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So let's put a clock at 2R. Now put one observer on earth and another on the moon. What do they see?
The clock at 2r will be GR time dilated, so conventional relativity describes what the moon observer will see in relation to what the Earth observer will see - is the answer to your question.The observation of the 3rd time dilation would be in that the clock without any energy input to maintain its position at 2r, would then be changing position from 2r back to Earth, where the increasingly shorter seconds of the g-field are increasing the speed the clock moves at through the g-field.
R is always taken from the centre of gravity, provided that R > the radius at mean sea level. It's a lot easier than asking where the atmosphere ends, because it doesn't.
R is indeed the shorter radius, but I've had my own 2nd thoughts. Even though the satellite is stationary with respect to the Earth observer, both are rotating within the SC coordinate system. It's not valid to assume that the SC coordinate system rotates with the Earth unless the satellite is replaced with a hovering rocket (co-rotating with the Earth observer) or another terrestrial observer at the top of a tall tower. Centripetal acceleration does not amount to the same thing because the satellite does not feel its own weight. We should revise our scenario accordingly to avoid that wrinkle. Constant linear velocity is even more complicated because you have to accelerate in a gravitational field in order to achieve that.
...just consider the calculation as a constant speed - no matter what is causing the motion, or consideration of that which is being moved - to remove gravitational and SR aspects from the calculation.
What I'm interested in is by how much GR time dilation would increase a constant speed between R and r if we held the speed relative to the shorter seconds at each h from M.What I'm looking for is a m/s^2 acceleration - so having taken into consideration that the shorter seconds of GR time dilation have accelerated this constant speed, clearly the 'acceleration' part described by m/s^2 would then be being held relative to the rate of an 'Earth second' at R, or 'standard second' as per the physics remit of holding metres per second squared relative to the standard second.
Do you (Timey) think this is a fair assessment of your theory?https://www.thenakedscientists.com/forum/index.php?topic=69882.msg510239#msg510239
I think Timey is proposing that spacetime is intrinsically dilated and that's what determines the location and movement of objects in space and time. It's an anthropic argument (i.e. chicken vs. egg) so it's really a matter of philosophy, not physics. The same could be said of string theory of course, but physics is supposed to be about the observables. It seeks to explain how one observable changes in relation to another. An explanation is worthless if it invokes undefined concepts like photon-to-electron ratio, electron cycle, electron travel distance, and oscillating mass. You might as well be talking about gnomes and fairies (or strings.)I expect you're eluding to wave-particle duality. If so, you are way off base because the amplitude of a matter wave is a distance in probability space, not conventional space. That is, matter wave power, which is proportional to amplitude squared, equates to a probability of finding a mass at a given location in space and time. GR and SR have nothing to say about any of that.At the risk of adding to your confusion, I should add that probability space is only one possible interpretation of QM. There is a respectable theory that the waves are actually electromagnetic in nature. It's incomplete and far from mainstream, though.
OK, I stand corrected. You are proposing a new twist on the aether theory. I assume you are aware that aether was the prevailing view before Einstein. You should be intimidated by the fact that he was able to sway so many of the greatest minds of the modern era, but even if you are not, you should study his arguments. Chances are he has already debunked your theory. For starters, you need to account for the Michelson-Morley result.
After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant, which he had designed to modify his equations of general relativity to allow them to produce a static solution, which he thought was the correct state of the universe. The Einstein equations in their simplest form model generally either an expanding or contracting universe, so Einstein's cosmological constant was artificially created to counter the expansion or contraction to get a perfect static and flat universe. After Hubble's discovery that the Universe was, in fact, expanding, Einstein called his faulty assumption that the Universe is static his "biggest mistake". On its own, general relativity could predict the expansion of the Universe, which (through observations such as the bending of light by large masses, or the precession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.