Sorry if this is a stupid question.

The formula for relativistic Velocity-addition is

$u = (v + u') / (1 + (vu'/c^2))$

It seems that v, v', u, and u' are vectors, while c is a scalar.

But 1 seems to also be a scalar?

$(vu'/c^2)$ results in a vector.

You can't add a scalar to a vector. $1 + (vu'/c^2)$

I can't seem to find any info about this specifically online.

What obvious thing am I missing here?

  • 3
    $\begingroup$ That’s a 1D formula and there are no vectors in it. That’s why there is no dot between $v$ and $u’$; $vu’$ is just ordinary multiplication of numbers, not a scalar product of vectors. Wikipedia has the vector formula. What kind of product did you think $vu’$ was that would have yielded a vector? $\endgroup$
    – Ghoster
    Sep 28 at 22:43
  • $\begingroup$ Oh, thank you. I thought it was a cross product. But in retrospect, it wouldn't be written that way. $\endgroup$
    – cowlinator
    Sep 28 at 22:46

1 Answer 1


The formula is a special case for a velocity and a boost along the same axis. All variables are scalars (or components along that axis).

The most elegant way to generalize it is to use the four-velocity $(\gamma_u,\gamma_u \vec u)$ in place of $\vec u$. It transforms by the same Lorentz transformation rule as $(t,\vec x)$, so you don't need to remember a special formula for velocities.


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