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On the Origin of Kaluza's Idea of Unification
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We argue that the starting point of Kaluzas idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluzas attention was turned to this point by the three papers on the Lense–Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluzas paper was submitted. We provide here also an English translation of the third of these papers (Phys. Zeits. 19: 204, 1918).
The main theoretical aspects of gravitoelectromagnetism ("GEM") are presented. Two basic approaches to this subject are described and the role of the gravitational Larmor theorem is emphasized. Some of the consequences of GEM are briefly mentioned.
The numerous ways of introducing spatial gravitational forces are fit
together in a single framework enabling their interrelationships to be
clarified. This framework is then used to treat the ``acceleration equals
force" equation and gyroscope precession, both of which are then discussed in
the post-Newtonian approximation, followed by a brief examination of the
Einstein equations themselves in that approximation.
During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956), the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge-invariance. In the second stage (1960-1975), it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. This book describes the first phase of the development. The author first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing for the first time in English. The articles illustrate that the reassessment of gauge-theory, due to in a large measure to Weyl, constituted a major philosophical as well as technical advances.
One of the major developments of twentieth-century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this article the authors review the early history of gauge theory, from Einstein's theory of gravitation to the appearance of non-Abelian gauge theories in the fifties. The authors also review the early history of dimensional reduction, which played an important role in the development of gauge theory. A description is given of how, in recent times, the ideas of gauge theory and dimensional reduction have emerged naturally in the context of string theory and noncommutative geometry.
This book is intended to provide a thorough introduction to the theory
of general relativity. It is intended to serve as both a text for
graduate students and a reference book for researchers. According to
general relativity, as formulated by Einstein in 1915, the intrinsic,
observer-independent, properties of spacetime are described by a
spacetime metric, as in special relativity. The structure of spacetime
is related to the matter content of spacetime. Manifolds and tensor
fields are considered along with curvature, Einstein's equation,
isotropic cosmology, the Schwarzschild solution, methods for solving
Einstein's equation, causal structure, singularities, the initial value
formulation, asymptotic flatness, black holes, spinors, and quantum
effects in strong gravitational fields. Attention is also given to
topological spaces, maps of manifolds, Lie derivatives, Killing fields,
conformal transformations, and Lagrangian and Hamiltonian formulations
of Einstein's equation.
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