Quote Originally Posted by Renton View Post
X approaches infinity in both observations. I think you got my meaning but I thought I'd fix the glaring typos here in case anyone else reads it and it confuses them.
Yes, the relativistic time dilation would affect the clocks in the way you describe, with appropriate handling of infinities, that is.

(The following is based on a loose understanding of the effects of relativistic velocity. I'm assuming they apply to gravitational effects as well.)
When the relativistic factor becomes high enough, atomic interactions become somewhat impossible.

Imagine a single molecule of water, H2O. Assume that by some un-described means, it experiences a constant accelerating force.

At some speed, the exchange of photons which mediates the attraction of the covalent bonds will be left behind. Meaning that the molecule of water will just be one atom of Hydrogen and another atom of Hydrogen and an atom of Oxygen speeding along, moving too quickly to "catch" the photons that are "thrown" by the other atoms. They outpace the exchange particles.

E.g. Assume 2 capable people are playing catch with a beach ball. They keep throwing the ball back and forth as the wind slowly but unfailingly picks up. No matter what angle the 2 people stand at, relative to the wind, eventually the wind will become so strong that they can't play catch anymore. Either the wind will blow the ball too far off coarse to be caught, or the wind will be too strong for the person downwind to throw it upwind without it coming straight back to them.

In the analogy, the beach ball is the exchange particles between the atoms, and the wind is the spacetime that the atoms are rushing through.

At some speed, the atoms are no longer a molecule.

At some greater speed, the same thing happens to the atoms. The electric fields emanated by the protons and electrons become shaped like an elongated tear drop behind them. When this deformation reaches a tipping point, the atoms are no longer really atoms. They're just a bunch of fundamental particles whizzing along near eachother, completely oblivious to each other's existence.