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| The goal of the Graph, Wall, Tome project is to solve this problem by building a portal anyone can use to travel to the amazing world that we call fundamental physics. | | The goal of the Graph, Wall, Tome project is to solve this problem by building a portal anyone can use to travel to the amazing world that we call fundamental physics. |
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| The name of the project stems from the fact that there are 3 resources that themselves contain all that you need for an almost complete understanding of the world. | | The name of the project stems from the fact that there are three resources that themselves contain all that you need for an almost complete understanding of the world. |
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| # '''The Graph''' - A paragraph written by Edward Witten | | # '''The Graph''' - A paragraph written by Edward Witten |
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| </blockquote> | | </blockquote> |
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| == The Graph == | | == The Graph, The Wall, The Tome == |
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| | ===The Graph=== |
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| | The Graph is a paragraph from Edward Witten's paper [https://cds.cern.ch/record/181783/files/cer-000093203.pdf Physics and Geometry]: |
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| <blockquote> | | <blockquote> |
| If one wants to summarise 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 $$M$$, 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 M is a vector bundle $$X$$ with a nonabelian gauge group $$G$$. | | (ii) Over M is a vector bundle $$X$$ with a non-abelian gauge group $$G$$. |
| (iii) Fermions are sections of $$(\hat{S}{+} \otimes V{R}) \oplus (\hat{S}_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ 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. | | (iii) Fermions are sections of $$(\hat{S}{+} \otimes V{R}) \oplus (\hat{S}_ \otimes V_{\bar{R}})$$. $$R$$ and $$\bar{R}$$ 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. |
| </blockquote> | | </blockquote> |
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| 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].
| | The paragraph is found at the bottom of page 20. |
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| === Editing the Pagragraph === | | ===The Wall=== |
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| Eric Weinstein suggested several alterations, that have been included below:
| | The following [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html image is carved into a wall at Stony Brook University]. It contains many of the most fundamental equations of physics, providing a formulaic representation of all reality. |
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| * In (ii), “vector bundle X” should be changed to principal G-bundle.
| | <gallery mode="packed" heights=600px> |
| * Also in (ii), “nonabelian gauge group G” should be changed to nonabelian structure group G.
| | File:Newwall.png|center|class=shadow|400px|The Wall |
| * In (iii), <math>\ R</math> and <math>\tilde R</math> should be (complex) linear representations of G and so they are not equivalent.
| | File:Key-to-wall.png|center|class=shadow|400px|Explanations for the Wall |
| * He mentioned that some info was not required, and that the Higgs is remarkably absent.
| | </gallery> |
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| This is a modified version of the paragraph:
| | === The Tome === |
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| <blockquote>
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| If one wants to summarise our knowledge of physics in the briefest possible terms, there are three really fundamental observations:
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| # [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].
| | [[File:The-tome.png|right|class=shadow|150px]] |
| # 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] $$G$$.
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| # [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.
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| # The masses of elementary particles are generated through the Higgs mechanism.
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| 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.
| | The Tome is the book Road to Reality by Roger Penrose which contains a comprehensive account of the physical universe. To gain an understanding and intuition for the information contained in 'The Graph', and 'The Wall', reading this book will provide a great head-start. With 34 chapters spread over 1000 pages, including diagrams, equations, and descriptions, there are multiple avenues for understanding all concepts. |
| </blockquote>
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| == The Wall ==
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| <div class="floatright" style="text-align: center">
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| [[File:Newwall.png|center|class=shadow|400px]]
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| [https://dev.theportal.dev/wall/ High Resolution Interactiv Version of the Wall]
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| [[File:Key-to-wall.png|center|class=shadow|400px]]
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| </div>
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| This [http://www.math.stonybrook.edu/~tony/scgp/wall-story/wall-story.html image is carved into a wall at Stony Brook University]. It contains many of the most fundamental equations of physics, providing a formulaic representation of all reality.
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| Several of the equations have been identified as having direct connections to statements in 'The Graph' (identified by numbers)
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| === Key and Explanations ===
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| ''The following should be completed according to the list of explanations on this page: http://scgp.stonybrook.edu/archives/6264''
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| <span class="highlight">[[Talk:Graph,_Wall,_Tome#EricRWeinstein_2020-02-02_at_1%3A31_PM | New suggestions from Eric]]</span>
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| *I. [[Jones polynomial]] for right trefoil knot; [https://theportal.wiki/wiki/Jones_polynomial Witten’s path-integral formulation] for Jones polynomial using Chern-Simons action
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| *II. [[Feynmann Diagram]] illustrating [[Associativity]] equation in [[Quantum Field Theory]]
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| *III. [[Yang-Baxter equation]]
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| *IV. [[Lorenz Attractor]]: Lorenz equations with orbit
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| *V. Diagram of a black hole with [[Schwarzschild radius]]
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| *VI. The five [[regular polyhedra]]
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| *VII. Equiangular spiral drawn in "golden" rectangle (side ratio = golden mean g), ratio of consecutive [[Fibonacci numbers]] approaches g, represented by its continued fraction expansion.
