# How to know is four-velocity is directed towards future or towards past?

Consider a four-velocity vector $$\mathrm{u}=(u^0,u^1,u^2,u^3)$$. The zeroth component of position is $$x^0=ct$$.

How do I know if $$\mathrm{u}$$ is directed towards the future or towards the past? Is it correct to look at the zeroth component of $$\mathrm{u}$$ and

• if $$u^0>0$$ then $$\mathrm{u}$$ is towards future
• if $$u^0<0$$ then $$\mathrm{u}$$ is towards past

?

For example $$\mathrm{u}=(3c,c,c,c)$$ is towards future, while $$\mathrm{u}=(-3c,c,c,c)$$is towards past.

If this is not correct, what is the way to know if $$\mathrm{u}$$ is directed towards the future or towards the past?

• What you have said is true assuming that your chosen coordinate $x^0$ increases towards the future. – Prahar Jun 6 at 15:17