Linearity vs. Nonlinearity in QM

All but the last 20 minutes of this episode should be comprehensible to non-physicists.

Steve explains where frontier AI models are in understanding frontier theoretical physics. The best analogy is to a “brilliant but unreliable genius colleague”!

He describes a specific example: the use of AI in recent research in quantum field theory (Tomonaga-Schwinger integrability conditions applied to state-dependent modifications of quantum mechanics), work now accepted for publication in Physics Letters B after peer review. Remarkably, the main idea in the paper originated de novo from GPT-5.

Links:

• X discussion - https://x.com/hsu_steve/status/1996034522308026435
• Companion paper: Theoretical Physics With Generative AI -  https://drive.google.com/file/d/16sxJuwsHoi-fvTFbri9Bu8B9bqA6lr1H/view
• Physics paper - https://arxiv.org/abs/2511.15935 | https://www.sciencedirect.com/science/article/pii/S0370269325008111
• Related discussion of AI and theoretical physics with Prof. Nirmalya Kajuri (IIT) and Prof. Jonathan Oppenheim (UCL) - https://youtu.be/BRuDd3l0e3k
• Related video: AIs Win Math Olympiad Gold: Prof. Lin Yang (UCLA) – Manifold #97 - https://youtu.be/8JeRCqNg7Rc

Chapter markers:

• (00:00) - Intro: AI discussion with specialized physics at the end
• (03:40) - The current AI landscape for science: frontier models, Co-Scientist, and recent math breakthroughs
• (11:01) - Why models help and why they fail: errors, deep confabulation, and the research risk
• (15:54) - The Generator–Verifier workflow: how chaining model inference suppresses mistakes
• (23:30) - Project origin: testing models on Hsu’s older nonlinear QM/QFT work
• (30:35) - The “GPT-5 moment”: Tomonaga–Schwinger angle appears and produces the key equation
• (40:35) - Wild goose chases & a practical heuristic: axiomatic QFT detour; Generator-Verifier convergence
• (51:44) - Referee-driven test case: Kaplan–Rajendran model, past-lightcone geometry, and verification
• (55:55) - Tooling & outlook: automation prototype, chaining into “supermodels,” where this is headed
• (59:39) - Physics slides (advanced): TS integrability, microcausality, and why nonlinearity threatens locality

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Steve Hsu is Professor of Theoretical Physics and of Computational Mathematics, Science, and Engineering at Michigan State University. Previously, he was Senior Vice President for Research and Innovation at MSU and Director of the Institute of Theoretical Science at the University of Oregon. Hsu is a startup founder (SuperFocus.ai, SafeWeb, Genomic Prediction, Othram) and advisor to venture capital and other investment firms. He was educated at Caltech and Berkeley, was a Harvard Junior Fellow, and has held faculty positions at Yale, the University of Oregon, and MSU. Please send any questions or suggestions to manifold1podcast@gmail.com or Steve on X @hsu_steve.