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The Truth About Uncertainty

  1. Dec 9, 2003 #1
    Maybe this belongs in the quantum field physics area of the forum, but I could never understand what the major significance of Heisenberg being able to predict velocity or location of the subatomic particles....Einstein said he rejected this idea because God Does not play dice, why is it that Einstein felt that the human being's inability to calculate both velocity and location means that a particle has what??? That a particle cannot have a definite location and velocity? Why is it that our lack of being able to measure what is going on leads Einstein to concentrate so much effort on trying to figure out a way to go about these measurements...its as if Einstein felt that since humans could not be accurate and would possibly always have to be uncertain (as a result of how measuring velocity effects location and measuring location effects velocity)that this meant that things are moving in ways which can be thought of as random in the sense that they are not moving in ways which are a result of "cause and effect".
     
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  3. Dec 10, 2003 #2
    Heisenburg's Uncertainty Principle doesn't have to do with human's inability to accurately measure both position and velocity. HUP means that if you know a particles position than it's velocity is intrinsically undefined, and vice versa.
     
  4. Dec 10, 2003 #3

    russ_watters

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    It is commonly described that way though (such as in "A Brief History of Time") and that leads to some confusion.
     
  5. Dec 11, 2003 #4
    Is the Heisenburg's Uncertainty Principle just a human measurement problem, or is it a phenomina of nature? What particle interactions require exact velocity information and no position information? What interactions make a particle's momentum undefined?
     
  6. Dec 11, 2003 #5
    It is NOT a human measurement problem. The HUP descibes the universe as it actually is at the quantam level. For example an electron orbiting a nucleus is not a little particle going round and round - it acts both like a particle and like a wave, but is neither. If you think of it as a wave, then where exactly IS the actual electron? There is no real answer to this. You can detect a wave, or you can detect a particle, but not both at the same time.
     
  7. Dec 16, 2003 #6
    Hello, everybody !

    I'm new in this forum (I discovered it by chance, while I was looking for pages on wormholes...Well I didn't find what I wanted but, at least, I discovered this very interesting forum !!! ).

    See, if you want, that link (of a book)...

    Heisenberg's uncertainty relations

    " The author of this book presents conceptual and experimental evidence showing that Heisenberg's uncertainty relations are not valid in all cases. Furthermore, he derives a more general set of uncertainty relations [...] "



    Best regards,
    Looker
     
    Last edited: Dec 16, 2003
  8. Dec 16, 2003 #7
    Uncertainty ..

    Is the uncertainty principle still a "stand-alone" principle that can not be derived from the formalism of quantum mechanics? Or is it a historical, ad-hoc principle that was only necessary before Shroedinger's equations and later developments?

    My familiarity with the subject is based only on elementary physics texts, where it is sometimes explained that the uncertainty comes in because of the wave aspect of the particle: the frequency of a wave becomes less distinct as the duration of the wave packet is reduced. As a communications engineer this is a familiar concept, and I am not sure if the uncertainty principle is a separate necessity once the wave property is accepted.
     
  9. Dec 16, 2003 #8
    oops...!

    I forgot the link in my previous post !...
    Sorry !


    What I think...
    Heisenberg's relations are a consequence of the type of waves that Quantum Mechanics uses (plane monocromatic waves and Fourier analysis are the basis of QM ).

    The link I intended to put in my previous post links to a reference page of a book where the author refutes the use of that kind of waves and begins to use another type of waves - the wavelets (localized in space and time).
    Then the author derives a more general uncertainty principle !



    Best regards,
    Looker
     
  10. Dec 17, 2003 #9

    selfAdjoint

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    Re: Uncertainty ..

    The uncertainty do to the wave nature is correct as far as it goes, but as we see from some of the posts on this thread, it can be confusing too. How much of the specificity of the waves is involved?

    The real origin of uncertainty is the fact that some of the operators on Hilbert space (representing measurements) do not commute with each other, that is doing A and then B gives a different result from doing B and then A. Thes "commutation relations" are at the heart of the difference between quantum behavior and classical behavior. To impose the commutiation relations on the set of operators in a classical theory is what is meant by "quantizing" it.

    And there is a straight proof of uncertainty from the commutation relations. So uncertainty is a deep fact of quantum nature. Einstein understood this, and that is why he reluctantly left quantum theory, of which he had been one of the founders.
     
