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Learn the Basics of Hilbert Spaces and Their Relatives: Definitions Hilbert spaces are at first real or complex vector spaces, or are Hilbert spaces So all the theorems and definitions of linear algebra apply to the finite-dimensional ones and many to the infinite-dimensional ones, and we start at known ground
Where does the Einstein-Hilbert action come from? - Physics Forums The Hilbert action comes from postulating that gravity comes from making the metric dynamical, and that the dynamical equations come from an action, which is a scalar There are more complex terms consistent with this idea, and the Hilbert action is only the simplest
Fundamental reality: Hilbert space - Physics Forums What do you guys think of this soberly elegant proposal by Sean Carroll? Reality as a Vector in Hilbert Space Fundamental reality lives in Hilbert space and everything else (space, fields, particles ) is emergent Seems to me a step in the right conceptual direction
Why are Hilbert spaces used in quantum mechanics? - Physics Forums Why do we distinguish between classical phase space and Hilbert spaces then? In all introductions that I've read on quantum mechanics , Hilbert spaces are introduced with little motivation and its also implied that they are a new space (that wasn't present in classical mechanics) in which quantum states exist
Does Hilbert Space Include Constants of Nature Beyond Basic Quantum . . . Does Hilbert Space contain the fine structure constant or store the values of other constants of nature or their information or does it only contain the position, momentum basis information of particles? Coming at this from a mathematical viewpoint, a Hilbert Space is a complete inner product space See, for example:
Derivation of the Einstein-Hilbert Action - Physics Forums Derivation of the Einstein-Hilbert Action Abstract Most people justify the form of the E-H action by saying that it is the simplest scalar possible But simplicity, one can argue, is a somewhat subjective and ill-defined criterion Also, simplicity does not shed light on the axiomatic structure of general relativity
Hilberts Sixth Problem: Can Physics Be Completely Axiomatized? If one assumes it is possible to axiomatize physics completely (a correct solution to Hilbert's sixth problem) could one then use Godels incompleteness theorem to prove that there are some parts of the physical universe that we can never truly understand (prove from this purportedly complete axiom system) thus contradicting the statement that