Which one is older after a year at different altitudes?

Question

One mans lives at an altitude of 3000km for a year and another at sea level. What is the difference of time how do you calculate it?

Answer 1

The man at sea level will experience less time than the one at altitude. This has to do with Einstein's Theory of GENERAL Relativity that objects lower in a gravitational field will experience a slower time than those higher up.

Even though Einstein's Theory of SPECIAL relativity would have you believe, that time would go slower in the mountains because of the higher velocity in the mountains caused by the earth's rotation, the gravitational effect prevails, and the clock at sea level goes slower. (The problem is that the time dilation caused by the increase in speed as you climb the mountain is less than the gravitational blueshift)

For an example see http://en.wikipedia.org/wiki/Time_dilation and go the sub-sections entitled: (a) Gravitational time dilation and (b) Velocity and gravitational time dilation combined-effect tests. The experiments cited by Major Bob, above, are referred to in the Wikipedia article and actually show that time goes slower at the base of the mountain not high up on the mountain.

The calculation to figure this out is pretty wicked.

Answer 2

The one at 3000 km has a higher velocity and according to time dilation in relativity that person, barring all other factors like solar radiation,etc. will physically be younger, if they live at the same distance from the equator and not at the axis of rotation.
The calculation is based upon the Lorentz Transform. First calculate the velocity of the person at sea level. then the velocity of the person at 3000 km. The greatest effect will be found at the equator, but it has been verified in buildings in the continental US. Take the difference in velocity between the two people and call that v. That is the apparent velocity of the higher person to the lower. This is then divided by c to give you a ratio of that velocity to the speed of light which is called V then:
t = [1/(1 - V^2)^0.5] t(H) where V = v(H)/c
You will notice that the higher persons aging will be slower, so will there clocks since all methods of time measurement we have depend upon a rate of decay (aging). When the velocity gets close to c the difference can be substantial. Also make sure that you don't make the mistake of thinking that a light-year is a measure of time, it is a measure of distance.

Answer 3

Hmm... are you suggesting the man living at the higher altitude ages more slowly because the Earth is spinning faster at his altitude, and, by the theory of relativity, that would produce a difference in how fast time moves?!! Well, maybe, but I'd be shocked if it is more than a small fraction of a second over the course of a year.

Answer 4

From one birthday to the next.

Answer 5

Time is constant. A year is a year.