Editing User:ConceptHut (section)

== The Graph ==

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]]

<blockquote>

'''Edward Witten (original)'''

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] : <math>M</math>, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws].
# 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 <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.
</blockquote>


Eric Weinstein suggested several alterations:

* 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".
* 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.

<blockquote>

'''Eric Weinstein (update)'''

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] : <math>M</math>, endowed with a [[metric tensor]] and governed by [https://en.wikipedia.org/wiki/Geometry geometrical laws].
# 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 <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

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>