Understanding the Universe

From foundations to frontiers. The full map of our journey.

▶ 1. Foundations Classical mechanics & mathematical tools
1.1 The Principle of Least Action
1.2 Lagrangian Mechanics
1.3 Symmetries & Conservation
1.4 Hamiltonian Mechanics
1.5 Mathematical Foundations
▶ 2. Quantum Mechanics The strange heart of reality
▶ 2.1 Foundations
2.1.1 Historical Motivations 2.1.2 The Postulates 2.1.3 Hilbert Space & Operators 2.1.4 Uncertainty Principle 2.1.5 Schrödinger vs Heisenberg Pictures
▶ 2.2 Exactly Solvable Problems
2.2.1 Free Particle & Wave Packets 2.2.2 Harmonic Oscillator 2.2.3 Hydrogen Atom 2.2.4 Angular Momentum & Spin
▶ 2.3 Approximation Methods
2.3.1 Perturbation Theory 2.3.2 Variational Methods 2.3.3 WKB Approximation
▶ 2.4 Entanglement & Measurement
2.4.1 Density Matrices 2.4.2 Entanglement 2.4.3 Bell Inequalities 2.4.4 Decoherence
▶ 2.5 Interpretations
2.5.1 Copenhagen 2.5.2 Many-Worlds (Everett) 2.5.3 Pilot Wave (de Broglie-Bohm) 2.5.4 Relational QM 2.5.5 QBism 2.5.6 Objective Collapse
▶ 2.6 Path Integrals
2.6.1 Feynman's Formulation 2.6.2 From Classical to Quantum 2.6.3 Applications
▶ 3. Electromagnetism Fields, waves, and gauge invariance
3.1 Maxwell's Equations
3.2 Electromagnetic Waves
3.3 Gauge Invariance
3.4 Relativistic Formulation
▶ 4. Special Relativity Spacetime geometry
4.1 Postulates & Lorentz Transformations 4.2 Spacetime Diagrams 4.3 4-Vectors & Invariants 4.4 Relativistic Mechanics 4.5 E = mc²
▶ 5. Statistical Physics From micro to macro
5.1 Entropy & the Second Law 5.2 Ensembles 5.3 Quantum Statistics 5.4 Phase Transitions 5.5 Information & Entropy
▶ 6. General Relativity Gravity as geometry
▶ 6.1 Differential Geometry
6.1.1 Manifolds 6.1.2 Tensors 6.1.3 Curvature 6.1.4 Geodesics
6.2 Einstein Field Equations 6.3 Schwarzschild Solution 6.4 Black Holes 6.5 Gravitational Waves 6.6 Cosmological Solutions
▶ 7. Quantum Field Theory Particles as field excitations
▶ 7.1 Free Fields
7.1.1 Klein-Gordon Field 7.1.2 Dirac Field 7.1.3 Electromagnetic Field
▶ 7.2 Interactions
7.2.1 S-Matrix 7.2.2 Feynman Diagrams 7.2.3 QED
▶ 7.3 Renormalization
7.3.1 UV Divergences 7.3.2 Regularization 7.3.3 Renormalization Group 7.3.4 Effective Field Theories
▶ 7.4 Gauge Theories
7.4.1 Yang-Mills Theory 7.4.2 Spontaneous Symmetry Breaking 7.4.3 Higgs Mechanism
▶ 8. The Standard Model Our best theory of matter
8.1 Particle Content 8.2 Electroweak Unification 8.3 QCD 8.4 Neutrino Physics 8.5 Beyond the Standard Model
▶ 9. Cosmology The universe at large
9.1 The Big Bang 9.2 Inflation 9.3 CMB Physics 9.4 Dark Matter 9.5 Dark Energy 9.6 Structure Formation
▶ 10. Frontiers Open problems & unification
▶ 10.1 Quantum Gravity
10.1.1 The Problem 10.1.2 String Theory 10.1.3 Loop Quantum Gravity 10.1.4 Causal Set Theory 10.1.5 Asymptotic Safety
▶ 10.2 Foundational Questions
10.2.1 The Measurement Problem 10.2.2 Time in Quantum Mechanics 10.2.3 The Arrow of Time 10.2.4 Why These Laws?
▶ 10.3 Information & Physics
10.3.1 Black Hole Information Paradox 10.3.2 Holographic Principle 10.3.3 It from Bit 10.3.4 ER = EPR
▶ 10.4 Cross-Field Connections
10.4.1 Emergence & Reduction 10.4.2 Mathematics & Physics 10.4.3 Computation & Physics