On the Status of Conservation Laws in Physics: Implications for Semiclassical Gravity

TL;DR

This paper reviews the historical and conceptual status of conservation laws in physics, highlighting their limitations in quantum and semiclassical contexts, and argues that Einstein's equations may not always be valid.

Contribution

It provides a comprehensive analysis of conservation laws across classical, quantum, and semiclassical regimes, challenging their universal applicability in gravity theories.

Findings

Conservation laws are useful but not essential in classical physics.

Quantum formalism complicates the definition of conserved energy.

Einstein's equations may not always hold in semiclassical gravity.

Abstract

We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not essential. Next we consider the quantum setting, where the conceptual problems of the standard formalism obstruct a rigorous analysis of the issue. We then analyze the fate of energy conservation within the various viable paths to address such conceptual problems; in all cases we find no satisfactory way to define a (useful) notion of energy that is generically conserved. Finally, we focus on the implications of this for the semiclassical gravity program and conclude that Einstein's equations cannot be said to always hold.