Physics Library

Physical models developed from explicit mathematical definitions, postulates and evidence, with physics theorems and worked examples.

Recent Updates

All 29 from the past 7 days →

In the past 7 days: 0 new pages · 29 pages revised · 141 results added

UpdatedAccelerated Observers10/10/2026
Special Relativity · 10 results added
UpdatedAlternative action formulation10/10/2026
Classical Electromagnetism · 3 results added
UpdatedCausality And Signals10/10/2026
Special Relativity · 10 results added
UpdatedElectrostatic boundaries and conductors10/10/2026
Classical Electromagnetism · 6 results added
UpdatedElectrostatic multipoles10/10/2026
Classical Electromagnetism · 1 result added

Classical Electromagnetism

Reading order →

36 published pages

Page	Companion	Dependency level
Primitives and postulates	Examples & counterexamples →	0
Energy momentum angular balance	Examples & counterexamples →	1
Integral Maxwell and constraints	Examples & counterexamples →	1
Potentials and gauge	Examples & counterexamples →	1
Electrostatics in vacuum	Examples & counterexamples →	2
Magnetostatics in vacuum	Examples & counterexamples →	2
Material response and stationary interfaces	Examples & counterexamples →	2
Vacuum waves and polarization	Examples & counterexamples →	2
Electrostatic boundaries and conductors	Examples & counterexamples →	3
Electrostatic multipoles	Examples & counterexamples →	3
Lorentz covariant formulation	Examples & counterexamples →	3
Wave interfaces and conductors	Examples & counterexamples →	3
Waveguides and cavities	Examples & counterexamples →	3
Alternative action formulation	Examples & counterexamples →	4
Induction and circuit approximations	Examples & counterexamples →	4
Retarded fields and radiation	Examples & counterexamples →	4
Empirical tests and limitations	Examples & counterexamples →	5
Vector PEC scattering, dipole limits and controlled scalar diffraction	Examples & counterexamples →	5

Classical Electromagnetism — Mathematics

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20 published pages

Page	Companion	Dependency level
Em Elementary Mathematical Prerequisites	Examples & counterexamples →	0
Em Minkowski Mathematical Prerequisites	Examples & counterexamples →	0
Em Expanded Analysis Prerequisites	Examples & counterexamples →	1
Em Variational Mathematical Prerequisites	Examples & counterexamples →	1
Em Boundary And Spectral Prerequisites	Examples & counterexamples →	2
Em Experiment Analysis Prerequisites	Examples & counterexamples →	2
Em Wave Equation Prerequisites	Examples & counterexamples →	2
Causal kernels, gauge and point fields after wave existence	Examples & counterexamples →	3
Em Causal Response And Radiation Prerequisites	Examples & counterexamples →	3
Complete retarded point fields	Examples & counterexamples →	4

Classical Statistical Mechanics

In preparation

Einstein–Maxwell Models

In preparation

Fluid Dynamics

In preparation

General Relativity

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30 published pages

Page	Companion	Dependency level
Framework And Geometry	Examples & counterexamples →	0
Tensors And Observers	Examples & counterexamples →	1
Connections And Free Fall	Examples & counterexamples →	2
Curvature And Tides	Examples & counterexamples →	3
Einstein And Matter	Examples & counterexamples →	4
Causal And Initial Value Boundaries	Examples & counterexamples →	5
Flat And Newtonian Bridges	Examples & counterexamples →	5
Homogeneous Cosmology	Examples & counterexamples →	5
Local And Global Energy	Examples & counterexamples →	5
Gr13 Convex Normal Neighborhoods	Examples & counterexamples →	6
Linearized Waves	Examples & counterexamples →	6
Spherical Vacuum Model	Examples & counterexamples →	6
Experimental Interface	Examples & counterexamples →	7
Gr14 Full High Regularity Symmetric Hyperbolic Proof	Examples & counterexamples →	7
Gr15 Exact Checked Sbierski Smooth Mghd Proof With Complete Local Prerequisites And Quotient Second Countability	Examples & counterexamples →	8

Non-relativistic Classical Mechanics

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36 published pages

Page	Companion	Dependency level
Framework, quantities and geometry	Examples & counterexamples →	0
Classical continua with explicit constitutive assumptions	Examples & counterexamples →	1
Forces, initial data and Newtonian flow	Examples & counterexamples →	1
Rigid-body configuration and inertia	Examples & counterexamples →	1
Momentum, work and energy balances	Examples & counterexamples →	2
Measurement, uncertainty and later bridges	Examples & counterexamples →	3
One-dimensional conservative and dissipative models	Examples & counterexamples →	3
Regular constraints and moving frames	Examples & counterexamples →	3
Two-body, central forces and gravitation	Examples & counterexamples →	3
Rigid-body dynamics and stability	Examples & counterexamples →	4
Scattering and impulse model boundaries	Examples & counterexamples →	4
Stationary action and Lagrangian dynamics	Examples & counterexamples →	4
Coupled oscillations and approximation	Examples & counterexamples →	5
Legendre transformation and Hamiltonian mechanics	Examples & counterexamples →	5
Symmetry, Noether and conditional conservation	Examples & counterexamples →	5
Symplectic geometry and canonical methods	Examples & counterexamples →	6
Hamilton–Jacobi and integrability	Examples & counterexamples →	7
Stability, perturbations and chaos	Examples & counterexamples →	7

