so, if I am correct and there is not any real orientation in space such as, up,down, left, and right. And people agree that the universe is inflating or getting bigger. so if there is no orientation in space how can we be certain that the universe isn't expanding,... but moving through its own individual space and we are just along for the ride.
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It sounds like you are asking, how do we know there isn't a single global inertial reference frame, with all the galaxies moving through the space in that frame. I would say there are two answers to that, one is that general relativity doesn't allow it-- we already know there is enough mass in the universe to create a gravity that does not permit a global inertial reference frame like that. The second answer is, in a model where space itself is expanding, light can get to us from galaxies whose distance from us is increasing at a rate faster than c, but if there was really a global inertial frame, such a speed would be impossible. Yet we do infer that galaxies we see have a rate of increase of distance that exceeds c.
Having said that, please note that you can always create a coordinate system that has the galaxies moving essentially any way you want, in those coordinates, including a coordinate system that has the galaxies moving away from us in such a way as to create a standard Doppler shift equal to the redshift we observe. But such a coordinate system would not respect the cosmological principle, and we wouldn't know how to generate a reference frame like that without first solving for the dynamics of the expansion within the cosmological principle. That would mean we would essentially first find the usual language of space itself expanding to explain the redshifts, and then we'd have to reverse engineer some highly artificial coordinate system, centered on Earth, to be able to interpret the redshifts in those coordinates as Doppler shifts. It wouldn't be very meaningful coordinates, it would be like forcing the answer to come out how we want by choosing artificial coordinates that we need the usual interpretation to solve for in the first place.
(And by the way, the term "inflation" applies to a very specific very early phase in the expansion, it's quite different from the general idea of "expansion.")
Ken G
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