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Photon divergence.

  1. May 26, 2010 #1
    I've been told time and again that any beam of light (think laser) exhibits divergence no matter how perfect. This prompts three questions:

    1) Theoretically, if a laser beam is emitted such that each photon is exactly parallel, (obviously more perfect than can be achieved in reality) does the beam still diverge?

    2) Consider a single photon propagating through space. Does it still exhibit divergence?

    3) Consider two coherent photons emitted exactly at the same time along exactly the same axis, do they exhibit divergence? If so, why?

    [a note to those who will undoubtedly say the situation is impossible, and not worth considering: you're missing the point]
     
  2. jcsd
  3. May 27, 2010 #2
    Good questions.
    Unlike charged particles(say, a stream of electrons), photons do not repel each other, so the photons divergence can not be associated with them repelling each other.

    I heard once that two strictly parallel lines will eventually diverge. So, perhaps this phenomenon is related to space/time divergence. Not sure though.
     
  4. May 27, 2010 #3
    Claiming that 2 photons are EXACTLY parralel means that you know EXACTLY their momentum. Then, based on HUP, you can't know their position and the beam diverges!

    If narrower the beam you make (you know the position), the faster it diverges (more uncertanity in momentum)

    Only infinitely wide beam does not diverge.
     
  5. May 27, 2010 #4
    My interpretation of the HUP is that there is a fundamental uncertainty (with regards to position and momentum) that can be measured experimentally -- if one is measured the other is perturbed by the measurement, thus both cannot be known experimentally. However, this is not to say that a photon does not have position and momentum, only that we can't know them both by measurement. For example, imagine you're looking at someone across the street and then a bus pulls in front of you, occluding your view. Now you can no longer see the person but it is safe to say they still exist. Can you be certain of the person's position? No, because they could walk away and you wouldn't know, but they do in fact have position even if you don't know what it is.
     
  6. May 27, 2010 #5
    No, your interpretation (instrumental) is wrong.
    This is not an issue how we measure these properties.
    They just don't exist at the same time - mathematically.
     
  7. May 27, 2010 #6
    What about the single photon case ? If we look at the propagation amplitude in the path integral picture, then the most of the amplitudes cancel except for the classical path (straight line). Most, but perhaps not all ?
     
  8. May 27, 2010 #7
    Single photon will hit a single point. In that sense, it does not diverge
    However, it can hit a point away from the axis of the beam. In that sense, it diverges.
     
  9. May 27, 2010 #8
    It would be lot easier to discuss this topic, if the mainstream quantum literature actually had told us what kind of equation to use for the wave function of a photon :rolleyes:
     
  10. May 27, 2010 #9
    I agree that a single photon can interact with a point away from the axis of travel. But isn't this because both the electric and magnetic field vectors have an amplitude (strongest perpendicular to the axis of travel) and therefor the photon has a certain minimum "width" in a sense. So if you could see the electric and magnetic fields, then sighting down the axis of travel would not reduce the photon to a single point.
     
  11. May 27, 2010 #10
    No, you can locate a photon of any wavelength in any arbitrary small region of space.
    Talking about HUP you cant use Maxwell equations (talking about electric and magnetic fields etc), you should use QM instead. Maxwell equations are just approximations of QFT
     
  12. May 27, 2010 #11
    Seems more like your talking about the curl of the field here. The divergence of a field is the change in flux over the entire surface of a sphere, so the direction should not matter.
     
  13. May 27, 2010 #12
    So then lets go back to the 19th century when they actually spoke intellegently about the nature of EM radiation! (Seriously... I'm not being sarcastic.)
     
  14. May 27, 2010 #13
    as opposed to uncertainly certain measurements where continuation requires an infinite dimensional space, and every value is an expectation in a world where not everything commutes?
     
  15. May 27, 2010 #14
    (single even) Photons don't travel in strait lines. They obey Maxwells equations which means they diverge.

    edit: Actually, I'll qualify this as follows: you can create a photon that moves in strait line using an infinitly large current plane to launch it. Any finite sized source of the photon will create a quantum (whose probability of detection) spreads out.
     
    Last edited: May 27, 2010
  16. May 27, 2010 #15
    It's hard to fathom how we got to this point, all because of one seemingly harmless little h!
     
  17. May 27, 2010 #16
    Maxwell's equation describe classical electromagnetic fields only, not wave functions of photons.
     
  18. May 29, 2010 #17
    It would give correct results to interpret the square of the electromagnetic field as being prportional to the probability of finding a photon there. That makes Maxwell's eqations work as an effective wavefunction for describing the motion of individual photons.
     
  19. May 29, 2010 #18
    There is some discussion on using E+iB as a single photon wave function http://www.uoregon.edu/~oco/Group_Pages/Raymer/Tutorials/TTRL5_V1.pdf" [Broken]
     
    Last edited by a moderator: May 4, 2017
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