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The Riemann Program James E. Beichler

The Riemann Program

James E. Beichler

Published August 2nd 2013
Kindle Edition
258 pages
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 About the Book 

According to the commonly held simplistic view of the history of science, Isaac Newton’s concept of absolute space was accepted without change until replaced by Albert Einstein’s special and general theories of relativity. Ernst Mach had successfully challenged the concept of an absolute space in the 1870s for the first time, while the concept of relative space slowly eroded the foundations of Newtonian absolute space during the final decades of the nineteenth century. Speculations were made by William K. Clifford and Bernhard Riemann that anticipated Einstein’s relativity, but neither amounted to much and had little or no influence on the science of the day. However, this common historical point of view is wrong as well as misleading, which calls into account what really happened during the Second Scientific Revolution. Riemann and Clifford did not just anticipate Einstein’s general relativity. Riemann suggested a specific mathematical program for changing the scientific concept of absolute space. This change represented a great advance over Newton’s concept of physical space without detracting from the rising influence of relative space in physics in the late nineteenth century. Riemann proposed that physical space had an infinitesimal structure that was quite possibly different from that expected by the physical investigation of macroscopic geometries and only experiment could verify which of several geometries was true. In this respect, he suggested that absolute space had real physical properties that should be studied in physics. Only Clifford and a small number of other investigators developed theories following and expanding upon Riemann’s suggestions, but everyone knew about them. Their ideas contended with other concepts of space, especially the aether theories, until Einstein finally established the dominance of relative space in 1905 and thereafter. Understanding Riemann’s program will change the way historians and scientists view both the physics of the late nineteenth century as well as the changes that science underwent during the Second Scientific Revolution.