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Graph, Wall, Tome: Difference between revisions
→Graph: This simplified version probably works better in mobile. Side-by-side seemed awkward to me. Let me know if I'm missing something.
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(→Graph: This simplified version probably works better in mobile. Side-by-side seemed awkward to me. Let me know if I'm missing something.) |
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=== Prime Directive === | === Prime Directive === | ||
<blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%; | <blockquote style="width: 600px; text-align: center; margin-left: auto; margin-right: auto; font-size: 125%;> | ||
A request: | A request: | ||
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=== Graph === | === Graph === | ||
The Graph is a paragraph from Edward Witten's 1987 paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry] at the bottom of page 20. In language it concisely encodes the general structure of reality: | The Graph is a paragraph from Edward Witten's 1987 paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry] at the bottom of page 20. In language it concisely encodes the general structure of reality: | ||
<blockquote style="font-size: 125%;"> | |||
<blockquote style=" | |||
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: | ||
(i) Spacetime is a pseudo-Riemannian manifold | (i) Spacetime is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws. | ||
(ii) Over | (ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>. | ||
(iii) Fermions are sections of | (iii) 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 isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference <math>\Delta</math> 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. | 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. | ||
</blockquote> | </blockquote> | ||
<div style="text-align: center"> | |||
Scan of the original paragraph: | |||
[[File:The-graph.png|class=shadow|650px]] | [[File:The-graph.png|class=shadow|650px]] | ||
</div> | </div> | ||
Implicit in each respective section is: | Implicit in each respective section is: | ||
# Spin-2 Force Field for Gravity, the Einstein Field Equations | # Spin-2 Force Field for Gravity, the Einstein Field Equations | ||
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[[Category:Projects]] | [[Category:Projects]] | ||
[[Category:Requested Project]] | [[Category:Requested Project]] | ||
{{ | {{SHORTDESC:A holistic view of math and physics}} | ||