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[OT[: Heisenberg Uncertainty Principle

Discussion in 'Electronic Design' started by Guy Macon, Sep 27, 2004.

  1. Guy Macon

    Guy Macon Guest

    There is an interesting thread that I started in sci.physics with
    the title "Heisenberg Uncertainty Principle." Think of it as a
    non-expert getting a second opinion... :)
     
  2. I read it. So, have you learned anything from it?

    Jon
     
  3. Guy Macon

    Guy Macon Guest

    Yes.
     
  4. You have told us where your article is, but not when you posted it. ;-)
     
  5. It would be interesting to know exactly what. I'll be more generous about my
    reply than you:

    I noted Gregory's response was congruent to the one I chose to write. Old Man
    got into some other details (but not incompatible ones, I believe.) If you are
    interested in the math, I'd recommend "Basic Quantum Mechanics" from the Oxford
    Physics Series. And for a general comment on what HUP means here, see pages 22
    and 23. Another place to go is Feynman undergrad Lectures on Physics, vol III,
    chapter 2, page 2-2ff. (And most of the rest of that volume, as well.)

    There are two different 'uncertainty' concepts being discussed, by the way. One
    is the uncertainty principle itself, which can be seen as a necessary outcome of
    applying the correspondence principle to Newtonian and quantum mechanics. The
    other is the uncertainty relation. It is here that is found the uncertainty
    inequality I mentioned, which is imposed because for any real numbered
    wavelength, the squared length vector is always real and non-negative. The
    quadratic solution then forces the important further restriction on the
    uncertainties of two observables (X and Y) for the same state. Here, generally,
    if the two observables do not commute (XY-YX is non-zero), then the uncertainty
    of X and the uncertainty of Y cannot both be made arbitrarily small
    __simultaneously__.

    Jon
     
  6. I will have to disagree here. My Bible is the Ballentine text book. In
    this book it explains in detail, that HUP isn't even about simultaneous
    measurements at all.

    "Quantum Mechanics, A Modern Development" ISBN981-02-4105-4 - Leslie E.
    Ballentine,

    p.225
    "...One must have a repeatable preparation procedure corresponding to
    the state p which is to be studied. Then on each one of a large number
    of similarly prepared systems, one performs a single measurement (either
    Q od O). The statistical distributions of the results are shown as
    histograms, and the root mean square half-widths or the two
    distributions deltaQ and deltaP, are indicated in fig. 8.2. The theory
    predicts that the product of these two half-widths can never be less
    then hbar/2, no matter what state is considered."

    The issue with much of what is written about HUP, is that it is usually
    based on un-rigorous definitions, and hand waving.

    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
     
  7. Guy Macon

    Guy Macon Guest

    I was terse for four reasons:

    [1] I couldn't tell whether what you wrote was an honest question
    or a subtle put-down.

    [2] I believe that any recounting of what has been posted in the
    sci.physics thread by a non-expert such as myself will be
    inferior to reading the thread itself.

    [3] I am asking questions, not providing answers.

    [4] Those who are providing answers appear to contracdict each other.

    In the case of the position and velocity of a single subatomic
    particle, do the two observables commute? Is XY-YX zero in
    that case?
     
  8. A 3rd opinion.

    http://www.anasoft.co.uk/quantummechanics/On the Postulates of Quantum
    Mechanics.pdf

    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
     
  9. Norm Dresner

    Norm Dresner Guest

    We live in a 3-D space. That means that there are three independent,
    mutually perpendicular coordinate axes that you can construct at a point.
    Actually there are an infinite number of these triads, all related by
    various rotations. Choose any one of them. The HUP implies that for each
    of these directions individually, the components of position and velocity of
    a single particle do not commute. That is, for, say, an electron, the
    position along the, say, X-axis and the velocity component along the X-axis
    are non-commuting observables. Same with Y-axis and Z-Axis. But the
    inter-axis variables are commuting. That is, you can simultaneously measure
    the positions on the three coordinate axes with unlimited precision -- or
    the three velocities; or the X-position and the Y-velocity, or ... It's the
    corresponding velocities and positions that don't commute and hence are
    limited by the HUP.

    Norm
     
  10. The observable operaters, X an P don't commute, this is not the same.
    According to the ensemble interpretation, X and P only have relevance
    statistically, not to individual particles, so HUP says nothing about
    individual particles.
    I think you have missed the point of the thread. Its about the *correct*
    interpretation of HUP. The summary is here,
    http://www.anasoft.co.uk/quantummechanics/index.html.

    Kevin Aylward

    http://www.anasoft.co.uk
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
     
  11. Norm Dresner

    Norm Dresner Guest

    The observables X & P for a single particle are non-commuting.
    I know the correct interpretation of HUP. I studied it in graduate school.

    Norm
     
  12. Well, Ballentine does have a perspective. Excellent book, though, I suspect.

    I think this whole thing may be leading us right into the EPR/Bohr debates,
    Bohm's early thinking on what then led to Bell's inequality, John Clauser's
    non-definitive experiments to test Bell's at Berkeley, later Aspect's much more
    conclusive work, and perhaps leading to the re-unearthing of the many-worlds
    viewpoint.

    It's my understanding that whether you choose to give up on locality, or the
    reality principle, or choose 'many world's as your forte', it's all the same
    thing -- 1:1 correspondences, regardless of the insight you choose. The
    mathematics may be easier for one problem or other, one choice versus another,
    but there is nothing yet to distinguish their predictions. Wheeler may lead you
    one way, Everett another, but so far as I'm aware none wins over the other.

    More specifically, position and momentum are fundamentally incompatible
    observables, in the sense that they do not share a complete orthogonal set of
    eigenvectors and therefore cannot be simultaneously measured. If you measure
    one, the system goes into some eigenstate. Then measure another, that into yet
    another eigenstate. But since they __do not__ commute (observables X and Y have
    such a complete set of orthogonal eigenvectors if and only if they commute),
    they are fundamentally incompatible and cannot be measured simultaneously. So
    what is the meaning, then, of making measurements arbitrarily small? It simply
    cannot be done.

    That was the question I'd been responding to, when I talked about the viewpoint
    of these kinds of dynamic attributes, which are just two faces or facets of some
    higher dimensioned volume.

    The inequality I mentioned resides at the heart of a debate over interpretation
    about the condition of a particle *before* measurement. But there is no way to
    measure both position and momentum simultaneously, as they do not commute. One
    could say it's a meaningless question and then just rely on the statistical
    interpretation. One could suggest that there is a deeper, reality position that
    implies more (a path I like to take, at times.) So I think this leads to
    cross-purposes types of answers -- and perhaps that is my fault alone. I can't
    say, for sure.

    Been interesting,
    Jon
     
  13. That's the understanding I've taken.

    Jon
     
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