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Geometric Unity - A Theory of Everything (Eric Weinstein)
Posted on Monday, July 04, 2022 @ 11:58:58 GMT by vlad

Science
Eric Ross Weinstein is the managing director of Thiel Capital, Peter Thiel's investment firm, since 2015. He and his brother Bret Weinstein coined the term Intellectual Dark Web to refer to an informal group of pundits.

From Lex Fridman interview with Eric on You Tube: Eric Weinstein is a mathematician with a bold and piercing intelligence, unafraid to explore the biggest questions in the universe and shine a light on the darkest corners of our society. He is the host of The Portal podcast, a part of which, he recently released his 2013 Oxford lecture on his theory of Geometric Unity that is at the center of his lifelong efforts in arriving at a theory of everything that unifies the fundamental laws of physics.


"Make things as simple as possible but no simpler" - Albert Einstein


 
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"Geometric Unity - A Theory of Everything (Eric Weinstein)" | Login/Create an Account | 1 comment | Search Discussion
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Re: Geometric Unity - A Theory of Everything (Eric Weinstein) (Score: 1)
by yru4 on Monday, July 04, 2022 @ 13:09:32 GMT
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Alex Omar's comment might be useful here: "Okay let me take a crack at explaining it. I've been wikipedia diving for a while. I tried to simplify the math in this explanation.

The problem with modern physics is that we have 2 models and both are good at describing things, but they cannot describe each other. For example, general relativity is useful but it doesn't have any concept of electricity. The Standard Model is also useful but it doesn't have any way to describe gravity. From a maths perspective there are also problems. GR uses maths relating to geometry and is concerned with the shape of space and time. The Standard Model uses maths relating to probability and individual particles.

Eric's theorem relates to the "Yang Mills Equations". These are equations which work on 4 dimensions and they have one really neat property. Dr. Yang and Dr. Mills showed that if you plug in certain values into their equations you actually can get equations which are identical to Maxwell's Equations (the 1800s classical electromagnetism equations). Physicists call this version of the Yang Mills Equations U(1).

U(1) is important in physics because it is one of the pieces of math which make up the Standard Model, specifically U(1) represents electromagnetism within the standard model. SU(3) is another set of equations which behave in the same way that we see the 12 particles behave. We use SU(3) to represent bosons, leptons, and quarks in the standard model. SU(2) is a set of equations which represent how spin particles (subatomic particles with spin) behave when undergoing special relativity. When physicists smash these equations together you get SU(3)xSU(2)xU(1), a very complex but very complete model of our universe. https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model

Still with me? Cool. Eric's PhD dissertation was on these Yang Mills Equations. He showed that these equations actually could represent more than 4 dimensions. All of the rules Dr. Yang and Dr. Mills proved about their equations on 4d vector spaces ALSO work on 8 dimensional vector spaces, and even more. Geometric Unity is this idea that, hey, if we use 14 dimensional Yang Mills Equations and we decide that 4 of dimensions are spacetime and the rest are rulers and protractors, not only can you get Maxwell's Equations but you can also get the rest of Einstein's equations! This is pretty neat. If physicists were able to continue work on this theory (which requires LOTS of math) and show that you can make a model like SU(3)xSU(2)xU(1) but with 14 dimensional versions of the pieces we might have a single theory which links general relativity and the standard model. We might also find that when extended into 14 dimensions the model stops working. We don't know yet.

Spinors: okay so spinors are a mathematical oddity that emerges when playing with equations that have to do with geometries and surfaces (Eric calls these manifolds). They are little things which, like Eric is saying, rotate 720 degrees. There's not much special about them, they just exist https://en.wikipedia.org/wiki/Spinor Eric's point is that there is a mathematical space he calls "the chimeric fiber bundle" which has pretty similar mathematical properties to his own 14 dimensional space. This chimeric fiber bundle also has spinors, but these spinors have a neat property where if you project/collapse the 14 dimensions down into just the 4 spacetime dimensions these spinors look just like the 12 particles of matter! They have internal quantum numbers and spin and angular momentum and all other things which we use to model particles within the standard model. So there is strong reason to believe that in Eric's mathematical model of the 14 dimensional yang mills equations we should try representing the 12 particles as spinors. If that works, Eric may have theory which is able to answer questions about electromagnetism, quantum mechanics, and relativity.

Why hasn't Eric shown that 14 dimension spinors inside his model are able to represent the 12 particles of matter? I'm not sure. Maybe he needs help, maybe he is exhausted, or both. I remember him mentioning somewhere that he was struggling with the math behind quantum electrodynamics. Maybe he is trying to recover the QED equations?"



 

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