Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Four-velocity of massless particle

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    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


    Staff: Mentor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook