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Quantum mechanics of time?

  1. Jan 28, 2004 #1
    does anyone know?
    time = ?
     
  2. jcsd
  3. Jan 28, 2004 #2

    chroot

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    Time plays the exact same role in (non-relativistic) quantum mechanics as it does in Newtonian mechanics. It's just a dynamical variable.

    - Warren
     
  4. Jan 28, 2004 #3

    Tom Mattson

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    That's true.

    Nope, it's a parameter. A "dynamical variable" satisfies an equation of motion in classical mechanics, and its expectation value satisfies the same equation in nonrelativistic quantum mechanics (NRQM). Also, an operator can be constructed for any dynamical variable in NRQM, but there is no sensible way to construct an operator whose eigenvalue is time.
     
  5. Jan 28, 2004 #4
    no t hat, remember?
     
  6. Jan 28, 2004 #5

    chroot

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    Eek, you're right.

    - Warren
     
  7. Jan 28, 2004 #6

    Tom Mattson

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    For a quick, yet clear, discussion of why that is, check out page 2 of this document.
     
  8. Jan 28, 2004 #7

    chroot

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    I'm aware that time is not an observable, has no corresponding operator, and so on, of course. I just goofed up and forgot the definition of the phrase "dynamical variable."

    - Warren
     
  9. Jan 28, 2004 #8

    Tom Mattson

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    Right, but I think we're talking over a lot of people's heads here. Rather than type out the math (still haven't mastered LaTeX), I posted a link to a reference.
     
  10. Jan 28, 2004 #9

    chroot

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    Oh by the way...
    How does a dynamical variable then differ from a generalized coordinate (or velocity, or whatever)? Is a generalized coordinate an example of a dynamical variable?

    - Warren
     
  11. Jan 28, 2004 #10
    Perimeter for what?
     
  12. Jan 28, 2004 #11

    Tom Mattson

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    Yes, generalized coordinates and generalized momenta together make up the set of dynamical variables.
     
  13. Jan 28, 2004 #12

    Tom Mattson

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    No, it's not "perimeter", it's "parameter". In both classical mechanics and NRQM, the dynamical variables can be considered functions (dependent variables) of the parameter, time (the independent variable).

    In relativity, position gets demoted to the status of a parameter as well.
     
  14. Jan 28, 2004 #13

    chroot

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    Great, thanks for clearing that up. I won't louse it up again. :wink:

    - Warren
     
  15. Jan 28, 2004 #14
    oppsss brain to hand signaling problem .....
    so is t constant, or relatively constant ?
     
    Last edited: Jan 28, 2004
  16. Jan 28, 2004 #15
    in Hamiltonian mechanics, yes, positions and conjugate momenta make up the dynamical variable.

    in Lagrangian mechanics, its positions and velocities instead.
     
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