- #1
snailhunter
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Say there are two atomic clocks floating through space, both completely stationary with respect to each other. They are exactly synchronized, and not under the influence of any significant gravitating bodies. One is significantly farther ahead in the direction of motion than the other, but they both move at the same speed. Let's call the one farthest ahead in the direction of motion clock A, and the other clock that trails behind it clock B.
They eventually begin to approach a large planet (it's straight ahead of them, so they will fall straight to the ground). Since clock A is closer to the planet than clock B at any given time (by a decent amount), clock A begins to feel the effects of the planet's gravity before clock B. From clock B's point of view, clock A begins to accelerate away. Now from what I understand, any object in free fall isn't undergoing any proper acceleration, and is still considered to be in inertial motion (it's just inertially moving through curved spacetime). So even though clock B sees clock A move away at an accelerated rate, would they still remain synchronized? Can they still be treated as though they're still in the same inertial frame of reference, even though technically their relative velocities are changing over time?
Feel free to replace "planet" with "black hole" as well, if that makes it any more interesting.
They eventually begin to approach a large planet (it's straight ahead of them, so they will fall straight to the ground). Since clock A is closer to the planet than clock B at any given time (by a decent amount), clock A begins to feel the effects of the planet's gravity before clock B. From clock B's point of view, clock A begins to accelerate away. Now from what I understand, any object in free fall isn't undergoing any proper acceleration, and is still considered to be in inertial motion (it's just inertially moving through curved spacetime). So even though clock B sees clock A move away at an accelerated rate, would they still remain synchronized? Can they still be treated as though they're still in the same inertial frame of reference, even though technically their relative velocities are changing over time?
Feel free to replace "planet" with "black hole" as well, if that makes it any more interesting.