Theories of Everything with Curt Jaimungal Eva Miranda: The Mathematical Bridge Between Classical and Quantum
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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.
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Computability of Physical Systems
- Miranda believes not all physical systems will be computationally simulatable, challenging the universe-as-a-computer view.
- She has proven some systems are Turing complete but emphasizes the difficulty of proving computability universally.
Symplectic Forms and Dirac's Dream
- Symplectic forms, governing classical mechanics, link energy conservation to area evolution, unlike Riemannian geometry.
- Dirac's dream of a universal quantization rule fails for even simple quadratic functions, necessitating observable selection.
Poisson Brackets and Noether's Principle
- Poisson brackets, key to quantization, reveal Noether's principle: a function's bracket with itself is zero, implying energy conservation.
- Symplectic forms, crucial for conservative systems, canonically link position and momenta, unlike Riemannian geometry.