notes from Preposterous Universe podcast episode 245

Notes from the podcast https://www.preposterousuniverse.com/podcast/2023/07/31/245-solo-the-crisis-in-physics/

Definitions of Understanding

• Strong understanding = unique, well-tested theory that accounts for all the data we have within the domain of applicability (defined by SMC at 14:00). 
• Consequences: There are no competing theories. Modifications or extensions are feasible, but the domain is "solved." The theory won't be displaced.
• Examples: general relativity, Newtonian dynamics, Newtonian gravity.
• Weak understanding = more than one theory can account for the data. Unable to discriminate which is relevant since theories make the same predictions. (defined by SMC at 15:44)
• Consequences: Not clear theory which is right. Right theory may not have been invented yet.
• Examples: 
• Foundations of quantum mechanics (e.g., Copenhagen interpretation, Bohemian, many worlds, jaggets platz)
• dark matter and dark energy in cosmology. Properties are known, but multiple theories
• dark matter: WIMPS, axions, 
• dark energy: vacuum energy, dynamical quintesense-like fields
• No understanding = have data but no theory (defined by SMC at 18:20)
• Examples: what happens at or before the big bang

SMC's claim: We have either a strong or weak understanding of everything that is accessible through measurement. (at 21:40) There's nothing that's experimentally accessible and not understood. That's new!

Survey of domains and relations

What is it that we know?

Newtonian dynamics. Space is separate from time. Deterministic Laplacian evolution.

Theory of relativity (1905, Einstein) explains space-time (as per Minkowski, 1907).  (SMC: 29:22)

Special Relativity: how space-time is when gravity is not important; when space-time is flat. (SMC 30:20)

General Relativity: space-time can be curved and that curvature is gravity. Predicts big bang, black holes. SMC 30:10)

Quantum Mechanics (1920, Heisenberg).
Replaces classical mechanics -- SMC 32:10

QM is about continuous wave function defined by Schrodinger Equation. 

Solving Schrodinger's Equation results in discrete solutions -- SMC 35:55

Quantum Field Theory. 
Under the umbrella of Quantum Mechanics -- SMC 32:33.
QFT is compatible with Special Relativity -- SMC 32:42

The world is made of fields, not particles. -- SMC 34:40

Fields resolve into particles when the fields are observed.

Relativistic QFT includes Special Relativity

Quantum Electrodynamics (QED) is the theory of interactions of electrons, positrons, photons.

Initial theory had infinities. Resolved infinities using renormalization by taking limit in a specific way.

Ken Wilson simulated QED using discretized space-time (rather than a continuous PDEs).
--> Lattice Quantum Field Theory eliminates the infinities. 

Infinities (represented as loops of Feynman diagrams) are reduced to (non-infinite) tree diagrams in Feynman diagrams. 

Rather than arbitrarily large momentum (small space), discretization constraints the infinities.

Limitation on the domain of applicability is the Planck scale. -- SMC 45:20

This is the ultraviolet cut-off. There's an energy above which we don't know what's going on. -- SMC 46:05

stopped at 53:30