# Usain Bolt and time dilation

**URL:** <https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923>\
**Category:** Factual Questions\
**Created:** [September 3, 2016, 7:22pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923 "2016-09-03T19:22:19Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\
**Post date:** [September 3, 2016, 7:22pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923/1 "2016-09-03T19:22:19Z")

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Here’s a good overview of his races and records: [Usain Bolt - Wikipedia](https://en.m.wikipedia.org/wiki/Usain_Bolt#Statistics)

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?

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [September 3, 2016, 7:27pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923/2 "2016-09-03T19:27:17Z")

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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.

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**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\
**Post date:** [September 3, 2016, 7:32pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923/3 "2016-09-03T19:32:12Z")

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What does the “simple” t (sqr(1-V_2-c_2)) leave us with?

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**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\
**Post date:** [September 3, 2016, 7:42pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923/4 "2016-09-03T19:42:41Z")

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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.

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**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\
**Post date:** [September 3, 2016, 7:48pm UTC](https://boards.straightdope.com/t/usain-bolt-and-time-dilation/764923/5 "2016-09-03T19:48:08Z")

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> [@Leo\_Bloom](#):
>
> What does the “simple” t (sqr(1-V_2-c_2)) leave us with?

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]