Reality Is Not What It Seems: The Journey to Quantum Gravity

by Carlo Rovelli

But the infinities of quantum field theory follow from an assumption at the basis of theory: the infinite divisibility of space. For example, to calculate the probabilities of a process, we sum up—as Feynman has taught us—all the ways in which the process could unfold, and these are infinite, because they can happen in any one of the infinite points of a spatial continuum. This is why the result can be infinite. When quantum gravity is taken into account, these infinities also disappear. The reason is clear: space is not infinitely divisible, there are no infinite points; there are no infinite things to add up. The granular discrete structure of space resolves the difficulties of the quantum theory of fields, eliminating the infinities by which it is afflicted. This is a tremendous result: on the one hand, taking quantum mechanics into account resolves the problems generated by the infinities of Einstein’s theory of gravity, that is to say, the singularities. On the other, taking gravity into account solves the problems generated by quantum field theory, that is to say, the divergences. Far from being contradictory, as they at first seemed, the two theories each offer the solution to the problems posed by the other!