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

[Alex K]

The perception and measurement of time is always based on the speed at which physical processes occur, right? In the scheme where everything shrinks, everything becomes faster. For example, how long does it take for a beam of light to cross a hydrogen atom? This is a basis of time and if the hydrogen atom shrinks, this time becomes shorter. So, in order to maintain formally the same laws of physics throughout the "expansion of space", now shrinking of all scales, the notion of how long is one second has to be adjusted to be shorter and shorter. I think...

As space expands, matter shrinks? That goes a long way toward answering my op question even without the calculus. BTW, I'm not afraid of calculus. I'm a mathemagician. I can take four 8s and turn them into three 1s. 888 / 8 = 111. So there.

Then again, if the galaxies are shrinking, then they may not necessarily be moving away from us but just be appearing to do so. will every galaxy eventually shrink into its own little black hole, then burst into billions of Big Bangs? Wish I had a camera, that would be so kewl.

Well, not really both - we are talking about two separate empirically equivalent interpretations of the same theory. Either space can be taken to expand, or, interestingly, stuff can be thought to shrink to create the same *observed* effect.
The shrinking in this picture would not as far as I can tell cause stuff to collapse into a black hole. The shrinking is, mathematically, only the outcome, the effect of all dimensionful quantities changing: particle masses become larger thus shrinking all atoms whose extent is inverse proportional to the mass, but the gravitational constant gets smaller in this scheme, and so collapse into a black hole is prevented.