  11. Dec 17, 2003 #10
    re: Uncertainty

    Thanks, selfAdjoint. I could not understand your answer in its entirety because (as I said in my earlier post) I have not studied QM in such depth.

    However I did gather that the wave picture is only a partial explanation for uncertainty, and that QM in its rigorous form leads necessarily to the UP.

    Thanks again.
    - S.T.
     
  12. Dec 17, 2003 #11
    Dear SelfAdjoint,

    I'm sorry but I don't agree with you !!!



    This is only one of the ways to derive the uncertainty relations...
    I recomend you to learn the Bohr's method !

    Niels Bohr derive Heisenberg's uncertainty relations as a direct consequence of Fourier non local analysis ! And so, Heisenberg's uncertainty relations assume the ontological status of expressing an aspect of Principle of Complementarity of Bohr !

    As you know, that principle is of extreme importance in the fundamentals of Quantum Mechanics.


    If you are referring to my post, I recomend you to learn a little bit of the fundamentals of Quantum Mechanics.
    Quantum Mechanics is not just a tool calculus !
    It has a deep meaning in our concept of Nature...


    Best regards,
    Looker
     
  13. Dec 17, 2003 #12
    Ex me, but could you explain this concept more detail (it could be language incopatibility, but i don't...)
     
  14. Dec 17, 2003 #13

    selfAdjoint

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    I could return the favor. You want to stay fixed back in Bohr's 1930's viewpoint and ignore the development of QM after that, which was spearheded by the introduction of Hilbert spaces.

    So we have two methods of deriving uncertainty:

    A) Bohr's, which uses wave mechanics, and
    B) von Neuman's which uses Hilbert space considerations

    To a large degree they coincide, but A is subject to people playing games with wave functions, based on "reifying" the wave function. Therefore I view B as a sounder way to introduce uncertainty, even if it is farther from our ordinary intuition. Our ordinary intuition is precisely what causes trouble when we try to interpret quantum mechanics.

    In another post I have expressed my opinion of people who brag about understanding the deep quantumness of the world while turning their back on actual QM and musing over old books from the early days.
     
  15. Dec 17, 2003 #14
    Hi jhirlo !

    Complementarity Principle is, for exemple, the wave-particle duality : in some experiences we detec particles (an electron, for exemple), in other experiences the same electrons have a ondulatory behaviour (they are waves).
    Other exemple of complementarity : the better we know velocity, the worst we know position (that's why Heisenberg's uncertainty relations derived by Bohr are related with complementarity principle)

    Complementarity is almost a philosophical principle.
    I can't explain it in few english words...OOPS !

    Link to Bohr :

    Niels Bohr


    Best regards,
    Looker


    (sorry my bad english...jhirlo !)

    :frown:
     
  16. Dec 17, 2003 #15
    Dear SelfAdjoint !

    I didn't study QM in old books, as you name it...
    My first "Bible" in QM was Mécanique Quantique, by Cohen-Tannoudji and others !

    But it didn't stop me to learn things about the beginning of QM.
    [My first QM teacher was (when he was younger), a collaborator of Louis de Broglie. And he marked me !!!]


    The philosophical principles are still the same, I guess...


    And if Heisenberg principle is not completelly correct ?
    There are situations that violates Heisenberg's principle ! How the actual and orthodox QM deals with it ?


    O.K., Hilbert spaces !

    But you must decompose a wave function (ket) in the base of eigenfunctions of the operator - and that are plane monocromatic waves (it is Fourier analysis).
    Plane monocromatics waves are infinite in space and time, as you know !
    They really don't exist !
    They are a mathematical construction !


    The author of the book I mencioned in other post, substitutes plane monocromatic waves by wavelets !
    Do you know what wavelets are ?

    It is very interesting because he derives more generally uncertainty relations !

    Is it really like this ?
    I don't know !!!
    I only know that orthodox QM has ideas that are very strange to me !...


    ...And we can also think of Bohmian Mechanics, that gives the same results of orthodox QM.
    Bohmian Mechanics is causal QM !

    Orthodox QM is not, probably, the only way...



    Best regards,
    Looker

    (sorry my bad english...I'm a little bit rusty...ops !):frown:
     
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