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Difference between spin and helicity for a photon

  1. Nov 10, 2014 #1
    First: a question about spin. When we say that an electron has spin 1/2, we mean that it can have the values ħ/2 or -ħ/2. So when we say that a photon has spin 1, I would expect this to mean that the measurement of a photon would give values either ħ or -ħ. But then I am confused by the following :
    "The magnitude of its spin is √(2ħ) ....."
    (from http://en.wikipedia.org/wiki/Photon)

    Further, when I continue reading that sentence:
    "The magnitude of its spin is √(2ħ) and the component measured along its direction of motion, its helicity, must be ± ħ."
    (still from http://en.wikipedia.org/wiki/Photon)
    and then compare it to the following pair of quotes:
    "helicity is the projection of the Spin S onto the direction of momentum, p,...."
    (from http://en.wikipedia.org/wiki/Helicity_(particle_physics))
    "a photon's spin must be exactly aligned with its momentum..."
    (from http://physics.unl.edu/~tgay/content/CPE.html)

    The last two quotes together makes it sound as if spin would be the same as helicity for a photon,

    Furthermore, I read,
    "For a particle of spin S, the eigenvalues of helicity are S, S − 1, ..., − S. The measured helicity of a spin S particle will range from − S to + S."
    (again from http://en.wikipedia.org/wiki/Helicity_(particle_physics))
    So for a photon , this would say that helicity can be in { -1, 0, 1}, but:
    (a) can a photon's helicity have a value 0?
    (b) If the measurement of a photon's spin would give one of two values, one positive and one negative, would the spin and the helicity have the same sign, or could you have the helicity being the opposite sign of the spin?

    I would be grateful to anyone clearing any or all of these questions up.
  2. jcsd
  3. Nov 11, 2014 #2

    Simon Bridge

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  4. Nov 11, 2014 #3
    Many thanks, Simon.
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