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| *VIII.[[Babylonian computation of the square root of 2]]
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| *IX. Visual proof of the [[Pythagorean Theorem]]
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| *X. [[Cell decomposition of torus; Euler characteristic; Gauss-Bonnet formula.]]
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| *XI. Archimedes: [[On the Sphere and Cylinder]].
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| *XII. [[Aharanov-Bohm effect]]
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| *XIII.[[Supergravity Langangian]]; root diagramm for [[Lie group E8]]
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| *XIV. [[Navier-Stokes equation]] with flow around cylinder.
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| *0. In Ellipse: ([[Kepler's 1st law]] represented by star, ellipse, planet)
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| *1. [[Kepler's 2nd law]]
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| *2. [[Newton's force-acceleration equation]]
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| *3. [[Kepler's 3rd law]]
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| *4. [[Newton's gravitational law]]
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| *5. [[Einstein's General Relativity equation]]
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| *6. [[Schrödinger's equation]]
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| *7. [[Dirac equation]]
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| *8. [[Atiyah-Singer Theorem]]
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| *9. [[Yang-Mills equations]]
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| *10. [[Defining relation of Supersymmetry]]
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| *A. [[Einstein’s mass-energy equation]]
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| *B. [[Maxwell's Equations]]
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| *C. [[Stoke's Theorem]]
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| *D. [[The boundary of a boundary is zero]]
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| *E. [[Heisenberg's indeterminacy relation]]
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| *F. [[Euler's formula for Zeta-function]]
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| *G. Interaction between two string; [[Feynman diagram]] shows corresponding interaction of particles, here the Compton scattering of a photon off an electron.
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| === Defacing the Wall ===
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| What should be in and what should be out of the future wall? Let's determine that[[https://theportal.wiki/wiki/Defacing_the_wall here]].
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| Eric talked about some of the important equations on the wall. There are 2 different recorded versions of the conversation if you want to listen to it. (Where? Is there a transcript or summary of the most important points?)
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| == The Tome ==
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| [[File:The-tome.png|right|class=shadow|250px]]
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| This book by Roger Penrose contains a comprehensive account of the physical universe.
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| To gain an understanding and intuition for the information contained in 'The Graph', and 'The Wall', reading this book will provide a great head-start. | |
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| With 34 chapters spread over 1000 pages, including diagrams, equations, and descriptions, there are multiple avenues for understanding all concepts. | |
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| See our [[The Road to Reality Study Notes|study notes]]
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| === Book Details ===
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| * ISBN: 978-0679776314 | | * ISBN: 978-0679776314 |
| * [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Roger Penrose (2004)] | | * [https://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679776311 Road to Reality by Roger Penrose (2004)] |
| | * Purchase the book somehow, then get the [https://www.academia.edu/351112/The_Road_to_Reality_Sir_Roger_Penrose PDF here] |
| * There appears to be a [https://www.amazon.com/Road-Reality-Complete-Guide-Universe-ebook/dp/B01BS7NTA6 Kindle Edition] that isn't available in the US. If anyone in the community has a way to get a Kindle version of the book, please add it here. | | * There appears to be a [https://www.amazon.com/Road-Reality-Complete-Guide-Universe-ebook/dp/B01BS7NTA6 Kindle Edition] that isn't available in the US. If anyone in the community has a way to get a Kindle version of the book, please add it here. |
| * Purchase the book somehow, then get the [https://www.academia.edu/351112/The_Road_to_Reality_Sir_Roger_Penrose pdf here]
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| == Methodology == | | == Ongoing Sub-Projects == |
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| * Create/assemble resources that allow uninitiated to quickly and easily get up to speed with state of project. | | * [[Editing the Graph]] |
| * Create/assemble resources that provide analogies for more complex principles - to demonstrate a key feature of the principle. | | * [[Annotating the Wall]] |
| * Create/assemble resources that provide a geometric intuition for the equations of fundamental physics - Geometric interpretations are most amenable to being visually represented. | | * [[Animating the Wall]] |
| * Create/assemble resources that allow the geometric visualisation/intuition for principles of foundational physics. | | * [[Defacing the Wall]] |
| * Rinse and repeat. | | * [[The Road to Reality Study Notes|Annotating the Tome]] |
| | * [[Decoding the Graph-Wall-Tome Connection]] |
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| == Project Files == | | == Further Project Ideas== |
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| A working area for the project is located in a [https://drive.google.com/drive/folders/1yPZHTNy47jUpmD-RMRCVtitfD-gQBRhP google drive].
