Difference between revisions of "Graph, Wall, Tome"

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== A Request From Eric ==
== Eric Weinstein's Prompt ==
 
<blockquote>
<blockquote>
A request: Try to draw the lines through the three. View it as a unified idea:<br>
A request: Try to draw the lines through the three. View it as a unified idea:<br>
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</blockquote>
</blockquote>


== Background ==
'''Imagine:''' It's 1915, and you've made one of the greatest discoveries in hundreds of years. You visit your mother and show her your work:
$$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
'That's nice dear', she responds, unaware of the implications of your discovery.
The problem, is that although this equation carries with it the secrets of gravity, to a layman it is merely a bunch of letters and symbols.
Now, consider this single image.
[[File:sheetsunx.gif||Curved Space-Time]]
Instantly, the meaning becomes clear. Gravity warps space(time), and matter, planets, and even light follows a path that is curved by the warped geometry.




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</blockquote>


The original publication  [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry by Edward Witten] can be accessed via the CERN Document Server. The paragraph is found at the bottom of page 20.  
The original publication  [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry by Edward Witten] can be accessed via the CERN Document Server. The paragraph is found at the bottom of page 20. Eric tweeted about the paragraph [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted here].
 
=== Editing the Pagragraph ===


Eric Weinstein suggested several alterations, that have been included below:
Eric Weinstein suggested several alterations, that have been included below:
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* 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 the Higgs is remarkably absent.


This is a modified version of the paragraph by Edward Witten as [https://twitter.com/EricRWeinstein/status/928296366853328896?s=20 posted by Eric via Twitter].
This is a modified version of the paragraph:


<blockquote>
<blockquote>
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# 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] $$G$$.
# 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.
# [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
# The masses of elementary particles are generated through the Higgs mechanism.


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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[[Accelerators:|Accelerators: 2 minute guides to fundamental principles.]]
[[Accelerators:|Accelerators: 2 minute guides to fundamental principles.]]
== An Example ==
'''Imagine:''' It's 1915, and you've made one of the greatest discoveries in hundreds of years. You visit your mother and show her your work:
$$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
'That's nice dear', she responds, unaware of the implications of your discovery.
The problem, is that although this equation carries with it the secrets of gravity, to a layman it is merely a bunch of letters and symbols.
Now, consider this single image.
[[File:sheetsunx.gif||Curved Space-Time]]
Instantly, the meaning becomes clear. Gravity warps space(time), and matter, planets, and even light follows a path that is curved by the warped geometry.


== Resources &amp; References ==
== Resources &amp; References ==
170

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