Seeliger's Gravitational Paradox and the Infinite Universe

摘要

Seeliger’s paradox is often regarded as an argument against Newtonian potentials in aninfinite universe. In this paper the argument is analyzed with the help of Riemann’sseries theorem. This theorem reveals that the paradox is a known consequence of therearrangement of conditionally convergent series or integrals, and so it demonstratesthat the same situation would arise with almost any other type of gravitational forcelaw. Therefore Seeliger’s argument is not a valid proof against Newton’s inverse squarelaw or even an infinite universe.