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Is Heisenberg principle applicable to a photon?

  1. Sep 17, 2010 #1

    fluidistic

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    I wonder if Heisenberg principle (both [tex]\Delta p \Delta x \geq \frac{\hbar }{2}[/tex] and [tex]\Delta E \Delta t \geq \frac{\hbar }{2}[/tex]) can be applied to photons.
    Say I have a laser emitting a flash. I know very well the wavelength of the photon, therefore its momentum. Also, I know well where it might be: it travels at c and must lie somewhere inside the cross section area of the laser beam situated at a distance ct from the laser, if I consider a time t after emission. Which seems to contradict that if I know well the momentum of the laser, I shouldn't know well where it is.
    The same doubt arises with the relation between [tex]\Delta E[/tex] and [tex]\Delta t[/tex]. I know very well the energy of a laser photon since I know very well its wavelength. And I do so at any time...
    Unless [tex]E\neq \frac{hc}{\lambda}[/tex]...
    So I don't understand if I'm missing something or if Heisenberg's principle cannot be applied to photons.
     
  2. jcsd
  3. Sep 17, 2010 #2
    It applies to lasers. You don't know the wavelength as well as you think. Common notion is that a laser is monochromatic, and compared to natural light, "it is", but there is a uncertainty to the wavelength that prevents it to be perfectly monochromatic.
     
  4. Sep 17, 2010 #3

    fluidistic

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    That explains everything... thanks a lot.
     
  5. Sep 18, 2010 #4
    I think you will find the discussion in Landau, vol 4, section 1, "The uncertainty principle in the relativistic case" to be very illuminating.

    "At first sight, one might expect that the change to a relativistic theory (of QM) is possible by a fairly direct generalization of the formalism of non-relativistic quantum mechanics. But further consideration shows that a logically complete relativistic theory cannot be constructed without invoking new physical principles..."
     
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