Theories of Everything with Curt Jaimungal

Quantum Physics Missing Link Discovered... [Geometric Quantization]

Jan 26, 2025

In this engaging discussion, Eva Miranda, a leading researcher in symplectic and Poisson geometry, explores how hidden geometric structures link classical and quantum frameworks. She reveals the art of geometric quantization and its promise in bridging theoretical physics gaps. Topics include integrable systems, Bohr–Sommerfeld leaves, and the fascinating relationship between fluid dynamics and computability. Eva's insights challenge traditional views, opening doors to a more unified understanding of the universe.

02:04:33

Episode guests

Eva Miranda

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Quick takeaways

The podcast discusses how hidden geometric structures can connect classical and quantum physics through geometric quantization techniques.

It emphasizes the wave-particle duality demonstrated in experiments like the double-slit, challenging classical physics interpretations.

Hamiltonian dynamics is presented as a way to transform classical mechanics, revealing the energy conservation in system evolution.

Integrable systems are highlighted for their predictability due to conserved quantities, offering insight into the behavior of dynamical systems.

Deep dives

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Intro

2min

Quantum Realities: Bridging Classical and Quantum Physics

12min

Exploring the Complexities of Classical and Quantum Systems

3min

Mysteries of Fluid Dynamics and Computability

7min

Unraveling Quantum Mechanics: From Classical Roots to Schrödinger's Equation

27min

Exploring Matrices and Rotational Symmetries in Quantum Physics

3min

Symplectic Geometry and Poisson Manifolds

29min

Exploring the Cotangent Bundle and Dirac's Quantization

5min

Exploring Lagrangian Foliations and Geometric Quantization

28min

10.

Exploring Quantization in Manifolds: A Productive Debate

2min

11.

Exploring Integrable Systems and Community Engagement in Theoretical Physics

5min

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.

As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe

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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#science #physics #theoreticalphysics

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