Posted: Feb 28, 2011 4:58 am
hackenslash wrote:twistor59 wrote:Well, it's 25 years since I did any relativity, but I'm pretty certain that at the centre of a massive body, clocks would be running slower compared to ones at a distance from the body.
Indeed, that would be my understanding as well. The effect that a body would feel would be equivalent to having been cancelled out, because the gravitational attraction is coming from all directions rather than being unidirectional, but the immersion in a gravitational field would be precisely the same as it was at the surface. All that has changed is the direction of mass from the perspective of the observer, because now the observer is surrounded by it as opposed to being outside it. The relativistic time dilation would be the same though, I think.
I disagree. I am pretty sure it is all dependent on what frame you are in. Let me explain.
Just as in the twin paradox, it is always the one who matches the acceleration of the other that travels a shorter path through time. Imagine a planet that moves close to the speed of light passes the earth. Both planets have sets of twins, all four are the same age at the time of passing. Let's call them twins 1a, 1b and 2a and 2 b. One twin-a from each planet decides to visit other twin-b on the opposite planet. Both will get there and find the opposite twin-b older than him and will return home to find his own twin-b even more older than him.
Why is this? You would think since from the perspective of twin 1a, twin 2b is traveling close to the speed of light and see his clock running slow. But it isn't. He is only seeing his time skewed from his frame of reference, just as twin 2a sees twin 1b's time skewed from his perspective.
Only when one accelerate to the other's velocity does the time difference resolve, and it can be resolve either way depending on who does the accelerating.
I am almost certain that this is the very same with gravitational fields. In order to reach the center of the earth you MUST experience an deceleration in order to reach a stable position in the center of a gravitational field, otherwise you will just yo-yo back and forth past the center of gravity.
The opposite is also true. You must accelerate in order to escape the gravity well.
Now take Rockman and Starman. Rockman is sitting in the center of a gravity well, he is in an inertial frame of reference because he is not experiencing any acceleration (gravity). Starman is in orbit and can say the same thing. Both are in inertial frames, neither is accelerating.
This next part I am having difficulty with, which is what does each see the other's clock doing. Do they both see the other's clock moving slowly? I'm guessing yes, but I would have to do some mental gymnastics to figure out why, but the fact that Rockman isn't in an accelerated state has got to do something with the way perceives Starman's clock as apposed to someone standing on the surface feeling the full force of gravity.
I believe if Starman does the acceleration necessary to visit Rockman, Rockman will be older than expected. And if Rockman does the acceleration nessisary to visit Starman, Starman will be older than expected.
I'll bet my lunch money on this.