How Do Scientists Know It's Space Expanding Not Galaxies Moving?

[Rhondazvous]

How do we know that rather than space expanding, matter isn't contracting, the idea being that light is exempt from shrinkage?  What, for example, if one of the fundamental four forces is actually in flux?

This would also lead to a red shift, no?

Absolutely, because the receiving atoms would be smaller, the received light would look more long-waved to them.

If you take the equations of matter and spacetime in General Relativity, both interpretations are possible. One can interpret the change of the space metric as an increase in distance by changing the coordinates, or one can model it by rescaling all the masses and strengths of forces, which would lead you to a picture where the mass of the electron rises making the atoms smaller. This should be equally consistent, but one still has to change the definition of time (which comes natural though because all the physical clocks are ticking differently as well).  The space expansion interpretation of the equations is much simpler though.

I see no change in time in the space expansion interpretation, since time is measured by the movements of celestial bodies not by the movement of space. Units of time such as days, months or years are based on movement of stars and planets within galaxies, while space expansion occurs between galaxies. To my knowledge humans do not base any calendar on intergalactic movement. But give us time (pun intended).