A ray of light propagates along the straight line

$$x(p) = \frac{p}{\sqrt{3}}$$ $$y(p) = \frac{p}{\sqrt{3}}$$ $$z(p) = \frac{p}{\sqrt{3}},$$

where $p$ is a parameter.

Reparameterize this curve with a new parameter $\lambda$, where $\lambda$ is an affine parameter. The metric is flat, $ds^2=dx^2+dy^2+dz^2-c^2dt^2$

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