Quote:
Originally Posted by Southtown
At present time, to me time is the flip-side of the space coin. Space is the distance between locations, and time is the distance between moments, however dynamic the relation amongst the things about which we know very little may be.
But the guy was asking about gravity. How could time pass by differently in orbit than it does on the surface. I can't answer, so I share in his desire to realize such an explanation.
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According to the equivalence principle of general relativity there is no descriptive difference between an accelerating frame of reference and a stationary frame in the presence of a gravitational field.
This means a person on a rocket ship with constant acceleration will feel like they are standing on the surface of a planet. In either case a person feels weight. Also, someone in an elevator that is free falling toward a massive body like earth will feel weightless just like someone who is stationary in deep space outside the influence of any gravitational field.
In fact, general relativity proposes that someone who conducts experiments of special relativity in a free falling elevator will get the same results as someone who does the same experiments in a stationary elevator in deep space.
This idea can be used to derive all the laws of General Relativity including gravitational time dilation. GR tells us that if we are on earth's surface looking up at a clock higher in the gravity well then the clock will appear to run faster than our clock.
To derive this with the equivalence principle we must consider what would happen in an accelerating frame (or elevator) with no gravitational field. Let's say we are in a very large elevator and there is a clock on the ceiling. The elevator is undergoing constant acceleration like a rocket. It is in deep space. Every second the elevator goes faster.
To make this situation simple we can consider the clock on the ceiling to simply be a strobe that is programmed to blink sixty times per second. Our own clock is also programmed to blink sixty times per second. If you consider this situation you will realize the person on the floor will not see the strobe on the ceiling flash sixty times a second but faster than that. Because the entire elevator is accelerating there is a Doppler-like effect where the strobe flashes are observed more quickly from flash to flash by the time they get to the floor. The change in velocity from the time of emission to observation accomplishes this.
The important things are:
- If the equivalence principle of general relativity is true then the time dilation I just described for our accelerated frame must extend to gravitational potential as well.
- Can this be described mathematically and applied to gravitational fields.
Number one has been found true and verified by atomic clocks (such as GPS)
Number two - mathematically, a person can use accelerated coordinates such as the
Rindler metric:
This can be used to describe the situation above and it can also be used to derive gravitational time dilation and redshift which is done here:
Gravitational redshift - Wikipedia, the free encyclopedia
So, I believe the reason for gravitational time dilation can be shown as a result of gravity as "curved spacetime". Actually, it was predicted on that basis. Why gravity curves spacetime?
-modest
