Time Coordinates and Clocks: Einstein's Struggle

TL;DR

This paper examines Einstein's conceptual struggles with the idea that coordinates are conventional and lack direct physical meaning, tracing his reasoning from special relativity to general relativity.

Contribution

It provides a detailed historical and conceptual analysis of Einstein's difficulties and methodology in developing the theory of general relativity, clarifying misconceptions.

Findings

Einstein's early difficulties were linked to his reliance on physical intuition.

Misinterpretations of Einstein's derivations have led to erroneous judgments.

The background of Einstein's reasoning has been underappreciated in modern commentaries.

Abstract

In his Autobiographical Notes, Einstein mentioned that on his road to the final theory of general relativity it was a major difficulty to accustom himself to the idea that coordinates need not possess an immediate physical meaning in terms of lengths and times. This appears strange: that coordinates are conventional markers of events seems an obvious fact, already familiar from pre-relativistic physics. In this paper we explore the background of Einsteins difficulties, going from his 1905 paper on special relativity, through his 1907 and 1911 papers on the consequences of the equivalence principle, to the 1916 review paper on the general theory. As we shall argue, Einstein's problems were intimately connected to his early methodology, in which clarity achieved by concrete physical pictures played an essential role; and to the related fact that on his route to the general theory he focused on special situations that were easily accessible to physical intuition. The details of this background of Einstein's early reasoning have not always been sufficiently appreciated in modern commentaries. As we shall see, this has led to erroneous judgments about the status and validity of some of the early relativistic derivations by Einstein and others, in particular concerning the gravitational redshift.