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== The Graph == | == The Graph == | ||
This is the version of "the paragraph" by Edward Witten [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted by Eric via Twitter]. | |||
[[file:The-graph.png|600px]] | [[file:The-graph.png|600px]] | ||
Eric Weinstein suggested several alterations | <blockquote> | ||
Edward Witten (original) | |||
If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations: | |||
# [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] : $$M$$, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws]. | |||
# Over $$M$$ is a [https://en.wikipedia.org/wiki/Principal_bundle principal bundle] : $$P_{G}$$, with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian structure group] : $$G$$. | |||
# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light. | |||
# Add something about Higgs | |||
All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the [https://en.wikipedia.org/wiki/Introduction_to_gauge_theory gauge fields], and the fermions are to be interpreted in [https://en.wikipedia.org/wiki/Quantum_mechanics quantum mechanical] terms. | |||
</blockquote> | |||
Eric Weinstein suggested several alterations: | |||
* In (ii), “vector bundle X” should be changed to principal G-bundle. | * In (ii), “vector bundle X” should be changed to principal G-bundle. | ||
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* He mentioned that some info was not required, and that higgs is remarkably absent. | * He mentioned that some info was not required, and that higgs is remarkably absent. | ||
<blockquote> | |||
Eric Weinstein (update) | |||
If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations: | If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations: | ||