J.C.MacSwell

We know the particle can be considered to be somewhat (have I qualified it enough yet?) in both states as it can "interfere with itself". What is the largest object, as a whole, that has been shown to interfere with itself?

My unproveable thought would be that even though the superposition is not disproveable it cannot be proven either.

f=ma

In the example given, everything in the universe was rotating (wrt what I do not know). Didn't the thought experiments when GR was developed assume that, in this type of case a Foucault pendulum would not read the "rotation" such as it is?

Once per day with respect to what?

Eye, Eye Captain! Scotty (and what do you mean I'm not real!)

I thought I knew what you meant. (I am never "absolutely" sure with frames) I actually believe the particle can be out of that frame in some respects (or approach "out" as c is approached, again in some respects) and that your point was relevant (pun intended) but that it might have lead to the "what determines the size of a frame?" post/question.

No longer at rest in the lab frame?

For the record...No. Water waves are gravitational/mass displacement waves. Compression/expansion waves in water are sonic (sound) waves.

The assumption would be straight lines are geodesics on the surface (read volume) of the hypersphere. If this acts like acceleration for a round trip then everything works out nicely as the symmetry balances everything out. However: If this was the case for a round trip, it would equivalently be the case for any portion of a round trip. Simultaneity would be alive and well. (note to casual readers: this is based on a specific set of hypothetical assumptions stated or implied in post 29, not the real world)

I assumed Johnny meant the Earth station frame, but I think his statement is true (contradictory but true given my assumptions) for any choice of inertial frame.

I think you can claim mathematically that they are (at rest wrt each other), although some laws of physics may require corrections/adjustments to allow for your frame/perspective.(which I think is a very useful frame for cosmology) To claim that they are also "absolutely" at rest is a bit of a "stretch" if you will excuse the pun. I think the experiment, which requires instant transmission of results and therefore is excluded as a possibility in SRT, would be expected to produce a null result in that no rest point on any inertial frame would be expected to have a faster clock than any other.

OK, what is wrong with this in principle: Two clocks go by the Earth at near c in opposite directions. As they go by they are synchronized by a signal from Earth. Each assumes the other clock to be much much slower. They go "straight" around the Universe/hypersphere. When they meet again Earth is long gone. As they pass by they prepare to resynchronize via an Earth station our descendants have built and positioned for the occasion. How do their watches compare?

Does such a point exist? I'm questioning your perspective, not your ideas which I think are interesting.

Then you would not be at the center of mass. Your first answer (8x) is correct.

Check again. Center of mass is linear and gravitation is inverse squared. Hint: You are closer to the bigger mass!