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ConceptHut
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SANDBOXING BELOW LINE | SANDBOXING BELOW LINE | ||
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[[Russel Conjugations Rewrite]] | |||
Russel Conjugations | |||
* Adding fuel to the fire | |||
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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]. | This is the original version of "the paragraph" by Edward Witten that was [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted by Eric via Twitter]. | ||
[[file:The-graph.png|600px]] | [[file:The-graph.png|600px]] | ||
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If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: | If one wants to summarize 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] : | # [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] : <math>M</math>, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws]. | ||
# Over | # Over <math>M</math> is a [https://en.wikipedia.org/wiki/Vector_bundle vector bundle] : <math>X</math>, with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian] [https://en.wikipedia.org/wiki/Gauge_theory gauge group] : <math>G</math>. | ||
# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of | # [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\tilde{R}})</math>. <math>R</math> and <math>\tilde{R}</math> are not [https://en.wikipedia.org/wiki/Isomorphism isomorphic]; their failure to be isomorphic explains why the light fermions are light. | ||
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. | 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. | ||
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Eric Weinstein suggested several alterations: | 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". | ||
* Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G. | * Also in (ii), “nonabelian gauge group G” should be changed to "nonabelian structure group G". | ||
* In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent. | * In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent. | ||
* 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. | ||
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<blockquote> | <blockquote> | ||
Eric Weinstein (update) | '''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: | ||
# [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] : | # [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] : <math>M</math>, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws]. | ||
# Over | # Over <math>M</math> is a [https://en.wikipedia.org/wiki/Principal_bundle principal bundle] : <math>P_{G}</math>, with a [https://en.wikipedia.org/wiki/Non-abelian_group non-abelian] [https://en.wikipedia.org/wiki/Fiber_bundle#Structure_groups_and_transition_functions structure group] : <math>G</math>. | ||
# [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of | # [https://en.wikipedia.org/wiki/Fermion Fermions] are sections of <math>(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}\_ \otimes V_{\bar{R}})</math>. <math>R</math> and <math>\bar{R}</math> 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 | # 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. | 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> | </blockquote> | ||