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The speed of light and the uncertainty principle

  1. May 13, 2006 #1
    The heisenberg uncertainty principle says that

    h-bar/2 <= dE * dt.

    Let's say we have this device that emitted very low energy radio waves. Does that mean there'd be a significant probability of these photons traveling faster than light?
  2. jcsd
  3. May 13, 2006 #2


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    Last edited: May 13, 2006
  4. May 14, 2006 #3
    It's more subtle than that. We can show from general principles that

    [tex]\frac{\Delta A}{|d\langle A\rangle/dt|}\Delta E \ge \hbar/2[/tex]

    If we now define the bit on the left as [itex]\Delta t,[/itex] we get the oft-quoted uncertainty relation between time and energy.

    The justification for making that identification is that it's the average time taken for the expectation of the operator A to change by its standard deviation, so it's roughly the time scale to measure a change in A.
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