Introduction to Volumes 1 and 2: The Zurich Notebook and the Genesis of General Relativity

Abstract

Unifying physics by describing a variety of interactions -or even all interactions -within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie's main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called solitons), and he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie's work has three main objectives. 1 The first is to explain how Mie's project fit into the contemporary development of the electromagnetic world view. Part of Mie's project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie's criticisms of Einstein, in particular, bring out the subtelty and novelty of the ideas that Einstein used to guide his development of general relativity.In September of 1913 Einstein presented a lecture on the current status of the problem of gravitation at the 85th Naturforscherversammlung. Einstein's lecture and the ensuing heated discussion, both published later that year in the Physikalische Zeitschrift, reflect the options available for those who took on the task of developing a new theory of gravitation. The 1 Our study of Mie has been aided considerably by several recent discussions of his work, including Kohl (2002), Corry (1999), and Vizgin (1994. Born (1914), included in this volume, gives an insightful, influential reformulation of Mie's framework, and Pauli (1921, §64, 188-192 in the English translation) and Weyl (1918, §25, 206-217 ( §26) in the English translation of the fourth edition) both give clear contemporary reviews.

Mass–Energy–Momentum: Only there Because of Spacetime?

“…In order to do that, quantities describing energy densities, en-10 The earliest explicit statement in favour of a reduction of physics to electromagnetism can be found in Wien [1900], but it found its most detailed and promising presentation in the works of Gustav Mie, who built on work of Max Abraham. For summaries and discussion of Mie's programme see Vizgin [1994], pp.26-38, Corry [1999 and Smeenk and Martin [2007]. ergy current densities, momentum densities and momentum current densities within the continuum were needed.…”

The 1895 Lorentz transformations: historical issues and present teaching

“…The link between both subjects is the 'equivalence principle' which tells us that, locally, an inertial frame with a gravitational field  g looks like an accelerated one with   =a g (see [15] for a critical discussion of this principle). We show in this section that in such systems the proper time of clocks (at rest) depends on their position as well as the proper length of rods parallel to  a (a point realized by Einstein only in 1915, see [16]).…”

Reason and Method in Einstein’s Relativity

“…On the other hand, he was also confronted with the challenge of formulating the theory of gravity as a field theory that would conform with the principle of GR. Others, such as Mie, Abraham and Nordstrom, were hankering after a field theory that would conform to the principle of SR. (Norton, 1992;Smeenk and Martin, 2007) In view of Mach, the new gravitational theory would have to incorporate inertial forces within it. According to Mach, inertial forces had nothing to do with absolute space, but were the result of physical interactions between material bodies.…”