The final tidally-locked orbit, if there are no remaining wobbles in the Earth or Moon, has to be circular. Of course there are really two circular orbits, one for each object.
But this is getting away from relativity. To get back on track, consider Wheeler's geon, an object that orbits itself...
Conceptually, we look at a black hole from the outside, but we are inside the universe. All of spacetime was collapsed at the Big Bang.
However, there are useful analogies between a black hole and the Big Bang. Like the event horizon beyond which we cannot see.
A clock is a device that counts cycles, where a motion repeatedly returns to a starting point in some frame of reference. The light clock is a special case of this. Maybe instead of questioning the generalization of the light clock to all clocks, we should simply be amazed that such a...
Getting back to the original question, the acceleration phases do not compensate for the time dilations. The accelerations just let you change inertial frames. The problem can be recast with instantaneous accelerations and still give the same result.
There are three inertial frames here: home...
Even though the start and end points are the same, the spacetime paths taken by the stay at home and traveler are different. The invariant interval is path-dependent.
There is another way to visualize this using square arrays of elements. In a square array that is m=n+1 elements on a side, the number of off-diagonal elements in the lower left (or upper right) is (m^2-m)/2. But this is also the sum of the number of elements in all of the rows in that part of...
The turn-around portion of the trip simply let's the traveler reverse direction, so that the distance traveled outbound can be subtracted on the in-bound. This makes the integrals of the invariant interval ds different for the home-base and traveler, while keeping the starting location the same...
For the special case of the "Lorentz" intervals of light rays, it is easy enough to justify that they are independent of the observer. That is what the Michelson-Morley experiments showed. The Michelson-Morley result was that the speed of light, r/t=c, is universal. This gives r^2-(ct)^2=0 for...
The guy at rest will see the watch of the moving guy running slow. But each has to age according to his own clock, so the moving guy is seen as aging slower. But how to do the comparison of ages? See the "twin paradox" in ZapperZ's reference.
Now, think about the fact that each guy sees the...
Einstein got rid of the ether with special relativity because the classical reasons for it were no longer necessary. But with general relativity, in which mass modifies spacetime, he felt that there was still "something" there. Nevertheless, physics has subsequently been developed without...
If you know about the invariant interval in relativity, ds, then you will know that ds is the proper time for the frame traveling along any path. But you will also know that a light-path is described by setting ds=0. So the proper time for the photon is not changing as it travels along the path...