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668 lines
71 KiB
Python
668 lines
71 KiB
Python
#!/usr/bin/env python3
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"""Build a comprehensive SQLite flatfile of all proven physics equations."""
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import sqlite3, os
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DB = "/home/allaun/physics_equations.db"
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if os.path.exists(DB): os.remove(DB)
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conn = sqlite3.connect(DB)
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cur = conn.cursor()
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cur.executescript("""
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CREATE TABLE domains (id INTEGER PRIMARY KEY, name TEXT UNIQUE, description TEXT, parent_domain_id INTEGER REFERENCES domains(id));
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CREATE TABLE equations (id INTEGER PRIMARY KEY, eq_number INTEGER, title TEXT, domain_id INTEGER REFERENCES domains(id), year_range TEXT, status TEXT DEFAULT 'Proven', significance TEXT, precision_note TEXT);
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CREATE TABLE sub_equations (id INTEGER PRIMARY KEY, equation_id INTEGER REFERENCES equations(id), subsection TEXT, name TEXT, latex_formula TEXT, description TEXT, conditions TEXT);
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CREATE TABLE constants (id INTEGER PRIMARY KEY, symbol TEXT, name TEXT, value_si TEXT, uncertainty TEXT, is_exact INTEGER DEFAULT 0);
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CREATE TABLE verifications (id INTEGER PRIMARY KEY, equation_id INTEGER REFERENCES equations(id), test_name TEXT, experiment TEXT, year INTEGER, precision_level TEXT, status TEXT DEFAULT 'Confirmed');
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CREATE TABLE open_problems (id INTEGER PRIMARY KEY, name TEXT, description TEXT, related_equation_ids TEXT);
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CREATE VIRTUAL TABLE IF NOT EXISTS eq_fts USING fts5(title, description, latex_formula, content='equations', content_rowid='id');
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""")
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domains = [
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(1,"Classical Mechanics","Forces, energy, momentum, rigid bodies, oscillations",None),
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(2,"Gravitation","Newtonian and relativistic gravity, orbits",None),
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(3,"Electromagnetism","Electric & magnetic fields, circuits, radiation",None),
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(4,"Thermodynamics","Heat, entropy, statistical mechanics, phase transitions",None),
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(5,"Quantum Mechanics","Wavefunctions, operators, uncertainty, spin",None),
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(6,"Relativity","Special and general relativity, spacetime, black holes",None),
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(7,"Quantum Field Theory","Standard Model, QED, QCD, electroweak, Yukawa",None),
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(8,"Cosmology","FLRW, Friedmann, CMB, BBN, dark energy",None),
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(9,"Fluid Dynamics","Navier-Stokes, turbulence, Bernoulli, aerodynamics",None),
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(10,"Optics","Wave optics, diffraction, interference, polarization, Snell",None),
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(11,"Acoustics","Sound waves, resonance, Doppler, standing waves",None),
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(12,"Condensed Matter","Solids, crystals, BCS, Josephson, magnetism, Bloch",None),
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(13,"Nuclear Physics","Decay, fission, fusion, shell model, neutrino oscillations",None),
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(14,"Astrophysics","Stellar structure, HR diagram, nucleosynthesis, compact objects",None),
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(15,"Plasma Physics","MHD, Debye screening, Alfvén waves, Saha ionization",None),
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(16,"Mathematical Physics","Noether, symmetry, Fourier, Stokes, Green, special functions",None),
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(17,"Statistical Mechanics","Ensembles, partition functions, fluctuation theorems",None),
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(18,"Continuum Mechanics","Hooke's law, Cauchy stress, Euler-Bernoulli beam",None),
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(19,"Information Theory","Shannon entropy, Landauer principle, channel capacity",None),
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(20,"Metrology","Fundamental constants, SI definitions",None),
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]
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cur.executemany("INSERT INTO domains VALUES (?,?,?,?)", domains)
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constants = [
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(1,"c","Speed of light","299792458 m/s","Exact",1),
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(2,"h","Planck constant","6.62607015e-34 J·s","Exact",1),
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(3,"hbar","Reduced Planck constant","1.054571817e-34 J·s","9.1e-9 rel",0),
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(4,"G","Gravitational constant","6.67430e-11 m³/(kg·s²)","2.2e-5 rel",0),
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(5,"k_B","Boltzmann constant","1.380649e-23 J/K","Exact",1),
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(6,"e","Elementary charge","1.602176634e-19 C","Exact",1),
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(7,"m_e","Electron mass","9.1093837015e-31 kg","3.0e-10 rel",0),
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(8,"m_p","Proton mass","1.67262192369e-27 kg","5.1e-11 rel",0),
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(9,"m_n","Neutron mass","1.67492749804e-27 kg","5.7e-11 rel",0),
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(10,"eps0","Vacuum permittivity","8.8541878128e-12 F/m","1.5e-10 rel",0),
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(11,"mu0","Vacuum permeability","1.25663706212e-6 N/A²","1.5e-10 rel",0),
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(12,"N_A","Avogadro number","6.02214076e23 mol⁻¹","Exact",1),
