Dualities

PHYSICS EQUIVALENCE AND CONVERGENCE HIERARCHY
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├── Interpretational Level
│   └── Interpretational Pluralism
│       ├── Quantum mechanics (Many-Worlds, Copenhagen, Pilot-wave)
│       ├── Thermodynamics (Entropy as information vs. disorder)
│       ├── Relativity (Block vs. evolving universe)
│       └── Quantum Measurement (Wavefunction collapse vs. decoherence)
│
├── Formal Level
│   ├── Mathematical Formulation Equivalence
│   │   ├── Newtonian ↔ Hamiltonian ↔ Lagrangian mechanics
│   │   ├── Quantum mechanics formulations (Schrödinger vs. Heisenberg vs. Path Integrals)
│   │   ├── Classical Electrodynamics (Vector potentials vs. Fields)
│   │   └── Perturbative vs. Geometric Formulations (Feynman diagrams ↔ intersecting fields/strings)
│   │
│   └── Duality (Structural Equivalence)
│       ├── AdS/CFT (Gauge/Gravity)
│       ├── Electromagnetic duality (Electric ↔ Magnetic fields)
│       ├── T-duality and S-duality in string theory
│       ├── Bosonization duality (Fermions ↔ Bosons in 1D)
│       └── Mirror symmetry in mathematics and string theory
│
└── Empirical Level
    ├── Principled Equivalence
    │   ├── Equivalence Principle (Gravity indistinguishable from acceleration)
    │   ├── Special relativity equivalence of inertial frames
    │   ├── Gauge invariance (Physical equivalence of gauge choices)
    │   └── Scale invariance (No absolute scale)
    │
    └── Phenomenological Convergence
        ├── Classical-Quantum Parallelism
        │   ├── Reflection and scattering (Quantum interference ↔ Classical bouncing)
        │   ├── Wave phenomena (Quantum diffraction ↔ Water/optical waves)
        │   └── Chaos (Quantum scars ↔ Classical chaotic orbits)
        │
        └── Emergent Universality
            ├── Statistical mechanics (Microscopic details ↔ Universal thermodynamic laws)
            ├── Central limit theorem universality
            ├── Renormalization group universality (Many microscopic theories → Few macroscopic fixed points)
            ├── Criticality and phase transitions (Spin systems ↔ Biological collective behavior)
            └── Complexity universality (Neural networks ↔ Bird flocking ↔ Econophysics)