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Four-velocity of massless particle

  1. Jun 10, 2015 #1
    is defined or not? Thanks.
  2. jcsd
  3. Jun 10, 2015 #2


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    Since it is the tangent vector of the particle's world line normalised to one, no. The world line of the particle still has a tangent vector, but it is a null vector and therefore cannot be normalised.
  4. Jun 10, 2015 #3
    Thanks a lot.
  5. Jun 11, 2015 #4
    Let me rethink about it. 4-momentum vector for massless particle is also a null vector. We may regard 4-momentum vector as 4-velocity vector multiplied by mass m.
    So 4-velocity vector as 4-momentum vector divided by m may be able to exist even in the limit of m to be zero. Normalizable to one but both time and space componebts are infinit. How do you think of that ? Best.
  6. Jun 11, 2015 #5


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    For a timelike 4-momentum, yes, because the mass m is just the norm of the 4-momentum, so expressing 4-momentum as 4-velocity times m is just another way of saying that the 4-velocity is the 4-momentum normalized to one.

    For a null 4-momentum, you can't do that, because, as Orodruin said, you can't normalize a null 4-vector.
  7. Jun 12, 2015 #6
    Thanks. Now I know better.
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