Do We Live in the Best of All Possible Worlds? The Fine-Tuning of the Constants of Nature

Abstract

Our existence depends on a variety of constants which appear to be extremely fine-tuned to allow for the existence of life as we know it. These include the number of spatial dimensions, the strengths of the forces, the masses of the particles, the composition of the Universe, and others. On the occasion of the 300th anniversary of the death of G.W. Leibniz, we discuss the question of whether we live in the "Best of all possible Worlds". The hypothesis of a multiverse could explain the mysterious fine tuning of so many fundamental quantities. Anthropic arguments are critically reviewed.

Universal Constants and Natural Systems of Units in a Spacetime of Arbitrary Dimension

“…either of the two parameters of the anti-de Sitter group can lead to the Poincare group, and the roles of these parameters are completely analogous. We can see this if we replace H with c 2 Ĥ in some of the commutation relations (11):…”

“…Finally, if one considers the algebra of quantum operators corresponding to (11), the Planck constant h appears on the right side of the commutators of operators. It makes its appearance because the dimension of operators is governed by canonical commutation relations and cannot be arbitrary.…”

“…Another related issue, which arises when one considers some set of physical constants, is the fact that their numerical values seem to be not so random as one might expect. The most common implication of this fact is the so-called anthropic principle, which postulates that the values of physical constants in the observable world must provide the existence of a certain observer (see, e.g., the recent review [11] and the references therein). The discussion of this principle has revived in recent years in connection with the concept of a multiverse, which is a feature of some inflationary theories [12,13].…”