Four-velocity of massless particle

1. Jun 10, 2015

sweet springs

is defined or not? Thanks.

2. Jun 10, 2015

Orodruin

Staff Emeritus
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.

3. Jun 10, 2015

sweet springs

Thanks a lot.

4. Jun 11, 2015

sweet springs

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.

5. Jun 11, 2015

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.

6. Jun 12, 2015

sweet springs

Thanks. Now I know better.