Concerning Energy

TL;DR

This paper explores the complex and ambiguous nature of energy in general relativity and cosmology, questioning the existence of a local energy density and examining various forms and implications of energy conservation.

Contribution

It critically analyzes the concept of energy in general relativity and cosmology, highlighting the lack of a local energy density and discussing various energy forms and conservation issues.

Findings

No local energy density invariant exists in general relativity.

Energy in cosmology can increase dramatically during inflation.

Different forms of energy have diverse implications for conservation laws.

Abstract

Energy has an ambiguous status in general relativity. For systems embedded in asymptotically flat space-times it is possible to construct an integral invariant that corresponds to total energy, however there is no local differential invariant that can be identified with energy density. Moreover, in cosmological 'big-bang' scenarios there is an energy gain of about 70 orders of magnitude between the initial detonation and final inflation. Nevertheless, there is a widespread belief that all physical systems, irrespective of their size or complexity, can be associated with a unique scalar measure --- their energy. This presumption suggests parallels with the mathematical concept of measure in set theory as well as with entropy. However, both analogies are limited in scope. We also discuss a wide variety of other forms of energy ranging from particle physics to information theory, and consider the implications for conservation laws. Finally, we recall several historical episodes in which energy conservation was at the center of controversy.