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(13,"alpha","Fine-structure constant","1/137.035999084","1.5e-10 rel",0),
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(14,"R_y","Rydberg energy","13.605693123 eV","1.1e-12 rel",0),
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(15,"a0","Bohr radius","5.29177210903e-11 m","1.1e-12 rel",0),
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(16,"mu_B","Bohr magneton","9.2740100783e-24 J/T","3.0e-10 rel",0),
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(17,"sigma_SB","Stefan-Boltzmann constant","5.670374419e-8 W/(m²·K⁴)","3.7e-7 rel",0),
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(18,"G_F","Fermi constant","1.1663787e-5 GeV⁻²","5.1e-7 rel",0),
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(19,"Lambda_QCD","QCD scale","~0.210 GeV","~7%",0),
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(20,"H0","Hubble constant","67.4 km/(s·Mpc)","0.7%",0),
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(21,"l_P","Planck length","1.616255e-35 m","Derived",0),
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(22,"t_P","Planck time","5.391247e-44 s","Derived",0),
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(23,"m_P","Planck mass","2.176434e-8 kg","Derived",0),
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(24,"T_CMB","CMB temperature today","2.72548 K","5.7e-4 rel",0),
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(25,"R_gas","Gas constant","8.314462618 J/(mol·K)","Exact",1),
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(26,"Phi0","Magnetic flux quantum","2.067833848e-15 Wb","1.9e-9 rel",0),
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(27,"sigma_el","Electrical conductivity (Cu)","5.96e7 S/m","Material",0),
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(28,"mu_N","Nuclear magneton","5.0507837461e-27 J/T","3.0e-10 rel",0),
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(29,"lambda_C","Electron Compton wavelength","2.42631023867e-12 m","3.0e-10 rel",0),
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(30,"r_e","Classical electron radius","2.8179403262e-15 m","Derived",0),
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]
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cur.executemany("INSERT INTO constants VALUES (?,?,?,?,?,?)", constants)
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# (id, eq_number, title, domain, year, status, significance, precision)
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eq = []
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def E(id, num, title, dom, year, status, sig, prec):
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eq.append((id, num, title, dom, year, status, sig, prec))
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# CLASSICAL MECHANICS (1-25)
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E(1,1,"Newton's Three Laws of Motion",1,"1687","Proven","Foundation of all classical mechanics; inertial frames; F=dp/dt; action=reaction","Exact in v<<c, weak gravity")
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E(2,2,"Lagrangian Mechanics (Principle of Least Action)",1,"1788","Proven","Action S=∫L dt; δS=0 → Euler-Lagrange equations","Mathematical theorem — exact")
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E(3,3,"Hamiltonian Mechanics",1,"1833","Proven","Canonical eqs: q̇=∂H/∂p, ṗ=−∂H/∂q; symplectic structure","Equivalent to Lagrangian; exact")
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E(4,4,"Hamilton-Jacobi Equation",1,"1834","Proven","∂S/∂t + H(q,∂S/∂q,t)=0; bridges classical→quantum","Exact; classical limit of Schrödinger")
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E(5,5,"Euler-Lagrange Equation",1,"1744–88","Proven","d/dt(∂L/∂q̇) − ∂L/∂q = 0; from δS=0","Exact consequence of calculus of variations")
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E(6,6,"D'Alembert's Principle",1,"1743","Proven","Virtual work for dynamics: Σ(F_i−ṗ_i)·δr_i=0","Exact; leads to Lagrange equations")
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E(7,7,"Euler's Rigid Body Rotation Equations",1,"1765","Proven","I·ω̇ + ω×(I·ω) = τ; angular momentum dynamics","Confirmed: gyroscopes, satellites, robots")
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E(8,8,"Conservation of Momentum",1,"1687","Proven","dP/dt = ΣF_ext; P constant when ΣF_ext=0","Spatial translation symmetry; Noether; never violated")
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E(9,9,"Conservation of Angular Momentum",1,"1687","Proven","dL/dt = τ_ext; L=Iω constant when τ=0","Rotational symmetry; never violated")
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E(10,10,"Conservation of Energy",1,"1847","Proven","dE/dt=0 for isolated system; time translation symmetry","Never violated in any closed system")
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E(11,11,"Work-Energy Theorem",1,"1829","Proven","W=ΔKE; ∫F·dr = ½mv²_f − ½mv²_i","Consequence of Newton's 2nd; exact for point particles")
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E(12,12,"Impulse-Momentum Theorem",1,"1687","Proven","J=∫F dt=Δp","Derived from F=dp/dt; exact")
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E(13,13,"Center of Mass Equation",1,"1687","Proven","MR̈_cm=ΣF_ext; COM moves like point particle","Exact consequence of Newton's 3rd")
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E(14,14,"Hooke's Law",18,"1660","Proven","F=−kx; σ=Eε; linear elastic response","Valid up to elastic limit")
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E(15,15,"Parallel Axis Theorem",1,"1673","Proven","I=I_cm+Md²","Exact geometric theorem")
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E(16,16,"Coriolis Force",1,"1835","Proven","F_cor=−2m ω×v' (rotating frame)","Foucault pendulum; weather; ballistics")
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E(17,17,"Centrifugal Force",1,"1687","Proven","F_cf=−m ω×(ω×r) (rotating frame)","Fictitious force in rotating frame; confirmed")
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E(18,18,"Simple Harmonic Motion",1,"1673","Proven","ẍ+ω²x=0; x=A cos(ωt+φ); T=2π/ω","All oscillators; exact for linear restoring force")
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E(19,19,"Damped Harmonic Oscillator",1,"19th c.","Proven","ẍ+2βẋ+ω₀²x=0; under/over/critically damped","Confirmed in all damped mechanical systems")
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E(20,20,"Forced Oscillator + Resonance",1,"19th c.","Proven","ẍ+2βẋ+ω₀²x=(F₀/m)cos ωt; A=F₀/m/√((ω₀²−ω²)²+4β²ω²)","All driven oscillators; confirmed")
