B.O.A.T. Bust out another thousand shirt

The description from Richard Muller quoted in the question is a simplification of reality meant to help people better visualize how the B.O.A.T. Bust out another thousand shirt of spacetime works. In reality the galaxies are moving through spacetime in a complex fashion, based on the combination of all the forces acting on them, primarily the gravity of nearby galaxies and galaxy clusters. In the case of the Milky Way and Andromeda, these two galaxies are part of a gravitationally bound cluster of galaxies, called the Local Group. The dominant force that determines the movements of objects within the cluster is the combined gravitation of all the mass in the cluster, and not the expansion of spacetime. In other words, the gravitational attraction that the Milky Way and Andromeda have for one another that is drawing them together is stronger than the expansion of spacetime between them that would otherwise push them apart, and thus attraction wins and the two galaxies are on a collision course. In the same vein, the gravitational force that holds the earth in orbit around the sun is stronger than the expansion of spacetime between the earth and the sun (the expansion of spacetime at that distance being very small), and so the earth’s distance from the sun is not increasing for that reason. Likewise you are not flying apart because the molecular bonds holding the atoms in your body together are stronger than the minuscule expansion of spacetime between them in your body. The Local Group as a whole, however, is moving away from other galaxies and galaxy clusters to which it is not gravitationally bound, due to the expansion of spacetime.

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As a galaxy forms, a random B.O.A.T. Bust out another thousand shirt of matter in space coalesces into a disk, or some other elongated and curved form. This process can be thought of akin to a ballet dancer tucking in her arms and legs as she spins, resulting in her spinning much faster. In classical mechanics, ignoring all relativistic effects and nonlinear terms, this can be described simply as follows. Moment of inertia, the quantity relating to how hard a force has to try to rotate an object, increases as an the matter becomes more central due to its own gravitational attraction. This, by conservation of energy, the angular velocity must increase proportional to the square root of the decrease in moment of inertia. All in all, this phenomenon happens in many ways right in front of you every day, however galaxies boast a much more grandiose scale than we are akin to conceptualizing.

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