Do Airline Pilots Live Longer? 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?
 A: 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)
A: 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.
A: 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.
