Question: what is the most direct experimental evidence to suggest that the galaxies in the universe are fixed in an expanding spacetime, as opposed to moving in a fixed spacetime?
- The notion of 'fixed in space' is inherently coordinate-dependent. I could rephrase the question: what is the most direct experimental evidence to suggest that the geometry of the universe is changing with time, rather than fixed?
- There are theoretical problems associated with setting up a collection of particles moving apart from each other (according to Hubble's law) in a fixed background. In special relativity, this forces some particles to travel faster than light. In Newtonian gravity, an infinite homogeneous universe does not obey Gauss' law. However, one can always suppose that these theories are not correct descriptions of our reality. I am looking for direct experimental evidence that spacetime is curved in some way.
- It has been claimed elsewhere on this site$^1$ that there is no physical difference between the two scenarios. This seems wrong to me. An expanding background has non-zero Riemann tensor, and in principle this should be physically detectable through measurements of geodesic deviation and geometric quantities such as angle defect.
$^1$This almost identical question doesn't have answers which satisfy me. For instance, with regards the top response, whilst it may be that the observed motion of galaxies becomes somewhat contrived in the case that spacetime is fixed, this doesn't rule it out categorically.