Aether
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JesseM said:As DaleSpam said, your use of the phrase "absolute" simultaneity is confusing, usually "absolute" means "the same in every coordinate system", yet you seem to allow different coordinate systems to have their own distinct "absolute simultaneity". Each coordinate system of course has its own well-defined notion of simultaneity, this is just as true of inertial coordinate systems in SR as it is of cosmological coordinate systems. According to the way you use the phrase "absolute simultaneity", can you imagine any coordinate system where it would not be true that "absolute simultaneity holds"? Doesn't every coordinate system by definition have a single yes-or-no answer to the question of whether two events have the same t-coordinate or not?
There is one notion of simultaneity in the FLRW metric, and if we zoom in on smaller and smaller regions of curved spacetime in GR until finally we make a transition to using SR spacetime (with or without inertial frames) then we are moving from one GR coordinate system that is convenient to use in cosmology to a set of SR coordinate systems that are convenient to use in a laboratory. Within this set of SR coordinate systems we could choose to have absolute simultaneity that is consistent with the cosmological coordinate system we are using, or we could choose to have relative simultaneity that is disconnected from our cosmological coordinate system.JesseM said:Again, this makes little sense if we interpret "absolute" to mean "coordinate-independent" as is normally done, so if you are using a different definition of "absolute", you need to spell out what that definition is. Why couldn't I just as easily talk about the "absolute simultaneity of the inertial coordinate system that is convenient for me to use in SR because it is the frame in which I am at rest"?
I agree, but you are the one who singled out inertial frames as being equivalent to the coordinate system of a freely falling observer in a small region of spacetime in GR. These are not the only valid coordinate systems for freely falling observers. They may be more convenient to use in a small region because they allow us to drop tensor notation, but is there any other reason that you singled them out?The point is that in both flat SR spacetime and the curved spacetime found in cosmology you are free to pick different coordinate systems with different definitions of simultaneity, and there is nothing in the laws of physics to cause you to prefer one coordinate system over another.