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E(21,21,"Coupled Oscillators (Normal Modes)",1,"18th c.","Proven","mẍ₁=−k x₁−k'(x₁−x₂); symmetric/antisymmetric modes","Confirmed: molecular vibrations, engineering")
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E(22,22,"Pendulum Equation",1,"1638","Proven","θ̈+(g/L)sin θ=0; small angle: ω=√(g/L)","Galileo's law of isochronism; confirmed")
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E(23,23,"Kinematics (Constant Acceleration)",1,"Ancient","Proven","v=v₀+at, x=x₀+v₀t+½at², v²=v₀²+2aΔx","Exact for constant a")
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E(24,24,"Universal Gravitation Law",2,"1687","Proven","F=−G m₁m₂/r² r̂","Weak-field limit of GR; inverse-square to 10⁻¹⁶")
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E(25,25,"Gravitational Potential Energy",2,"1773","Proven","U=−GMm/r; F=−∇U","Scalar potential; confirmed")
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# GRAVITATION (26-35)
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E(26,26,"Kepler's First Law",2,"1609","Proven","Planetary orbits are ellipses with Sun at one focus","Derived from inverse-square force")
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E(27,27,"Kepler's Second Law",2,"1609","Proven","Equal areas swept in equal times (areal velocity constant)","Angular momentum conservation")
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E(28,28,"Kepler's Third Law",2,"1619","Proven","T²∝a³; T²=(4π²/GM)a³","Confirmed for all gravitational two-body systems")
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E(29,29,"Escape Velocity",2,"1687","Proven","v_esc=√(2GM/r)","Energy conservation; spaceflight confirmed")
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E(30,30,"Orbital Velocity (Circular)",2,"1687","Proven","v_orb=√(GM/r)","Exact for circular two-body orbits")
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E(31,31,"Poisson Equation (Gravity)",2,"1813","Proven","∇²Φ=4πGρ","Newtonian limit of Einstein field eqs")
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E(32,32,"Tidal Force",2,"1687","Proven","F_tide≈2GMmΔr/r³","Earth-Moon tides; Roche limit; confirmed")
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E(33,33,"Gravitational Time Dilation (GR)",6,"1907","Proven","Δt'=Δt√(1−2GM/rc²)","Pound-Rebka 1960; GPS correction; confirmed")
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E(34,34,"Precession of Perihelion (GR)",6,"1915","Proven","Δφ=6πGM/(a(1−e²)c²) per orbit","Mercury 43\"/century; confirmed to <0.1%")
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E(35,35,"Lense-Thirring Precession (Frame Dragging)",6,"1918","Proven","Ω_LT=GJ/(2c²r³)(3(r̂·Ĵ)r̂−Ĵ)","Gravity Probe B; LAGEOS; ~10% precision")
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# ELECTROMAGNETISM (36-65)
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E(36,36,"Coulomb's Law",3,"1785","Proven","F=(1/4πε₀)q₁q₂/r² r̂","Inverse-square confirmed to δ<10⁻¹⁶")
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E(37,37,"Lorentz Force Law",3,"1895","Proven","F=q(E+v×B)","Every accelerator validates it")
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E(38,38,"Maxwell's Equations (Differential)",3,"1861–65","Proven","∇·E=ρ/ε₀, ∇·B=0, ∇×E=−∂B/∂t, ∇×B=μ₀J+μ₀ε₀∂E/∂t","Most tested equations; unified E&M+optics")
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E(39,39,"Maxwell's Equations (Integral)",3,"1861–65","Proven","∮E·dA=Q/ε₀, ∮B·dA=0, ∮E·dl=−dΦ_B/dt, ∮B·dl=μ₀I+μ₀ε₀dΦ_E/dt","Equivalent; engineering applications")
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E(40,40,"Maxwell's Equations (Covariant / Tensor)",3,"1908","Proven","∂_μF^{μν}=μ₀J^ν; ∂_μF̃^{μν}=0","Relativistic form; exact")
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E(41,41,"Scalar and Vector Potentials",3,"19th c.","Proven","B=∇×A; E=−∇φ−∂A/∂t","Gauge-dependent potentials; EM fields gauge-invariant")
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E(42,42,"Gauge Invariance (U(1) in E&M)",3,"1918","Proven","A_μ→A_μ+∂_μΛ; E,B unchanged","Exact; foundation of QED")
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E(43,43,"Biot-Savart Law",3,"1820","Proven","dB=(μ₀/4π) I dl×r̂/r²","Magnetostatics; exact for steady currents")
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E(44,44,"Ampère's Force Law (Wire)",3,"1825","Proven","dF=I dl×B","Exact in magnetostatics")
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E(45,45,"Ohm's Law",3,"1827","Proven","V=IR; J=σE","Universal in ohmic materials")
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E(46,46,"Kirchhoff's Current Law (KCL)",3,"1845","Proven","ΣI_in=ΣI_out at junction","Charge conservation; exact")
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E(47,47,"Kirchhoff's Voltage Law (KVL)",3,"1845","Proven","ΣV around closed loop=0","Conservative E field in lumped circuits; exact")
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E(48,48,"Faraday's Law of Induction",3,"1831","Proven","ε=−dΦ_B/dt; induced EMF=−flux change","Every generator, transformer, MRI")
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E(49,49,"Lenz's Law",3,"1834","Proven","Induced current opposes flux change","Consequence of energy conservation")
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E(50,50,"Poynting's Theorem",3,"1884","Proven","∂u/∂t+∇·S=−J·E; S=(1/μ₀)E×B","Energy conservation in EM fields")
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E(51,51,"Electromagnetic Wave Equation",3,"1865","Proven","□E=0; □B=0; c=1/√(μ₀ε₀)","Maxwell predicted EM waves; Hertz 1887")
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E(52,52,"EM Stress-Energy Tensor",3,"1908","Proven","T^{μν}=(1/μ₀)[F^μ_α F^{να}+¼g^{μν}F²]","Relativistic formulation; exact")
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E(53,53,"Lienard-Wiechert Potentials",3,"1898–1900","Proven","Retarded potentials for arbitrarily moving point charge","Radiation from accelerated charges")
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E(54,54,"Larmor Formula (Non-rel. Radiation)",3,"1897","Proven","P=q² a²/(6πε₀ c³)","Synchrotron radiation confirmed")
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E(55,55,"Liénard Formula (Relativistic Radiation)",3,"1898","Proven","P=(q²γ⁶/6πε₀c³)[a²−(v×a)²/c²]","Accelerator beam energy loss confirmed")
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E(56,56,"Abraham-Lorentz Force (Radiation Reaction)",3,"1905","Proven","F_rad=(q²/6πε₀c³)d³r/dt³","Qualitatively confirmed; pathological pre-accel.")
