Infinities in Physics and Transfinite numbers in Mathematics

Abstract

Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known mathematical theory of infinities, we conclude that apparent inconsistencies in physics are a result of unfamiliar and unusual rules obeyed by mathematical infinities. We show that a re-examination of some familiar limiting results in physics leads to surprising and unfamiliar conclusions. It is not the purpose of this work to resolve the problem of infinities but the intent of this analysis is to point out that the study of real infinities in mathematics may be the first step towards delineating and understanding the problem of infinities in physics.