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When do Newtonian mechanics breakdown

  1. Apr 4, 2014 #1
    What would be the scale, in which Newtonian mechanics dissolve and QM becomes the sole victor for accurate predictions? A physics colleague told me that it was from the nanoscale to the planck scale, but I am not entirely sure that it has been used near infinitesimally small ranges as 10^–34.
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  3. Apr 4, 2014 #2


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    What would whether or not it has been used at that small a scale have to do with whether or not it is known to be the best predictor (or, at least better than classical mechanics) at that scale? As I understand it, current technology cannot conduct any experiment below about 20 orders of magnitude larger than the Plank scale and we will likely never get all the way there, but classical physics breaks down way before then.

    EDIT: "breaks down" is sloppy terminology. Better to say "is no longer applicable"
  4. Apr 4, 2014 #3
    It's not just a matter of a certain length scale--time scales and mass scales also matter. The physical constant ##\hbar## determines whether quantum mechanics is important or whether classical mechanics is a good approximation. To figure out if quantum mechanics is likely to be important, express ##\hbar## in units appropriate to your situation. For example, in our daily lives we work on length scales of order 1 meter, time scales of order 1 second, and mass scales of order 1 kilogram. Expressed in these units, ##\hbar## is

    ##\hbar \approx 10^{-34}## kg m^2 /s

    ##10^{-34}## is much smaller than 1, so classical mechanics is fine in ordinary life.

    Now, electrons in atoms are confined to regions of order 1 nanometer, orbit the nucleus in timescales of order 1 femtosecond, and weigh of order ##10^{-30 kg}##. Expressed in these units we have

    ##\hbar \approx 0.1## (10^(-30) kg) nm^2 / fs

    0.1 is not so small compared to 1, so QM is important for electrons in atoms.
  5. Apr 5, 2014 #4


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    Newtonian mechanics breaks down when quantum effects begin to appear ... for quantum fluids this happens at the macroscopic scale. For some devices (e.g., transistors) this appears at every scale. For some nanoparticle applications you can go a long ways with classical mechanics.

    Thus there is no particular scale - but if temperatures are very cold, or objects are very small, or distances are very short ... then you will probably see quantum effects.

    There is no definite system to tell you when this will occur - we use experience to guide us.

    PS: See http://physics.aps.org/articles/v7/35
    "Focus: Thermodynamics Confronts Quantum Mechanics"
    Last edited: Apr 5, 2014
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