Eigenbros ep 120 - Timothy Nguyen (Problems with Eric Weinstein's Geometric Unity)
Juan & Terence interview mathematician PhD, with a background in gauge theory, Timothy Nguyen. Tim along with Theo Polya wrote a paper titled "A Response to Geometric Unity," which went through the major flaws in Eric's Weinstein's theory of physics. 1) Problems with the shiab operator, 2) gauge anomalies, 3) Supersymmetry issues in 14 dimensions, and 4) a lack of technical details.
#GeometricUnity #EricWeinstein #TOE
Timestamps:
0:00 : Eigenbros intro
1:41 : Introduction
6:43 : Comment about level of presentation
7:31 : Basic setup (manifolds, observerse, metrics)
11:40 : Fiber bundles
15:24 : Gauge theory
21:29 : Trivial fiber bundle
22:17 : Why fiber bundles?
25:20 : Which way is the wind blowing? Example of a nontrivial fiber bundle
29:28 : Hairy Ball Theorem
34:48 : Start of Geometric Unity; unitary matrices
39:38 : U(128)
42:40 : Start of GU as a Theory of Everything
42:47 : Standard Model
46:18 : General Relativity
46:48 : What is a Theory of Everything?
49:55 : Red flag for GU as a Theory of Everything
54:41 : A more modest proposal
56:20 : Why is Eric presenting GU in his way?
58:08 : Start of technical details of GU
1:06:29 : Equations of motion
1:08:22 : Shiab operator
1:15:50 : Objection #1: Shiab operator
1:26:59 : What is a cotangent space?
1:29:01 : Momentum is a cotangent vector
1:31:11 : A very concrete way to understand Objection #1 in dimension 2
1:32:36 : Mistakes in science
1:36:35 : Pauli matrices
1:38:00 : Multiplication rule is with respect to the Clifford algebra structure, not the exterior algebra structure. (Forgot to state this!)
1:42:14 : Quaternions
1:46:45 : Complexification and explicit failure mode
1:50:58 : Bott periodicity (Raoul Bott was Eric’s advisor)
1:54:14 : Shiab operator wrapup
1:56:10 : Objection #2: Gauge Anomaly
1:57:08 : Renormalization
1:57:50 : Anomalies
2:01:22 : Qualitative, simple illustration example of anomalies in terms of 1D integrals
2:12:05 : Why is it a gauge anomaly?
2:15:48 : Objection #3: Supersymmetry
2:18:08 : Objection #4: Numerous Omissions
2:19:33 : Seiberg-Witten equations
2:22:57 : First red flag: the right sign
2:24:24 : Second red flag: no mention of Spin^c
2:26:44 : Closing words: Terence hopes Eric Weinstein responds
Corrections:
2:07:44 : Should be no e^(i*theta)
2:17:57 : You can’t have fermions in 14 dimensions and super symmetry without additional work
2:20:50 : There should be a + superscript over F (to denote the self-dual part of the curvature)
References:
Books:
Differential geometry / fiber bundles / spinors: Jost, Riemannian geometry
Seiberg-Witten equations: See Morgan, The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds or Kronheimer & Mrowka, Monopoles and Three-Manifolds
Momentum is a cotangent vector: See Arnold, Mathematical Methods of Classical Mechanics
Response to Geometric Unity: https://timothynguyen.files.wordpress...
Decoding the Gurus podcast episode with Tim Nguyen: https://decoding-the-gurus.captivate....
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