We all know about relativity and the effects of speed and time. When we put two atomic clocks one on earth and one on a rocket we noticed a significant time difference. I believe the rocket was traveling around 25,000mph and it was a shift of about 4-5 minutes. So if we take this idea and apply it to a pilot that is only traveling 600-700mph but for a much greater time, 50+ years depending on when they retire, and the flights lasting longer then a rocket launch. Would the smaller incremental times add up eventually?
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asked Oct 4, 2016 at 3:08
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10$\begingroup$ I suspect that the increased doses of radiation over that time would more than offset any time dilation-induced life span increases... $\endgroup$– tpg2114Commented Oct 4, 2016 at 3:12
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1$\begingroup$ Welcome to Physics Stack Exchange! This is a great site for physics questions and answers. Note, however, that we generally expect questions to not be "lazy", i.e. if the question asks something that could be looked up easily, we often consider it off-topic under the so-called "homework policy" (see the help center). Could you maybe look up the formula for time dilation in special relativity and apply it to the case of an airline pilot? I'm not saying this question is necessarily off topic, but it's kind of borderline and might get closed. Some users here are pretty strict about this issue. $\endgroup$– DanielSankCommented Oct 4, 2016 at 3:31
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$\begingroup$ Pilots may be more strongly motivated than most of us to maintain a healthy lifestyle. I know a retired pilot who is approaching the age of ninety. $\endgroup$– R.W. BirdCommented Apr 2, 2021 at 14:12
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$\begingroup$ @R.W.Bird What kind of evidence is that? $\endgroup$– Norbert SchuchCommented Apr 2, 2021 at 19:17
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1$\begingroup$ That is anecdotal evidence. $\endgroup$– R.W. BirdCommented Apr 4, 2021 at 15:51
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3 Answers
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There are two fundamental physics effects at work here. One is special relativity, where a moving clock appears to run slow at a rate given approximately by $1 - v^2/2c^2$. For 24 hours flying at 1000 km/h, a clock in a plane appears to run slow by 37 nanoseconds.
However, this is for a plane going around in circles. The real effects of SR time dilation need to take account of route and the Earth's spin - see the Hafele-Keating experiment. For instance a clock at the equator will be running slow compared with one at the pole (ignoring the GR effect - see below). It also depends whether you fly east or west, since neither clock on the ground or clock on the plane are inertial frames. Eastward results in slower ageing, whilst westwards results in more rapid ageing. A more general approximate result is that the clock rate goes as $ 1 + (2R\omega v - v^2)/2c^2$, where $R$ and $\omega$ are the distance to the Earth's rotation axis and angular velocity of the Earth, and $v$ has a sign (positive for westward, negative for eastward).
The second effect is General Relativity. A clock that is higher up in a gravitational potential well will appear to run faster. The difference in clock rate here is approximately $1 + gh/c^2$.
For every 24 hours in an airliner at 10000m a clock will gain about 100 nanoseconds compared with one on the ground.
Thus airline pilots appear to age faster to those on the ground unless they indulge in lots of low level flying or make a careful choice of routes (lots of eastward round the world trips)
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$\begingroup$ +1 for adding general relativity to the mix. A nit regarding "For instance a clock at the equator will be running slow compared with one at the pole." This is incorrect. Clocks at sea level and at rest with respect to the rotating Earth tick at pretty much the same rate, worldwide. $\endgroup$ Commented Oct 4, 2016 at 10:52
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$\begingroup$ @DavidHammen I'll have to think about that - isn't it because they are on equipotentials such that the SR and GR effects exactly cancel? My comment was merely concerned with the SR "component". $\endgroup$– ProfRobCommented Oct 4, 2016 at 10:56
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$\begingroup$ Correct, with a caveat. You have to account for the Earth's equatorial bulge, which results in the poles being 21 km closer to the center of the Earth than is the equator. $\endgroup$ Commented Oct 4, 2016 at 11:07
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$\begingroup$ @DavidHammen Do you mean a bulge additional to the equipotential surface? That the poles are "deeper" in the gravitational potential makes them run slower wrt a clock at the equator, but the clock at the equator is moving wrt to the one at the pole which makes the clock at the pole run faster wrt one at the equator. The two effects almost cancel. $\endgroup$– ProfRobCommented Oct 4, 2016 at 12:06
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The difference is given by $$t^\prime=\frac t{\sqrt{(1-v^2/c^2)}}$$
From this, at $1,000~\mathrm{km/h}$ time is dilated by a factor of $1.00000000000042866$. In other words, after 24 hours at that speed you will have gained $0.000000037$ seconds.
I agree with tpg2114's comment that the effect of increased radiation will more than offset the extra longevity. Also, note that the altitude of the satellite has a greater effect than its speed, but it speeds up your clock instead of slowing it down.
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$\begingroup$ Awww, why stop so short of computing the expected time dilation of the pilot's life?! $\endgroup$ Commented Oct 4, 2016 at 3:56
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1$\begingroup$ @Daniel Aww, just because you ask... After 30 years of 3000 flying hours per year (would that be a record?), he will have gained just over 0.1 ms (millisecond) $\endgroup$– hdhondtCommented Oct 4, 2016 at 4:17
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$\begingroup$ The air pressure in the airplane cabin corresponds to an altitude of ca. 2000m. I has been shown that people living at higher altitude have extra longevity. This has also to be taken into account. What about checking the statistics of insurance companies about the life expectancy of airline pilots. $\endgroup$ Commented Oct 4, 2016 at 4:19
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It depends on the speed of the airplane. If the plane has speed zero, then they will return older. If they travel around the Earth at the speed for which time goes equally slow as the time on Earth, then they will return with the same age as the people who stayed on the ground. If they travel faster than this speed they will return younger.
