Question 3

(a) Show that the square of the magnitude of the 4-velocity ${\sf v}$ of a particle is $-c^2$ for all values of the 3-velocity.

(b) The 4-acceleration of a particle is defined by

$${\sf a}={{\rm d}{\sf v}\over{\rm d}\tau},$$

where $\tau$ denotes proper time. Use the result of part (a) to show that the 4-acceleration of a particle must be perpendicular to its 4-velocity.

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]