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In their 1997 Science paper, [B 2] Corry, Renn and Stachel quote the above passage and comment that "the arguments by which Einstein is exculpated are rather weak, turning on his slowness in fully grasping Hilbert's mathematics", and so they attempted to find more definitive evidence of the relationship between the work of Hilbert and Einstein ...
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature , the gravitational part of the action is given as [ 1 ]
The Einstein–Hilbert action for general relativity was first formulated purely in terms of the space-time metric. To take the metric and affine connection as independent variables in the action principle was first considered by Palatini. [1]
p. 172: "Although Poincaré's principle of relativity is stated in a manner similar to Einstein's, the difference in content is sharp. The critical difference is that Poincaré's principle admits the existence of the ether, and so considers the velocity of light to be exactly c only when it is measured in coordinate systems at rest in the ether.
The differences between Einstein–Cartan theory and general relativity (formulated either in terms of the Einstein–Hilbert action on Riemannian geometry or the Palatini action on Riemann–Cartan geometry) rest solely on what happens to the geometry inside matter sources. That is: "torsion does not propagate".
A Hilbert space is a vector space equipped with an inner product operation, which allows lengths and angles to be defined. Furthermore, Hilbert spaces are complete, which means that there are enough limits in the space to allow the techniques of calculus to be used. A Hilbert space is a special case of a Banach space.
A quantum description normally consists of a Hilbert space of states, observables are self-adjoint operators on the space of states, time evolution is given by a one-parameter group of unitary transformations on the Hilbert space of states, and physical symmetries are realized by unitary transformations.
An important distinction in physics is the difference between local and global structures. Measurements in physics are performed in a relatively small region of spacetime and this is one reason for studying the local structure of spacetime in general relativity, whereas determining the global spacetime structure is important, especially in ...