Local versus Global Time in Early Relativity Theory

TL;DR

This paper examines Einstein's evolving understanding of time in relativity, defending his early reasoning against modern criticisms.

Contribution

The paper provides a historical and conceptual defense of Einstein's early reasoning on global time in relativity.

Findings

Einstein's early work on global time is consistent with his later derivations.

Modern criticisms of Einstein's reasoning are shown to be unfounded in specific contexts.

Examining Einstein's early methods clarifies his later work in general relativity.

Abstract

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein’s methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein’s early work clarifies his later reasoning and demonstrates its consistency and validity.