The classical and quantum worlds are not as apart as we thought.
Eva Miranda, a renowned researcher in symplectic and Poisson geometry, explains how “hidden” geometric structures can unite classical and quantum frameworks. Eva dives into integrable systems, Bohr–Sommerfeld leaves, and the art of geometric quantization, revealing a promising path to bridging longstanding gaps in theoretical physics.
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Links Mentioned:
• Eva Miranda’s website: https://web.mat.upc.edu/eva.miranda/nova/
• Roger Penrose on TOE: https://www.youtube.com/watch?v=sGm505TFMbU
• Curt’s post on LinkedIn: https://www.linkedin.com/feed/update/urn:li:activity:7284265597671034880/
Timestamps:
00:00 – Introduction
06:12 – Classical vs. Quantum Mechanics
15:32 – Poisson Brackets & Symplectic Forms
24:14 – Integrable Systems
32:01 – Dirac’s Dream & No‐Go Results
39:04 – Action‐Angle Coordinates
47:05 – Toric Manifolds & Polytopes
54:55 – Geometric Quantization Basics
1:03:46 – Bohr–Sommerfeld Leaves
1:12:03 – Handling Singularities
1:20:23 – Poisson Manifolds Beyond Symplectic
1:28:50 – Turing Completeness & Fluid Mechanics Tie‐In
1:35:06 – Topological QFT Overview
1:45:53 – Open Questions in Quantization
1:53:20 – Conclusion
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