[El Gato]

So if this experiment suggests there is no dark matter, and if it turns out that, indeed, there is no dark matter, then what's preventing the galaxies from falling apart as they whirl through space. It seems like getting rid of dark matter as a possibility introduces as many problems as it solves.

That's the way it goes. That is that's the way our theories are honed to more closely match reality. Once they no longer fit the observed reality, we need new theories.

For example Newtonian mechanics are just for every day use, (where every day is any events with relative velocities well below the speed of light), but at high speeds/energies, they no longer "work", and are replaced by Einstein's special relativity. (But only for constant motions, add acceleration, and even that no longer fits)

[samtheman]

So you’re suggesting there’s some completely as-yet-undiscovered, as-yet-unconceived-of, mechanism holding each galaxy in tight rotation around it’s center, despite the lack of mass to account for that rotation...

Interesting.