Can special relativity explain any of the life extending benefit of exercise?

Posted on July 10, 2017

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People who exercise live longer than those who don’t. So much so, getting physically active (and at a healthy weight) could do more to extend lives than curing cancer.

Special relativity is one of the theories which made Einstein famous. National Geographic had a well done series on him, Genius, which put some of this at the forethought of my mind again.

The theory of special relativity says as we move faster, time slows down. For the best explanation of this I’ve seen, see Anthony Yeh’s answer here.

-> Burn Math Class: And Reinvent Mathematics for Yourself has an elegant derivation as well.

(Anybody familiar with this theory will know the answer to the following, but it’s fun to calculate these things.)

If we think about people who say, run a couple hours every day vs the sedentary, those runners move faster, at least while running, than the sedentary. That means time moves slower for them, where seconds don’t tick as quickly. (For everything, including the brain. So time moves normally from the faster moving person’s perspective. The difference is relative to a non-mover.) If we add up that amount of lesser time each day they run, could that, over a life span, explain the reason these people live longer? That is, because they make time tick slower, they age less relative to the other person.

From the local frame of reference (the blue clock), the relatively accelerated red clock moves slower. We could think of the red clock as a person running laps.

Average pace

Let’s say our runners move at 10 miles per hour, 6 minutes per mile, 4.5 meters per second.

Timeline

We’ll be generous and say they move at this pace for two hours, 7200 seconds per day, for 70 years.

Calculating

We can use Wolfram Alpha’s time dilation calculator.

For the person being sedentary, while the runner moves at 4.5 meters per second, then as 7200 seconds will have passed for the runner, 7200.00000000000081 seconds will have passed for the observer.

7200.00000000000081 – 7200 = 0.00000000000081 seconds per day

0.00000000000081 seconds per day * 365 days per year * 70 years = 0.0000000206955 seconds

Physics has helped biology in various ways; this isn’t one of them!

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Posted in: Miscellaneous