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Quote of the day: Physics

If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Space-time is a pseudo-Riemannian manifold \(M\), endowed with a metric tensor and goverened by geometrical laws. (ii) Over \(M\) is a vector bundle \(X\) with a nonabelian gauge group \(G\). (iii) Fermions are sections of \((\tilde{S}_{+} \otimes V_R) \oplus (\tilde{S}_{-} \otimes V_{\tilde{R}})\). \(R\) and \(\tilde{R}\) are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference \(\Delta\) in some underlying theory. All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.

-Edward Witten, “Physics and Geometry”, 1986

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