Supplemental Material
Many cosmologists expect the universe to be finite. Part of the reason may be simple comfort: the human mind encompasses the finite more readily than the infinite. But there are also two scientific lines of argument that favor finitude. The first involves a thought experiment devised by Isaac Newton and revisited by George Berkeley and Ernst Mach. Grappling with the causes of inertia, Newton imagined two buckets partially filled with water. The first bucket is left still, and the surface of the water is flat. The second bucket is spun rapidly, and the surface of the water is concave. Why?
The naive answer is centrifugal force. But how does the second bucket know it is spinning? In particular, what defines the inertial reference frame relative to which the second bucket spins and the first does not? Berkeley and Mach's answer was that all the matter in the universe collectively provides the reference frame. The first bucket is at rest relative to distant galaxies, so its surface remains flat. The second bucket spins relative to those galaxies, so its surface is concave. If there were no distant galaxies, there would be no reason to prefer one reference frame over the other. The surface in both buckets would have to remain flat, and therefore the water would require no centripetal force to keep it rotating. In short, it would have no inertia. Mach inferred that the amount of inertia a body experiences is proportional to the total amount of matter in the universe. An infinite universe would cause infinite inertia. Nothing could ever move.