Non-relativistic Classical Mechanics — Mathematics

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32 published pages

Page	Companion	Dependency level
Cm Math Balances	Examples & counterexamples →	0
Cm Math Evidence	Examples & counterexamples →	0
Cm Math Fluid	Examples & counterexamples →	0
Cm Math Geometry	Examples & counterexamples →	0
Cm Math Central	Examples & counterexamples →	1
Cm Math Continuum	Examples & counterexamples →	1
Cm Math Dynamics	Examples & counterexamples →	1
Cm Math Rigid	Examples & counterexamples →	1
Rotation Double Cover	Examples & counterexamples →	1
Cm Math Approximation	Examples & counterexamples →	2
Cm Math Canonical	Examples & counterexamples →	2
Cm Math Variations	Examples & counterexamples →	2
Cm Math Chaos	Examples & counterexamples →	3
Cm Math Kam	Examples & counterexamples →	3
Cm Math Verification	Examples & counterexamples →	3
Symplectic Verlet and analytic backward error	Examples & counterexamples →	3

Non-relativistic Quantum Mechanics

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44 published pages

Page	Companion	Dependency level
Qm Framework And Quantities	Examples & counterexamples →	0
Qm State Geometry	Examples & counterexamples →	1
Qm Observables And Born Probabilities	Examples & counterexamples →	2
Qm Autonomous Dynamics	Examples & counterexamples →	3
Qm Measurement And Instruments	Examples & counterexamples →	3
Qm Massive Particle Kinematics	Examples & counterexamples →	4
Qm Composites Entanglement And Reduced States	Examples & counterexamples →	5
Qm Interference And Local Detection	Examples & counterexamples →	5
Qm One Dimensional Potentials	Examples & counterexamples →	5
Qm Symmetries And Conservation	Examples & counterexamples →	5
Qm Uncertainty And Compatibility	Examples & counterexamples →	5
Qm Angular Momentum And Spin	Examples & counterexamples →	6
Qm Central Potentials And Hydrogen	Examples & counterexamples →	6
Qm Harmonic Oscillator	Examples & counterexamples →	6
Qm Bell Models And Measurement Limits	Examples & counterexamples →	7
Qm Controlled Approximations	Examples & counterexamples →	7
Qm Driven Dynamics And Adiabatic Limits	Examples & counterexamples →	7
Qm Identical Particles And Exclusion	Examples & counterexamples →	7
Qm Three Dimensional Scattering	Examples & counterexamples →	7
Qm Many Body And Equilibrium Models	Examples & counterexamples →	8
Qm Photons And Radiation Modes	Examples & counterexamples →	8
Qm Light Matter And Spectral Transitions	Examples & counterexamples →	9

Non-relativistic Quantum Mechanics — Mathematics

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16 published pages

Page	Companion	Dependency level
Qm Math Composites	Examples & counterexamples →	0
Qm Math Oscillator	Examples & counterexamples →	1
Qm Math Intervals And Contacts	Examples & counterexamples →	2
Qm Math Orbital And Spin	Examples & counterexamples →	2
Qm Math Coulomb	Examples & counterexamples →	3
Qm Math Magnetic And Detection	Examples & counterexamples →	3
Qm Math Controlled Dynamics	Examples & counterexamples →	4
Qm Math Fock And Equilibrium	Examples & counterexamples →	4

Quantum Field Theory and QED

In preparation

Quantum Statistical Mechanics

In preparation

Relativistic Particle Mechanics

In preparation

Special Relativity

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24 published pages

Page	Companion	Dependency level
Spacetime Primitives	Examples & counterexamples →	0
Lorentz Transformations	Examples & counterexamples →	1
Worldlines And Clocks	Examples & counterexamples →	1
Causality And Signals	Examples & counterexamples →	2
Energy Momentum	Examples & counterexamples →	2
Light and Doppler	Examples & counterexamples →	2
Observer Measurements	Examples & counterexamples →	2
Accelerated Observers	Examples & counterexamples →	3
Experimental Interface	Examples & counterexamples →	3
Forces and Continuum	Examples & counterexamples →	3
Newtonian Bridge	Examples & counterexamples →	3
Proper Time Comparisons	Examples & counterexamples →	3

Thermodynamics

In preparation

Thermodynamics and General Relativity

In preparation