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By measurements of the movement of cosmic masses.

It is a common question, if everything is expanding what gives the scale? The answer: by measurements of the movement of cosmic masses.

If space itself is expanding, how could we ever tell?

is that we have a General Relativity mathematical model that fits all the data and observations at present, including the redshifts, by the hypothesis that four dimensional space is expanding from and original four dimensional "region". The expansion is measurable because matter is held together much more strongly than the expansion rate.

This shows a two dimensional cut of the four dimensions, time being the x axis and space the y. It is a fit to the observations, including the Hubble velocity. The other two dimensions not shown have the curvature of space too. It is the mathematical equations that give these plots, and they depend on general relativity

If spacetime itself is expanding, how could we ever tell?

By measurements of the movement of cosmic masses.

I'm talking about statements made by physicists that "space itself" is expanding.

is that we have a General Relativity mathematical model that fits all the data and observations at present, including the redshifts, by the hypothesis that four dimensional space is expanding from an original four dimensional "region". The expansion is measurable because matter is held together much more strongly than the expansion rate.

This shows a two dimensional cut of the four dimensions, time being the x axis and space the y. It is a fit to the observations, including the Hubble velocity. The other two dimensions not shown have the curvature of space too. It is the mathematical equations that give these plots, and they depend on general relativity.

We can tell, because the G.R. model fits all the data we have up to now.

See this extensive answer here.

This shows a two dimensional cut of the four dimensions, time being the x axis and space the y. It is a fit to the observations, including the Hubble velocity. The other two dimensions not shown have the curvature of space too. It is the mathematical equations that give these plots, and they depend on general relativity

See this extensive answer here.