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E(57,57,"Coulomb Gauge",3,"1867","Proven","∇·A=0","Gauge choice for radiation problems")
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E(58,58,"Lorenz Gauge",3,"1867","Proven","∂_μ A^μ=0","Covariant gauge; Maxwell eqs diagonalize")
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E(59,59,"RC Circuit Charging",3,"19th c.","Proven","q(t)=C ε(1−e^{−t/RC}); τ=RC","Every RC circuit")
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E(60,60,"RL Circuit Time Constant",3,"19th c.","Proven","I(t)=I₀ e^{−tR/L}; τ=L/R","Every RL circuit")
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E(61,61,"LC Oscillation",3,"19th c.","Proven","ω₀=1/√(LC); q̈+ω₀² q=0","Radios, resonant circuits")
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E(62,62,"RLC Damped Oscillation",3,"19th c.","Proven","q̈+(R/L)q̇+(1/LC)q=0; γ=R/(2L)","All RLC circuits")
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E(63,63,"Skin Effect",3,"1883","Proven","δ=√(2/ωμσ); penetration depth","High-frequency conductors")
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E(64,64,"Dielectric Polarization (Linear)",3,"19th c.","Proven","D=ε₀E+P=ε_r ε₀ E","Linear dielectric response confirmed")
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E(65,65,"Magnetic Susceptibility",3,"19th c.","Proven","M=χ_m H; B=μ₀(H+M)=μ_r μ₀ H","Paramagnets, diamagnets, ferromagnets confirmed")
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# THERMODYNAMICS (66-85)
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E(66,66,"Zeroth Law of Thermodynamics",4,"1931","Proven","Thermal equilibrium is transitive; defines temperature","Every thermometer")
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E(67,67,"First Law of Thermodynamics",4,"1850","Proven","dU=δQ−δW; ΔU=Q−W","Energy conservation; never violated")
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E(68,68,"Second Law of Thermodynamics",4,"1850","Proven","dS_total≥0; entropy never decreases","Statistical law; no macro violation")
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E(69,69,"Third Law of Thermodynamics",4,"1912","Proven","S→0 as T→0 (perfect crystal)","Confirmed; residual entropy in glasses, ice")
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E(70,70,"Ideal Gas Law",4,"1834","Proven","pV=nRT=N k_B T","Limit of real gases at low P/high T")
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E(71,71,"Van der Waals Equation of State",4,"1873","Proven","(p+an²/V²)(V−nb)=nRT","Real gas corrections; qualitatively correct")
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E(72,72,"Kinetic Theory: Pressure",4,"1857","Proven","p=(1/3) N m ⟨v²⟩/V","Microscopic derivation of ideal gas law")
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E(73,73,"Equipartition Theorem",4,"1845","Proven","⟨E⟩=f k_B T/2; C_V=(f/2)R","Confirmed at high T; quantum corrections at low T")
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E(74,74,"Maxwell-Boltzmann Speed Distribution",4,"1860","Proven","f(v)=4π(m/2πk_B T)^{3/2} v² e^{−mv²/2kBT}","Molecular beams; Stern-Gerlach confirmed")
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E(75,75,"Carnot Efficiency",4,"1824","Proven","η_max=1−T_c/T_h","Upper bound; all heat engines obey")
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E(76,76,"Clausius-Clapeyron Relation",4,"1834","Proven","dP/dT=L/(T ΔV) for phase coexistence","Phase boundary slopes; confirmed")
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E(77,77,"Gibbs Phase Rule",4,"1876","Proven","F=C−P+2","Multi-component equilibrium; confirmed")
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E(78,78,"Helmholtz Free Energy",4,"1882","Proven","F=U−TS; ΔF≤0 at const T,V (spontaneous)","Legendre transform; exact")
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E(79,79,"Gibbs Free Energy",4,"1876","Proven","G=H−TS; ΔG≤0 at const T,P (spontaneous)","Chemical thermodynamics workhorse")
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E(80,80,"Enthalpy",4,"1875","Proven","H=U+pV; ΔH=Q_p","Constant pressure heat; exact")
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E(81,81,"Maxwell Relations (Thermodynamics)",4,"1871","Proven","(∂T/∂V)_S=−(∂p/∂S)_V; (∂T/∂p)_S=(∂V/∂S)_p; (∂S/∂V)_T=(∂p/∂T)_V; (∂S/∂p)_T=−(∂V/∂T)_p","Cross-derivative equalities; exact")
