One of the implications of General Relativity is that the nearer a clock is to a "gravitational body" (planet or star) the slower it runs. This may seem counter-intuitive, but when you take the law of conservation of energy into consideration, you realize that this has to be true.

If you throw a ball straight upward, it loses velocity as it moves up. Since velocity is related to kinetic energy,

It is known that matter can be converted into energy in the form of light. If matter (here, a ball) loses energy as it moves away from the Earth, and if matter can be converted into light, then shouldn’t light lose energy as it moves away from the Earth? If this were not true, and the light lost no energy, you could devise an energy-producing system, in which matter would be converted into light at the Earth’s surface, with the light then re-converted into matter somewhere above. The energy of the falling matter could be utilized again and again as the matter fell back to the Earth’s surface, where it could again be re-converted to light. (remember that light, unlike the ball, does not fall back to Earth. This system, which would have no energy input, would continue producing energy, operating forever.

The energy of light is given by the equation: energy = Planck’s constant x light frequency, or,

Planck’s constant doesn’t change under any known circumstances, so for light to lose energy, it must lose frequency. So, if you are high above the Earth and see light that was produced at the surface of the Earth, the light that you see will have a slightly lower frequency than will be seen by someone on the ground. Everything with a frequency that you see below you (the light itself or a clock the light is coming from) appears slower than it appears to someone at the surface of the earth, because the frequency is lower.

Conversely, light gains energy as it moves toward a gravitational field , just as the ball gains kinetic energy as it falls, so if you shine a light down toward the Earth, it will arrive with a slightly higher frequency than the frequency you measure when you produce it.

As a consequence of all this, when you are high above the Earth, you will see activities happening on the ground in slightly slow motion, while someone on the ground will see your activities in slightly fast motion. So, bizarre as it seems, time moves slower near a gravitational body, even though no one on gravitational body will notice it himself.

1. when the photon is at the Earth’s surface
2. when the photon is 10,000 meters above the Earth’s surface

In the following two equations, since the numerators are identical, and since the denominators differ by exactly 10,000 meters, all terms can be treated as if they had an infinite number of significant figures.

Since the energy of a photon is proportional to its frequency,

This factor represents how much slower time passes at the Earth’s surface than it does 10,000 meters above it. In terms of actual measured time, this amounts to

So, a clock at the Earth’s surface should be slower by one second every 29,100 years than a clock 10,000 meters above it.