# Usain Bolt and time dilation

Here’s a good overview of his races and records: Usain Bolt - Wikipedia

I was doing the numbers for how much younger he was at the end of his record 100 meter, relative to a seated scorer.

But then I began to think about all his races. Is there some kind of cumulative?

And who, then, is he younger than, over the course of his races?

Clearly I need to get my head straightened out on this. Any help?

Well, to do this properly, we’d need to know the direction that he’s running, with or against the rotation of the Earth, and we’d also need to take into account the Earth’s gravitational field.

What does the “simple” t (sqr(1-V2-c2)) leave us with?

The plane ride to Rio had about a million times more effect (around 10 nanoseconds) than his 100-m race. His moving at a relatively slow pace (in comparison to other forms of human motion) for such a short time (some seconds) is far, far from the determining factor in his relativity-modified age.

Close: 1/sqrt(1-(v/c)[sup]2[/sup]) is the “gamma factor”. Given the small velocity relative to c, a good approximation to the age change is simply:

0.5 x (trip duration) x (v/c)[sup]2[/sup]