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E(82,82,"TdS Equations",4,"19th c.","Proven","T dS=C_V dT+T(∂p/∂T)_V dV; T dS=C_p dT−T(∂V/∂T)_p dp","General thermodynamic identities")
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E(83,83,"Specific Heat Relations (C_p−C_V)",4,"19th c.","Proven","C_p−C_V=−T(∂V/∂T)_p²/(∂V/∂p)_T=TVα²/κ_T","Confirmed for all substances")
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E(84,84,"Joule-Thomson Coefficient",4,"1852","Proven","μ_JT=(∂T/∂p)_H=(V/C_p)(Tα−1)","Gas liquefaction; confirmed")
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E(85,85,"Entropy of Mixing",4,"19th c.","Proven","ΔS_mix=−k_B(N₁ ln x₁+N₂ ln x₂)","Ideal mixing; confirmed")
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# QUANTUM MECHANICS (86-120)
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E(86,86,"Planck's Blackbody Radiation Law",5,"1900","Proven","B_ν=(2hν³/c²)/(e^{hν/kT}−1)","CMB fits to 50ppm; COBE/FIRAS 1990")
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E(87,87,"Wien's Displacement Law",5,"1893","Proven","λ_max T=2.898×10⁻³ m·K","All thermal radiation")
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E(88,88,"Stefan-Boltzmann Law",5,"1879–84","Proven","j*=σ T⁴; σ=2π⁵k_B⁴/(15h³c²)","Confirmed; consequence of Planck")
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E(89,89,"Photoelectric Effect Equation (Einstein)",5,"1905","Proven","K_max=hν−φ; photon quanta","Millikan 1916 confirmed; quantum foundation")
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E(90,90,"Einstein A and B Coefficients",5,"1917","Proven","A_21/B_21=8πhν³/c³; B_12/B_21=g₂/g₁","Laser theory foundation; confirmed")
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E(91,91,"Compton Scattering Formula",5,"1923","Proven","Δλ=(h/m_e c)(1−cos θ); Δλ_max≈0.00486 nm","Every Compton experiment confirmed")
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E(92,92,"de Broglie Wavelength",5,"1924","Proven","λ=h/p=h/(γmv)","Davisson-Germer 1927; every electron microscope")
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E(93,93,"Schrödinger Equation (Time-Dependent)",5,"1926","Proven","iℏ∂ψ/∂t=Ĥψ","Never falsified for non-relativistic QM")
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E(94,94,"Time-Independent Schrödinger Equation",5,"1926","Proven","Ĥψ=Eψ","All atomic/molecular spectra")
|
||
E(95,95,"Born Rule (Probability Interpretation)",5,"1926","Proven","ρ(r,t)=|ψ(r,t)|²","All quantum measurements; never violated")
|
||
E(96,96,"Probability Current (QM)",5,"1926","Proven","j=(ℏ/2mi)(ψ*∇ψ−ψ∇ψ*); ∂ρ/∂t+∇·j=0","Continuity equation; exact")
|
||
E(97,97,"Canonical Commutation Relations",5,"1925","Proven","[x̂_i,p̂_j]=iℏδ_{ij}","Quantization postulate; exact")
|
||
E(98,98,"Heisenberg Uncertainty Principle",5,"1927","Proven","Δx·Δp≥ℏ/2; ΔE·Δt≥ℏ/2","Operator non-commutation; confirmed")
|
||
E(99,99,"Harmonic Oscillator Energy Levels (QM)",5,"1926","Proven","E_n=ℏω(n+½); â|n⟩=√n|n−1⟩, â†|n⟩=√(n+1)|n+1⟩","Molecular vibrations, trapped ions")
|
||
E(100,100,"Hydrogen Atom Energy Levels",5,"1913–26","Proven","E_n=−R_y/n²; R_y=13.605693123 eV","1S-2S to 10⁻¹⁰; QED corrections confirmed")
|
||
E(101,101,"Angular Momentum Quantization",5,"1926","Proven","L²|l,m⟩=ℏ² l(l+1); L_z|l,m⟩=ℏ m","Universally confirmed")
|
||
E(102,102,"Spin-½ Algebra (Pauli Matrices)",5,"1927","Proven","S=(ℏ/2)σ; [σ_i,σ_j]=2iε_{ijk}σ_k; {σ_i,σ_j}=2δ_{ij}","All spin-½ systems; exact")
|
||
E(103,103,"Spin-Orbit Coupling",5,"1926","Proven","H_SO=(1/2m²c²)(1/r)(dV/dr) L·S","Fine structure; nuclear shell model")
|
||
E(104,104,"Dirac Equation",5,"1928","Proven","(iℏγ^μ∂_μ−mc)ψ=0","Predicted positron; g-2 to 10⁻¹²")
|
||
E(105,105,"Klein-Gordon Equation",5,"1926","Proven","(□+m²c²/ℏ²)φ=0","Scalar particles; pions, Higgs")
|
||
E(106,106,"Fine Structure Formula (Hydrogen)",5,"1928","Proven","ΔE_FS=(R_y α²/n³)[1/(j+½)−3/(4n)]","Dirac+SO+Darwin; confirmed")
|
||
E(107,107,"Lamb Shift",5,"1947","Proven","ΔE(2S−2P)≈1057.8 MHz; QED vacuum effects","Lamb-Retherford 1947; confirmed QED")
|
||
E(108,108,"Anomalous Magnetic Moment (Electron)",7,"1948","Proven","a_e=(g−2)/2≈0.00115965218091; QED+EW+hadronic","Most precise QFT test: 10⁻¹²")
|
||
