Editing Editing the Graph

Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 1: Line 1:
{{InfoboxProject
Though the original Graph aptly describes our physical knowledge, there are some minor alterations and additions to be made for it to wholly capture the current state of physics.
|project=Editing the Graph
|image=[[File:Ascending and Descending.jpg]]
|topic=[[Graph, Wall, Tome]]
|leader=Aardvark
|startdate=27 January 2020
|customlabel1=Edited Graph
|customdata1=[https://drive.google.com/file/d/10_bMEnvwRRrX6Yf3EOtw5WSvgG9Njkee/view?usp=sharing This or Better]
|customlabel2=Graph Mind Map
|customdata2=[https://drive.google.com/file/d/16r60-56mhYCx4KKBvZv_6HDLOLw43X7y/view?usp=sharing Link]
|customlabel3=Google Drive
|customdata3=[https://drive.google.com/drive/folders/1706CBEJQEMppV60OU8OtcXxicluk2T3Y?usp=sharing Drive]
|customlabel4=Master Planning
|customdata4=[https://docs.google.com/document/d/1t9AvvFZzODw1WiGRZwRsFFZdPdBzYVJGLHiqWNrMtIA/edit?usp=sharing Doc]
|link1title=Website
|link1=[https://graphwalltome.com/ Homepage]
|link2title=
|link2=
|link3title=
|link3=
|link4title=Discord
|link4=[https://discord.gg/Z3u3pPm Invite]
}}


Though the original Graph aptly describes our physical knowledge, there are some minor alterations and additions to be made for it to accurately capture the current state of fundamental physics.
Eric Weinstein suggested several alterations, listed below:
Β 
* In (ii), β€œvector bundle X” should be changed to principal G-bundle.
[[Eric Weinstein|Eric]] has suggested several alterations, listed below:
* In (ii), β€œvector bundle <math>X</math>” should be changed to principal G-bundle.
* Also in (ii), β€œnonabelian gauge group G” should be changed to nonabelian structure group G.
* Also in (ii), β€œnonabelian 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 the Higgs is remarkably absent.
* He mentioned that some info was not required, and that the Higgs is remarkably absent.


Line 39: Line 15:
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations:
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 <math>M</math>, endowed with a metric tensor and governed by geometrical laws.
(i) Spacetime is a pseudo-Riemannian manifold $$M$$, endowed with a metric tensor and governed by geometrical laws.


(ii) Over <math>M</math> is a vector bundle <math>X</math> with a non-abelian gauge group <math>G</math>.
(ii) Over $$M$$ is a vector bundle $$X$$ with a non-abelian gauge group $$G$$.


(iii) 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 isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in representation difference <math>\Delta</math> in some underlying theory.
(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.
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.
Line 59: Line 35:
If one wants to summarize our knowledge of physics in the briefest possible terms, there are four really fundamental observations:
If one wants to summarize our knowledge of physics in the briefest possible terms, there are four really fundamental observations:


1. Space-time is a pseudo-Riemannian manifold <math>M</math>, endowed with a metric tensor and governed by geometrical laws
1. Space-time is a pseudo-Riemannian manifold `M`, endowed with a metric tensor and governed be geometrical laws


2. Over <math>M</math> is a principal G-bundle <math>P_{G}</math> with a nonabelian structure group <math>G</math>.
2. Over `M` is a principal bundle with a nonabelian structure group `G`.


3. 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 complex linear representations of <math>G</math> and thus are not isomorphic. Their failure to be isomorphic explains why the light fermions are light.
3. Fermions are sections of `(\hat{S}_+ \otimes V_R) \oplus (\hat{S}_- \otimes V_{\tilde{R}})`. `R` and `\tilde{R}` are complex linear representations of `G` and thus are not isomorphic. Their failure to be isomorphic explains why the light fermions are light.


4. Yukawa couplings between the fermion field and the Higgs field endow fermions with the property of mass. Massive bosons also acquire their mass through this Higgs mechanism.
4. Yukawa couplings between the fermion field and the Higgs field endow fermions with the property of mass. Massive bosons also acquire their mass through this Higgs mechanism.


All of this must be supplemented with the understanding that the above geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
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>
Line 79: Line 55:
If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations:
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].
# [https://en.wikipedia.org/wiki/Spacetime Spacetime] is a [https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold pseudo-Riemannian manifold] $$M$$, 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 structure group] <math>G</math>.
# 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 <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.
# [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.
# The masses of elementary particles are generated through the Higgs mechanism.


All of this must be supplemented with the understanding that the above 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.
</blockquote>
</blockquote>
</div>
</div>
Line 94: Line 70:
[[Category:Graph, Wall, Tome]]
[[Category:Graph, Wall, Tome]]
[[Category:Projects]]
[[Category:Projects]]
[[Category:Requested Project]]
Please note that all contributions to The Portal Wiki may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see The Portal:Copyrights for details). Do not submit copyrighted work without permission!
Cancel Editing help (opens in new window)

Templates used on this page: