So I've been thinking a lot about theoretical space colonies recently like O'Neil cylinders and it occurred to me that an observer under real gravity and an observer under simulated gravity generated by centrifugal force are both affected by time dilation as a result of whatever is anchoring the observer to the ground, as both gravity itself and motion affect the perception of time.
So I wonder, how would the experienced time of an observer under a given gravitational pull (we'll say 1 G if anyone comes through that might be able to work this out) fare vs an observer anchored to a point on the inside of a ring that is constantly turning to the degree where it generates a centrifugal force of equivalent potency?
We'll say that the reference point for the Real gravity scenario is some spot in geostationary orbit of whatever Earth-like planet the observer is one, far enough away that the gravitational field of the planet does not really affect the reference point very much (thereby eliminating the rotation of the planet from calculations) and that for the ring, the reference point is the middle of the ring.
My gut says the observer on the ring experiences less time dilation than the one on the planet, but of course the ring could be a small radius, fast spinning one, or it could be a very large radius one that spins relatively slowly. I don't know how or whether this affects the scenario at all, but what do you guys think? Is there any particular configuration of ring that would give the same time dilation under simulated gravity as that under equivalent real gravity? Do the numbers work out to where they're actually fundamentally equivalent? Or is there some extenuating circumstance like maybe observers on the ring not experiencing any significant time dilation because the movement is oscillatory or something?
So I wonder, how would the experienced time of an observer under a given gravitational pull (we'll say 1 G if anyone comes through that might be able to work this out) fare vs an observer anchored to a point on the inside of a ring that is constantly turning to the degree where it generates a centrifugal force of equivalent potency?
We'll say that the reference point for the Real gravity scenario is some spot in geostationary orbit of whatever Earth-like planet the observer is one, far enough away that the gravitational field of the planet does not really affect the reference point very much (thereby eliminating the rotation of the planet from calculations) and that for the ring, the reference point is the middle of the ring.
My gut says the observer on the ring experiences less time dilation than the one on the planet, but of course the ring could be a small radius, fast spinning one, or it could be a very large radius one that spins relatively slowly. I don't know how or whether this affects the scenario at all, but what do you guys think? Is there any particular configuration of ring that would give the same time dilation under simulated gravity as that under equivalent real gravity? Do the numbers work out to where they're actually fundamentally equivalent? Or is there some extenuating circumstance like maybe observers on the ring not experiencing any significant time dilation because the movement is oscillatory or something?
