Some remarks on the notions of general covariance and background independence

TL;DR

This paper reviews the conceptual challenges in defining general covariance and background independence, and examines Einstein's 1913 argument against scalar gravity theories to highlight historical debates in gravitational theory.

Contribution

It provides a critical analysis of the difficulties in formalizing general covariance and background independence, and offers a historical perspective on Einstein's early arguments against scalar theories.

Findings

Identifies key conceptual obstacles in defining general covariance and background independence.

Analyzes Einstein's 1913 argument to understand historical development of gravitational theory.

Highlights the importance of historical context in the conceptual foundations of gravity theories.

Abstract

In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. Grossmann to discredit scalar theories of gravity in order to promote general covariance.