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Editing the Graph: Difference between revisions
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Though the original graph describes, there are some minor alterations and additions to be made for it to capture the current state of physics. | |||
Eric Weinstein suggested several alterations, that have been included below: | Eric Weinstein suggested several alterations, that have been included below: | ||
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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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The Graph is a paragraph from Edward Witten's paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry], at the bottom of page 20: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow:auto;"> | |||
<div style="font-weight:bold;line-height:1.6;">The Original Graph</div> | |||
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<blockquote style="max-width:575px; min-width:300px; font-size: 125%; background: #f3f3ff; border-color: #ddd;"> | |||
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 $$M$$, endowed with a metric tensor and governed by geometrical laws. | |||
(ii) Over $$M$$ is a vector bundle $$X$$ with a non-abelian gauge group $$G$$. | |||
(iii) Fermions are sections of $$(\hat{S}_{+} \otimes V_{R}) \oplus (\hat{S}_{-} \otimes V_{\tilde{R}})$$. $$R$$ and $$\tilde{R}$$ are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in 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. | |||
</blockquote> | </blockquote> | ||
</div> | </div> | ||