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Riemann's Flat ( inertial, non - accelerating ) Spacetime Metric

"This theory of surfaces by Gauss has been extended by Riemann to continua of any arbitrary number of dimensions and has thus paved the way for the general theory of relativity" - Albert Einstein ( 1879 - 1955 )

 Riemann spacetime "gravity" curvature parametersEinstein's 1916 General Relativity paperflat spacetime is Einstein's special case for Newton's fixed space and time

Finally and most importantly, Einstein is not telling us what gravity is, but rather he is giving us a geometric proxy as to how to best operationally describe a gravitational field as explained as follows:


Time Relativity


"and the 'curvature' of space is dependent on the matter distributed over space ... so in the general theory of relativity ... the laws regulating the behavior of these objects ( clocks and measuring rods ) depend on where they happen to be", from "Space - Time", 1926, by Albert Einstein ( 1879 - 1955 )

ยง References:

  "On the Hypothesis That Lie at the Foundations of Geometry", by Bernhard Riemann ( 1826 - 1866, brilliant German mathematician whose n - tuple mathematical space geometry forms the basis of general relativity ), 1854 doctoral thesis presented to the Philosophical Faculty of the University of Göttingen, finally published posthumously in 1868 - English version

  German version: "On the Hypothesis That Lie at the Foundations of Geometry", 1854 doctoral thesis paper by Bernhard Riemann




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