Subluxa

Meet Subluxa, who never quite reaches light speed, however hard she tries to add up speeds.

In everyday life speeds simply add: walk forward at 1 m/s on a train doing 30 m/s and you move at 31 m/s relative to the ground. Special relativity says this is only an approximation. Because clocks and rulers in moving frames disagree, the correct combination of two collinear velocities v and w is u = (v + w)/(1 + vw/c²).

At everyday speeds vw/c² is tiny and the formula reduces to plain addition. Near light speed it bites. Two speeds of 0.5c each combine to 0.8c, not 1.0c. And if either speed equals c, the result is exactly c: a light beam fired from a speeding rocket still travels at c for everyone.

This is the reason no ordinary object can be pushed past light speed by stacking boosts, and it agrees with measurements of fast particles in accelerators.

The simple form holds for motion along one line. For velocities at an angle, the transformation is more complicated.