| | * Create/assemble resources that provide a geometric intuition for the equations and principles of fundamental physics - Geometric interpretations are most amenable to being visually represented. An example, is shown [[Example Visualization|here]]. |
| | | * Create [[Accelerators:|Accelerators: 2 minute guides to fundamental principles.]] |
| It includes a [https://docs.google.com/document/d/1sB_LTltdq8J6mIKyPRaHQWKEuLk0ZXuwYQZb78BnNuk/edit?usp=sharing list of tasks] that can be worked on by individuals or groups of individuals. (add a comment to let people know if you're working on something)
| | * Create/assemble resources that allow uninitiated to quickly and easily get up to speed with state of the project. |
| | | * Create/assemble resources that provide analogies for more complex principles - to demonstrate a key feature of the principle. |
| This file also has an area to list specific areas of aptitude or interest for those people who are not sure how to contribute.
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| == Accelerators ==
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| [[Accelerators:|Accelerators: 2 minute guides to fundamental principles.]] | |
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| == An Example ==
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| '''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:
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| $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
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| 'That's nice dear', she responds, unaware of the implications of your discovery.
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| 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.
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| Now, consider this single image.
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| [[File:sheetsunx.gif||Curved Space-Time]]
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| 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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| == Resources & References == | | == Resources & References == |
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| * [https://drive.google.com/open?id=1sB_LTltdq8J6mIKyPRaHQWKEuLk0ZXuwYQZb78BnNuk Working folder for Projects] | | * Files related to the projected can be found in a [https://drive.google.com/drive/folders/1yPZHTNy47jUpmD-RMRCVtitfD-gQBRhP Google Drive Folder]. |
| | * [https://drive.google.com/open?id=1sB_LTltdq8J6mIKyPRaHQWKEuLk0ZXuwYQZb78BnNuk List of Tasks related to the Project (no longer up to date)] |
| * [https://www.dropbox.com/s/xdickldblj574mf/eric%20wall%20-%20tome%20-%20graph.m4a?dl=0| Recording of original call w/ Eric] | | * [https://www.dropbox.com/s/xdickldblj574mf/eric%20wall%20-%20tome%20-%20graph.m4a?dl=0| Recording of original call w/ Eric] |
| * <span class="highlight">[[Eric’s Most Important Set of Books]]<span> | | * [[Eric’s Most Important Set of Books]] |
| * [https://physicstravelguide.com/ The Physics Travel Guide] (A didactic Wiki that explains concepts in three levels of difficulty.) | | * [https://physicstravelguide.com/ The Physics Travel Guide] (A didactic Wiki that explains concepts in three levels of difficulty.) |
| * Information about the GWT project were first collected in a Google Doc titled [https://docs.google.com/document/d/1Bo5ny0UyC8gEHiAaDR2Al2OSGscUWPS8NFI-hvB1z4o/edit?pli=1 Graph, Wall, Tome - Problem Solving]. | | * Information about the GWT project were first collected in a Google Doc titled [https://docs.google.com/document/d/1Bo5ny0UyC8gEHiAaDR2Al2OSGscUWPS8NFI-hvB1z4o/edit?pli=1 Graph, Wall, Tome - Problem Solving]. |
| | | * [https://www.youtube.com/playlist?list=PL5TiDYF_g45BA3abSyNl7M4pFzihZdoHT Relevant conversations with Eric on The Portal Discord Server] |
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| === Video Playlists ===
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| * [https://www.youtube.com/playlist?list=PL5TiDYF_g45BA3abSyNl7M4pFzihZdoHT Conversations with Eric on The Portal Discord Server] | |
| * [https://www.youtube.com/playlist?list=PL5TiDYF_g45Az5qgAP5Lj8Y3qKPSib1eP Misc recordings on The Portal Server for project and other notable conversations] | | * [https://www.youtube.com/playlist?list=PL5TiDYF_g45Az5qgAP5Lj8Y3qKPSib1eP Misc recordings on The Portal Server for project and other notable conversations] |
| * [https://www.youtube.com/playlist?list=PL5TiDYF_g45CyK7w7ZXH24FiuASYes2VO Wall-Tome-Graph Concept Explanation Videos]
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