General Relativity as a Hybrid theory: The Genesis of Einstein's work on the problem of motion

TL;DR

This paper explores Einstein's early view of general relativity as a hybrid theory, emphasizing his focus on vacuum solutions and his skepticism of energy-momentum tensors, aiming to understand the origin of his approach to the problem of motion.

Contribution

It reveals Einstein's early perspective of GR as a hybrid theory and uncovers the historical development of his vacuum approach through new correspondence analysis.

Findings

Einstein favored vacuum solutions over energy-momentum tensors.

He viewed singularities as placeholders for a future theory of matter.

The work highlights the influence of Einstein's quest for a unified field theory.

Abstract

In this paper I describe the genesis of Einstein's early work on the problem of motion in general relativity (GR): the question of whether the motion of matter subject to gravity can be derived directly from the Einstein field equations. In addressing this question, Einstein himself always preferred the vacuum approach to the problem: the attempt to derive geodesic motion of matter from the vacuum Einstein equations. The paper first investigates why Einstein was so skeptical of the energy-momentum tensor and its role in GR. Drawing on hitherto unknown correspondence between Einstein and George Yuri Rainich, I then show step by step how his work on the vacuum approach came about, and how his quest for a unified field theory informed his interpretation of GR. I show that Einstein saw GR as a hybrid theory from very early on: fundamental and correct as far as gravity was concerned but phenomenological and effective in how it accounted for matter. As a result, Einstein saw energy-momentum tensors and singularities in GR as placeholders for a theory of matter not yet delivered. The reason he preferred singularities was that he hoped that their mathematical treatment would give a hint as to the sought after theory of matter, a theory that would do justice to quantum features of matter.