E(109,109,"Pauli Exclusion Principle",5,"1925","Proven","No two identical fermions in same quantum state; ψ antisymmetric","Periodic table; neutron stars; violation <10⁻²⁹")
|
||
E(110,110,"Spin-Statistics Theorem",5,"1939–40","Proven","Half-int spin→fermion (anticommutators); int→boson (commutators)","Relativistic QFT theorem; never violated")
|
||
E(111,111,"Fermi's Golden Rule",5,"1927","Proven","Γ_{i→f}=(2π/ℏ)|⟨f|V|i⟩|² ρ(E_f)","Transition rates; all spectroscopy")
|
||
E(112,112,"Time-Dependent Perturbation Theory (1st Order)",5,"1926","Proven","c_f(t)=−(i/ℏ)∫₀ᵗ ⟨f|V(t')|i⟩ e^{iω_fi t'} dt'","Transition amplitudes; exact to 1st order")
|
||
E(113,113,"WKB Approximation",5,"1926","Proven","ψ∼(1/√p)exp(±i∫ p dx/ℏ); Bohr-Sommerfeld quantization","Semiclassical; α-decay, tunneling")
|
||
E(114,114,"Born Approximation (Scattering)",5,"1926","Proven","f(θ,φ)=−(2m/ℏ²)(1/4π)∫ e^{−iq·r} V(r) d³r","1st-order scattering; nuclear physics")
|
||
E(115,115,"Partial Wave Expansion (Scattering)",5,"1947","Proven","f(θ)=(1/k)Σ(2l+1)e^{iδ_l} sin δ_l P_l(cos θ)","Exact scattering; phase shift analysis")
|
||
E(116,116,"Optical Theorem",5,"1951","Proven","Im f(0)=(k/4π)σ_total","Unitarity of scattering; exact")
|
||
E(117,117,"Feynman Path Integral",5,"1948","Proven","⟨x_f,t_f|x_i,t_i⟩=∫ D[x(t)] exp(iS[x]/ℏ)","Equivalent to Schrödinger/Heisenberg; QFT foundation")
|
||
E(118,118,"Von Neumann Equation",5,"1927","Proven","iℏ ∂ρ̂/∂t=[Ĥ,ρ̂]","Quantum Liouville; mixed states; exact")
|
||
E(119,119,"Ehrenfest Theorem",5,"1927","Proven","d⟨A⟩/dt=(1/iℏ)⟨[A,Ĥ]⟩+⟨∂A/∂t⟩","Quantum expectation values obey classical EOM")
|
||
E(120,120,"Bell's Inequality",5,"1964","Proven","|E(a,b)−E(a,c)|≤1+E(b,c)","Local realism ruled out at >40σ")
|
||
|
||
# RELATIVITY (121-135)
|
||
E(121,121,"Lorentz Transformations (Boost)",6,"1905","Proven","x'=γ(x−vt); t'=γ(t−vx/c²); γ=1/√(1−v²/c²)","All SR applications; confirmed to 10⁻¹⁷")
|
||
E(122,122,"Minkowski Spacetime Interval",6,"1908","Proven","ds²=−c²dt²+dx²+dy²+dz²=η_μν dx^μ dx^ν","Flat spacetime; Lorentz invariant")
|
||
E(123,123,"Time Dilation",6,"1905","Proven","Δt'=γΔt (moving clock runs slow)","Muon lifetime; GPS; Hafele-Keating 1971")
|
||
E(124,124,"Length Contraction",6,"1905","Proven","L'=L/γ (moving object contracts)","Particle physics; confirmed")
|
||
E(125,125,"Relativistic Energy-Momentum Relation",6,"1905","Proven","E²=(pc)²+(mc²)²; E=γmc²; p=γmv","Every accelerator; confirmed")
|
||
E(126,126,"Mass-Energy Equivalence",6,"1905","Proven","E=mc²; ΔE=Δm c²","Nuclear reactions; particle-antiparticle annihilation")
|
||
E(127,127,"Relativistic Doppler Effect",6,"1905","Proven","f_obs=f_s√[(1+β)/(1−β)] (longitudinal); transverse: f_obs=γf_s","Ives-Stilwell 1938; confirmed")
|
||
E(128,128,"Relativistic Velocity Addition",6,"1905","Proven","u=(u'+v)/(1+u'v/c²)","Never exceeds c; confirmed")
|
||
E(129,129,"Einstein Field Equations (GR)",6,"1915","Proven","G_μν+Λg_μν=(8πG/c⁴)T_μν","All GR tests; GPS, LIGO, EHT; confirmed")
|
||
E(130,130,"Einstein-Hilbert Action",6,"1915","Proven","S=(c⁴/16πG)∫ d⁴x√(−g)(R−2Λ)+S_matter","Action principle for GR; exact")
|
||
E(131,131,"Schwarzschild Metric",6,"1916","Proven","ds²=−(1−r_s/r)c²dt²+dr²/(1−r_s/r)+r²dΩ²; r_s=2GM/c²","Non-rotating BH; gravitational redshift confirmed")
|
||
E(132,132,"Kerr Metric (Rotating Black Hole)",6,"1963","Proven","Rotating axisymmetric vacuum solution; a=J/Mc","Frame-dragging; EHT imaging; confirmed")
|
||
E(133,133,"FLRW Metric",6,"1922–35","Proven","ds²=−c²dt²+a²(t)[dr²/(1−kr²)+r²dΩ²]","Homogeneous isotropic cosmology; ΛCDM found.")
|
||
E(134,134,"Geodesic Equation",6,"1915","Proven","d²x^μ/dτ²+Γ^μ_αβ(dx^α/dτ)(dx^β/dτ)=0","Free-fall in curved spacetime; exact")
|
||
E(135,135,"Gravitational Wave (TT Gauge)",6,"1918","Proven","h_μν^{TT} has only h_+,h_× spatial transverse components","LIGO; PSR B1913+16 energy loss; confirmed")
|
||
|
||
# BLACK HOLE THERMODYNAMICS
|
||
E(136,136,"Bekenstein-Hawking Black Hole Entropy",6,"1972–74","Proven","S_BH=k_B A/4ℓ_P²=k_B c³A/(4Gℏ)","Horizon area/4; 4 laws map to thermodynamics")
|
||
E(137,137,"Hawking Temperature",6,"1974","Proven","T_H=ℏc³/(8πGMk_B); T_H(M⊙)≈6.2×10⁻⁸ K","Hawking radiation; analog gravity confirmed")
|
||
E(138,138,"Black Hole Area Theorem (Hawking 1971)",6,"1971","Proven","dA/dt≥0; horizon area never decreases","BH mechanics 2nd law; LIGO ringdown ~97% conf.")
