Einstein's Uniformly Rotating Disk and the Hole Argument

TL;DR

This paper explores the historical and conceptual connections between Einstein's rotating disk problem, the Hole Argument, and the development of foundational principles in general relativity, highlighting their philosophical implications.

Contribution

It analyzes Einstein's evolving views on the rotating disk, the Hole Argument, and their relation to the Point Coincidence and Mach's principle, offering new historical insights.

Findings

The rotating disk problem was linked to the Hole Argument in Einstein's early work.

Einstein replaced the Hole Argument with the Point Coincidence Argument in 1916.

Mach's ideas influenced Einstein's rejection of empty holes in spacetime.

Abstract

Einstein's first mention of the uniformly rotating disk in print was in 1912, in his paper dealing with the static gravitational fields. After the 1912 paper, the rotating disk problem occurred in Einstein's writings only in a 1916 review paper, "The Foundation of the General Theory of Relativity". Einstein did not mention the rotating disk problem in any of his papers on gravitation theory from 1912 until 1916. However, between 1912 and 1914 Einstein invoked the Hole Argument. I discuss the possible connection between the 1912 rotating disk problem and the Hole Argument and the connection between the 1916 rotating disk problem and the Point Coincident Argument. Finally, according to Mach's ideas we see that the possibility of an empty hole is unacceptable. In 1916 Einstein replaced the Hole Argument with the Point Coincidence Argument and later in 1918 with Mach's principle.