Four-velocity of massless particle

[sweet springs]

is defined or not? Thanks.

 

[Orodruin]

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.

 

[sweet springs]

Thanks a lot.

 

[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.

 

[PeterDonis]

We may regard 4-momentum vector as 4-velocity vector multiplied by mass m.

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.

 

[sweet springs]

Thanks. Now I know better.