|
||
|
||
# QFT / STANDARD MODEL (139-158)
|
||
E(139,139,"Standard Model Lagrangian (Full)",7,"1973","Proven","ℒ_SM=ℒ_gauge+ℒ_fermion+ℒ_Higgs+ℒ_Yukawa; SU(3)×SU(2)×U(1)","Most precise physical theory; all LHC data matches")
|
||
E(140,140,"Yang-Mills Field Strength",7,"1954","Proven","F_μν^a=∂_μA_ν^a−∂_νA_μ^a+gf^{abc}A_μ^bA_ν^c","Non-abelian gauge; QCD+EW foundation")
|
||
E(141,141,"QED Lagrangian",7,"1948","Proven","ℒ_QED=ψ̄(i∂̸−m)ψ−eψ̄γ^μψA_μ−¼F_μνF^{μν}","g-2 to 10⁻¹²; most precise theory")
|
||
E(142,142,"QCD Lagrangian",7,"1973","Proven","ℒ_QCD=Σψ̄_f(iD̸−m_f)ψ_f−¼G_a^{μν}G^a_{μν}","Asymptotic freedom; confinement; 0 falsifications")
|
||
E(143,143,"Electroweak Symmetry Breaking",7,"1967–68","Proven","SU(2)_L×U(1)_Y→U(1)_EM via Higgs VEV","W,Z masses predicted→confirmed")
|
||
E(144,144,"QCD Beta Function (1-loop)",7,"1973","Proven","β(α_s)=−(b₀/2π)α_s²; b₀=11−2n_f/3","Asymptotic freedom; α_s running over 4 decades")
|
||
E(145,145,"DGLAP Evolution Equations",7,"1972–77","Proven","∂q/∂lnQ²=(α_s/2π)∫(dz/z)[P_qq q+P_qg g]; gluon evolution similarly","HERA→LHC scaling confirmed")
|
||
E(146,146,"CKM Matrix (Quark Mixing)",7,"1973","Proven","3×3 unitary; 4 parameters (3 angles+1 CP phase)","All flavor physics; CP violation confirmed")
|
||
E(147,147,"PMNS Matrix (Neutrino Mixing)",7,"1962","Proven","3×3 leptonic mixing; θ₁₂≈33°,θ₂₃≈45°,θ₁₃≈8.5°","Neutrino oscillations; confirmed")
|
||
E(148,148,"Gell-Mann–Oakes–Renner Relation",7,"1968","Proven","m_π²=−(m_u+m_d)⟨ψ̄ψ⟩/f_π²","Chiral symmetry breaking; pion mass from quark masses")
|
||
E(149,149,"Higgs Mechanism (Mass Generation)",7,"1964","Proven","Scalar VEV v=246 GeV→W,Z masses; fermion masses via Yukawa","Higgs boson 2012; m_H=125.25 GeV")
|
||
E(150,150,"Weinberg Angle",7,"1967","Proven","sin²θ_W=1−M_W²/M_Z²; 0.23121±0.00004","EW precision parameter")
|
||
E(151,151,"Faddeev-Popov Gauge Fixing + Ghosts",7,"1967","Proven","Anticommuting scalar ghosts cancel unphysical gluon d.o.f.","Perturbative unitarity in non-abelian theories")
|
||
E(152,152,"BRST Symmetry",7,"1975","Proven","Residual global symmetry after gauge fixing","Exact; ensures unitarity and renormalizability")
|
||
E(153,153,"Running Coupling (RGE, General)",7,"1950s","Proven","μ dg/dμ=β(g); μ d m/dμ=γ_m m","Renormalization group; all QFT")
|
||
E(154,154,"Fermi's Theory (4-Fermion, Low-Energy EW)",7,"1934","Proven","ℒ_eff=−(G_F/√2) J_μ^{CC} J^{CC†μ}","Low-energy limit of SM; muon decay; confirmed")
|
||
E(155,155,"Pati-Salam Model (SU(4)×SU(2)×SU(2))",7,"1974","Proposed","Partial unification with lepton as 4th color","Not proven; historically important")
|
||
E(156,156,"Grand Unified Theories (GUTs)",7,"1974–","Proposed","SU(5), SO(10), E₆ unification at ~10¹⁶ GeV","Not confirmed; proton decay >10³⁴ yr")
|
||
E(157,157,"Axion (Peccei-Quinn Solution to Strong CP)",7,"1977","Proposed","a→γγ; m_a~μeV−meV","Strong CP solution candidate; searches ongoing")
|
||
E(158,158,"Muon g−2 Anomaly",7,"2021","Tension","a_μ(exp)−a_μ(SM)=251(59)×10⁻¹¹ (4.2σ)","Possible new physics; lattice vs R-ratio dispute")
|
||
|
||
# COSMOLOGY (159-175)
|
||
E(159,159,"First Friedmann Equation",8,"1922","Proven","H²=(ȧ/a)²=8πGρ/3−kc²/a²+Λc²/3; H₀=67.4 km/s/Mpc","ΛCDM; CMB, SNe, BAO consistent")
|
||
E(160,160,"Second Friedmann Equation",8,"1922","Proven","ä/a=−4πG(ρ+3p/c²)/3+Λc²/3","Cosmic acceleration from Λ; confirmed")
|
||
E(161,161,"Cosmological Fluid Equation",8,"1922","Proven","ρ̇+3H(ρ+p/c²)=0","Stress-energy conservation; exact")
|
||
E(162,162,"Redshift Relation",8,"1929","Proven","1+z=a₀/a(t); λ_obs=λ_emit(1+z)","Hubble law; all observational cosmology")
|
||
E(163,163,"Hubble-Lemaître Law",8,"1929","Proven","v=H₀ d (low z)","Hubble 1929; SN, CMB confirmed")
|
||
E(164,164,"CMB Blackbody Spectrum",8,"1965","Proven","T₀=2.72548±0.00057 K; ΔT/T₀<50 ppm","COBE/FIRAS; Planck 2018")
|
||
E(165,165,"BBN Primordial Element Abundances",8,"1948–66","Proven","Y_p=0.24709±0.00025; D/H=(2.527±0.030)×10⁻⁵","All except ⁷Li (tension) match BBN+CMB")
|
||
E(166,166,"Sound Horizon at Recombination",8,"1970","Proven","r_s≈147 Mpc (comoving); BAO standard ruler","SDSS/BOSS/DESI; confirmed")
|
||
E(167,167,"Sachs-Wolfe Effect (CMB)",8,"1967","Proven","ΔT/T=−Φ/(3c²) at large angular scales","CMB gravitational redshift; confirmed")
|
||
E(168,168,"Dark Energy Equation of State",8,"1998","Proven","w=p/ρc²=−1.03±0.03","Consistent with cosmological constant Λ")
|
||
E(169,169,"Deceleration Parameter",8,"1970","Proven","q₀=−äa/ȧ²=−0.53±0.02","Universe accelerating; SNe Nobel 2011")
|
||
E(170,170,"Matter Power Spectrum",8,"1990s","Proven","P(k)~k^{n_s}; n_s=0.9649±0.0042","Planck 2018; primordial fluctuations")
|
||
E(171,171,"Cosmic Distance Ladder Relations",8,"20th c.","Proven","d_L=(1+z)χ; μ=5log₁₀(d_L/10pc)","SNe, Cepheids, TRGB; confirmed")
|
||
E(172,172,"Inflation (Slow-Roll)",8,"1981","Proposed","ε=−Ḣ/H²≪1; η≪1 scalar spectral index","Fits data; no direct inflaton detection")
|
||
E(173,173,"Hubble Tension",8,"2020s","Tension","H₀(CMB)=67.4±0.5 vs H₀(local)=73.0±1.0 (5σ)","New physics or systematics?")
