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Hole argument and Entwurf theory
Main article: Hole argumentHP Pavilion dv7-1222ez Battery
While developing general relativity, Einstein became confused about the gauge invariance in the theory. He formulated an argument that led him to conclude that a general relativistic field theory is impossible. He gave up looking for fully generally covariant tensor equations, HP Pavilion dv7-1223ca Battery and searched for equations that would be invariant under general linear transformations only.
In June, 1913 the Entwurf (”draft”) theory was the result of these investigations. As its name suggests, it was a sketch of a theory, with the equations of motion supplemented by additional gauge fixing conditions. HP Pavilion dv7-1225ef Battery Simultaneously less elegant and more difficult than general relativity, after more than two years of intensive work Einstein abandoned the theory in November, 1915 after realizing that the hole argument was mistaken.
CosmologyHP Pavilion dv7-1225eo Battery
Main article: Cosmology
In 1917, Einstein applied the General theory of relativity to model the structure of the universe as a whole. He wanted the universe to be eternal and unchanging, HP Pavilion dv7-1225ez Battery but this type of universe is not consistent with relativity. To fix this, Einstein modified the general theory by introducing a new notion, the cosmological constant. With a positive cosmological constant, the universe could be an eternal static sphere.
Einstein in his office at the University of Berlin. HP Pavilion dv7-1228ca Battery
Einstein believed a spherical static universe is philosophically preferred, because it would obey Mach’s principle. He had shown that general relativity incorporates Mach’s principle to a certain extent in frame dragging by gravitomagnetic fields, but he knew that Mach’s idea would not work if space goes on forever. HP Pavilion dv7-1230eb BatteryIn a closed universe, he believed that Mach’s principle would hold. Mach’s principle has generated much controversy over the years.