The ACES project may spend research on the quantities involved when g changes as atomic clocks are read on different places. One should no longer talk about trains with almost the speed of light going throug tunnels or about twins travelling in space but keep things simple and know that g determines the speed of physical processes. Which affects atomic clocks. Below suggestion to mathematicians for working on this subject, which can also be done by ESA.
Read The Quantum Theory of Gravitation (2003) by Vasily Yanchilin and his paper in the Canadian Journal of Pure and Applied Science regarding the opinion of Poincaré on measurement.
Modern way of saying is that since Creation everywhere a same amount of time has passed, but atomic clocks show differently because speeds within atoms depend on local gravity. That varies in space and time, so NIST is wrong maintaining it has a clock precise to one second in a billion years or so. The universe changes and NIST might correct telling their clock is right up to one billionth of a second, but this seems wrong too:
As g is a little bit different on Earth and where satelites orbit the processes within the atoms of clocks here and there won't have the same speed. But the difference is very, very small and not measurable yet. The GPS won't be affected. Therefore mathematicians are sought to do research on this topic. Electrons changing orbits are in spheres with quadratic surface dimensions while change of g is linear and movement, energy content of the electron waves may reflect this. Note that emitted travelling photons change the mass distribution of the universe according the energy-mass relation. If on its way a photon does not receive from outside the energy to pass different g zones than it has to furnish that itself. Which may cause a little red shift. Then the present time scale of the universe needs adjustment.
This stuff should be handled in a chapter of an up to date book on physics and maths.
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