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__TOC__ | __TOC__ | ||
== | == 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> | ||
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</blockquote> | </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 | * He mentioned that some info was not required, and that the Higgs is remarkably absent. | ||
This is a modified version of the paragraph | 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. | ||
# | # 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 & References == | == Resources & References == | ||