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Theory of Geometric Unity: Difference between revisions
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Geometric Unity is an attempt to produce a complete theory of fundamental physics through geometry. | |||
* A first video presentation of the theory is available on [https://www.youtube.com/watch?v=Z7rd04KzLcg Youtube] | * A first video presentation of the theory is available on [https://www.youtube.com/watch?v=Z7rd04KzLcg Youtube] | ||
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* Preliminary notes by the community on the talk are available in a [https://docs.google.com/document/d/1gPU_bJR5wBs7MCsNGCW5Y06Jh3SzarX5OnJHyLxQfDQ/edit Google Doc] | * Preliminary notes by the community on the talk are available in a [https://docs.google.com/document/d/1gPU_bJR5wBs7MCsNGCW5Y06Jh3SzarX5OnJHyLxQfDQ/edit Google Doc] | ||
* [https://www.youtube.com/watch?v=wf0_nMaQ6tA#t=2h16m27s Discussion on the Joe Rogan show] | * [https://www.youtube.com/watch?v=wf0_nMaQ6tA#t=2h16m27s Discussion on the Joe Rogan show] | ||
* [https://www.youtube.com/watch?v=N_aN8NnoeO0 PBS SpaceTime] | |||
<div style="float:right;padding:20px;">__TOC__</div> | |||
<blockquote style="width:500px">"The source code of the universe is overwhelmingly likely to determine a purely geometric operating system written in a uniform programming language." - Eric Weinstein </blockquote> | <blockquote style="width:500px">"The source code of the universe is overwhelmingly likely to determine a purely geometric operating system written in a uniform programming language." - Eric Weinstein </blockquote> | ||
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{| class="wikitable" | {| class="wikitable" | ||
| '''1.''' The Arena (<math> Xg_{\mu\nu}</math>) | | '''1.''' The Arena (<math> Xg_{\mu\nu}</math>) | ||
| <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \left( \ | | <math>R_{\mu\nu} - \frac{1}{2} Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \left( \dfrac{8 \pi G}{c^4} T_{\mu\nu}\right)</math> | ||
| the Einstein | | the Einstein field equations, which describe gravity in the theory of general relativity | ||
|- | |- | ||
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| '''3.''' Matter | | '''3.''' Matter | ||
Antisymmetric, therefore light | Antisymmetric, therefore light | ||
| <math>\ | | <math>(i \hbar \gamma^\mu \partial_\mu - m) \psi = 0</math> | ||
| the Dirac equation, | | the Dirac equation, the equation of motion describing matter particles, or fermions | ||
|} | |} | ||
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'''Idea:''' What if the $$F$$'s are the same in both contexts? | '''Idea:''' What if the $$F$$'s are the same in both contexts? | ||
Further, supposing these $$F$$'s are the same, then why apply two different operators? | |||
'''Thus the question becomes:''' Is there any opportunity to combine these two operators? | '''Thus the question becomes:''' Is there any opportunity to combine these two operators? | ||
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</blockquote> | </blockquote> | ||
<div class="toccolours mw-collapsible mw-collapsed" style="width:1000px; overflow:auto;"> | |||
<div style="font-weight:bold;line-height:1.6;">Comments</div> | |||
<div class="mw-collapsible-content"> | |||
'''Mark-Moon:''' Can anyone explicate Eric's point about spinor fields depending (in a bad way) on the metric in conventional theories, in a way that is no longer the case in GU? I feel like this is the original idea in GU that I'm closest to being able to understand, but I don't think I quite get it yet. | '''Mark-Moon:''' Can anyone explicate Eric's point about spinor fields depending (in a bad way) on the metric in conventional theories, in a way that is no longer the case in GU? I feel like this is the original idea in GU that I'm closest to being able to understand, but I don't think I quite get it yet. | ||
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'''Chain:''' Yeah I was wondering this as well, as far as I was aware you just need a spin structure, which only depends on the topology and atlas on the manifold and not on the choice of metric [https://math.stackexchange.com/questions/2836814/dependence-of-spinor-bundle-on-choice-of-metric]. Perhaps the point is that although each choice of metric yields an isomorphic spin structure, perhaps there is not a canonical isomorphism in the same way as in GU where the bundle of metrics Y (U in the talk) is isomorphic to the Chimeric bundle C, but the choice of isomorphism is given by a choice of connection on Y. Although I don't know why the chimeric bundle would come with a canonical choice of spin structure either, which seems to be Eric's claim | '''Chain:''' Yeah I was wondering this as well, as far as I was aware you just need a spin structure, which only depends on the topology and atlas on the manifold and not on the choice of metric [https://math.stackexchange.com/questions/2836814/dependence-of-spinor-bundle-on-choice-of-metric]. Perhaps the point is that although each choice of metric yields an isomorphic spin structure, perhaps there is not a canonical isomorphism in the same way as in GU where the bundle of metrics Y (U in the talk) is isomorphic to the Chimeric bundle C, but the choice of isomorphism is given by a choice of connection on Y. Although I don't know why the chimeric bundle would come with a canonical choice of spin structure either, which seems to be Eric's claim | ||
to define spinors you would need a clifford bundle and hence a choice of metric on the chimeric bundle | to define spinors you would need a clifford bundle and hence a choice of metric on the chimeric bundle | ||
</div></div> | |||
=== Problem Nr. 3: The Higgs field introduces a lot of arbitrariness === | === Problem Nr. 3: The Higgs field introduces a lot of arbitrariness === | ||