350
    Re: EXTENDED TENSOR AS QUANTUM

    Way to go, Paul. That was one of the most incoherent catenations of scientific words I've ever seen. You're really outdoing yourself these days.

    - Warren
     
  22. lethe Registered Senior Member

    Messages:
    2,009
    Re: EXTENDED TENSOR AS QUANTUM

    this is a bit off-topic. also, a bit outside my range of knowledge, but i will attempt an answer anyway.

    It may indeed be conjectured that the GR metric can be substituted into a quantized field equation. schrodingers equation would not be appropriate, because a, schrodingers equation is nonrelativistic, and b, it describes a particles motion, not a fields propogation.

    however, it does obey a field equation (einstein s equation), and one could try to quantize this equation, i believe. the standard methods of quantum field theory do not work for einsteins metric because the gravity model is nonrenormalizable, but there are a lot of people trying to come up with modified models to allow that to happen.

    i don t really follow what any of that has to do with the possibility of interpreting quantum mechanics as a hidden variables theory.
     
  23. Paul W. Dixon Registered Senior Member

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    505
    g(mu)(nu) and the hidden variable

    g(mu)(nu) and the hidden variable interpretation of quantum phenomena

    Should we consider the hidden variable as carrier wave for quantum phenomena, this interpretation would not require a hidden variable interpretation nor would quantum entanglement require nondeterministic probabilistic mathematical interpretation since the extended tensor for the individual particle extends to infinity in all directions. Subsitutions of this formulation, it is conjectured, would be compatible with relativistic Schrodinger equations. The advantage, therefore, of this approach is to substitute complex deterministic wave interactions for the current probability values of standard quantum mechanics. This is what Heisenberg stated was his eventual goal in the formulations of quantum mechanics but was not quite at this stage in the development of science at that time. Thus what is proposed here, is not to change the accuracy of the predictions of quantum mechanics but rather to subsitute a concrete physical interpretation for a statistical one.

    All Best Wishes for the New Year !!!

    Best Aloha,

    Paul W. Dixon, Ph.D.
     
    Last edited: Jan 12, 2003

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