Constants and cosmology: The nature and origin of fundamental constants in astrophysics and particle physics

Abstract

We ask about the nature and origin of the fundamental constants of astrophysics and particle physics, notably the speed of light c, the gravitational constant G, Planck's constant h, and the magnitude of the electron charge e. We consider general relativity and the theories of the electromagnetic, weak and strong interactions that make up the Standard Model; together with the Lagrangians of Einstein, Maxwell, Schrodinger, Klein-Gordon, Dirac, Proca, and Yang-Mills. Then we look in a more qualitative way at how the equations of physics are set up, their dimensional content, and the removal of constants from them by a suitable choice of units. We conclude with Hoyle and Narlikar, Jeffreys and McCrea that parameters like c, G, and h are merely manmade dimensional conversion constants. They arise because of our subjective view that mass, length, and time are different concepts. These constants can be removed in a manner analogous to the removal of the permittivity of free space ɛ 0 from electrodynamics, and none are really fundamental. The charge e is different, being the low-energy limit of a function related to properties of the vacuum, but because of this it is not a fundamental constant either. We suggest there are no constants which truly deserve to be called fundamental, and that an aim of physics ought to be to write down laws in which no constants appear.