|
||
E(174,174,"S₈ Tension",8,"2020s","Tension","σ₈(Ω_m/0.3)^{0.5}=0.832±0.013 (CMB) vs ~0.76 (WL)","Clustering lower than ΛCDM predicts")
|
||
E(175,175,"Age of the Universe",8,"2018","Proven","t₀=13.797±0.023 Gyr (Planck 2018)","Consistent with oldest globular clusters, WDs")
|
||
|
||
# FLUID DYNAMICS (176-190)
|
||
E(176,176,"Navier-Stokes Equation (Incompressible)",9,"1822–45","Proven","∂v/∂t+(v·∇)v=−(1/ρ)∇p+ν∇²v+g; ∇·v=0","All Newtonian fluids; empirically perfect")
|
||
E(177,177,"Continuity Equation (Fluid)",9,"1757","Proven","∂ρ/∂t+∇·(ρv)=0","Mass conservation; exact")
|
||
E(178,178,"Euler Equation (Inviscid)",9,"1757","Proven","∂v/∂t+(v·∇)v=−(1/ρ)∇p+g (μ=0 limit)","Inviscid flow; exact limit of N-S")
|
||
E(179,179,"Bernoulli's Equation",9,"1738","Proven","p+½ρv²+ρgz=constant (steady, incompressible, inviscid)","Confirmed in wind tunnels, pipe flow, flight")
|
||
E(180,180,"Stokes Law (Drag on Sphere)",9,"1851","Proven","F_d=6πμRv (Re≪1)","Creeping flow; Millikan oil-drop; confirmed")
|
||
E(181,181,"Poiseuille Flow (Hagen-Poiseuille)",9,"1840","Proven","Q=πGR⁴/(8μ); v_z(r)=(G/4μ)(R²−r²)","Laminar pipe flow; viscometry")
|
||
E(182,182,"Reynolds Number",9,"1883","Proven","Re=ρUL/μ; transition at Re~2300 (pipe)","Universally confirmed scaling")
|
||
E(183,183,"Kolmogorov Energy Spectrum",9,"1941","Proven","E(k)=C_K ε^{2/3}k^{−5/3}; C_K≈1.5","Turbulence; ~5 decades confirmed")
|
||
E(184,184,"Froude Number",9,"19th c.","Proven","Fr=v/√(gL); wave/gravity scaling","Open channels; ship design")
|
||
E(185,185,"Mach Number",9,"1887","Proven","Ma=v/c_s; compressibility measure","Aerodynamics; shock waves")
|
||
E(186,186,"Kutta-Joukowski Theorem (Lift)",9,"1906","Proven","L'=ρvΓ (lift per unit span)","Airfoil lift confirmed")
|
||
E(187,187,"Torricelli's Law (Efflux Speed)",9,"1643","Proven","v=√(2gh); speed of fluid from orifice","Confirmed; energy conservation")
|
||
E(188,188,"Archimedes' Principle",9,"~250 BCE","Proven","F_b=ρ_fluid V_displaced g","Buoyancy; confirmed")
|
||
E(189,189,"Surface Tension (Young-Laplace)",9,"1805","Proven","Δp=2γ/R (spherical); Δp=γ(1/R₁+1/R₂)","Capillarity; confirmed")
|
||
E(190,190,"Kelvin-Helmholtz Instability Condition",9,"1871","Proven","Instability when (ρ₁ρ₂/ρ₁+ρ₂)(v₁−v₂)²>2√(ρ₁ρ₂)gγ","Shear flow instability; clouds, ocean waves")
|
||
|
||
# OPTICS (191-210)
|
||
E(191,191,"Snell's Law of Refraction",10,"1621","Proven","n₁ sinθ₁=n₂ sinθ₂","Fermat's principle; exact for isotropic media")
|
||
E(192,192,"Thin Lens Equation",10,"17th c.","Proven","1/f=1/d_o+1/d_i","Paraxial imaging; confirmed")
|
||
E(193,193,"Lens Maker's Formula",10,"17th c.","Proven","1/f=(n−1)(1/R₁−1/R₂)","Thin lens; paraxial; confirmed")
|
||
E(194,194,"Magnification (Geometric Optics)",10,"17th c.","Proven","M=−d_i/d_o=h_i/h_o","Geometric optics; exact")
|
||
E(195,195,"Scalar Wave Equation (d'Alembert)",10,"1747","Proven","∂²u/∂t²=c²∇²u","All wave phenomena; exact")
|
||
E(196,196,"Young's Double-Slit Interference",10,"1801","Proven","Δy=λL/d (fringe spacing); d sinθ=mλ (maxima)","Wave nature of light confirmed")
|
||
E(197,197,"Single-Slit Diffraction",10,"1835","Proven","I(θ)=I₀[sin(β/2)/(β/2)]²; β=2πa sinθ/λ","All diffraction; confirmed")
|
||
E(198,198,"Grating Equation",10,"1821","Proven","d(sinθ_i+sinθ_m)=mλ","Diffraction gratings; spectroscopy")
|
||
E(199,199,"Bragg's Law (X-ray Diffraction)",10,"1913","Proven","nλ=2d sinθ","All crystal structures solved")
|
||
E(200,200,"Fresnel Equations (Amplitude Reflection/Transmission)",10,"1823","Proven","r_s=(n₁cosθ_i−n₂cosθ_t)/(n₁cosθ_i+n₂cosθ_t); etc.","All dielectric interfaces; confirmed")
|
||
E(201,201,"Brewster's Angle",10,"1815","Proven","θ_B=arctan(n₂/n₁); reflected p-pol vanishes","Polarization; confirmed")
|
||
E(202,202,"Malus's Law",10,"1809","Proven","I=I₀ cos²θ","Polarizer transmission; confirmed")
|
||
E(203,203,"Rayleigh Criterion (Resolution Limit)",10,"1879","Proven","θ_min=1.22λ/D","Diffraction limit; telescopes, microscopes")
|
||
E(204,204,"Abbe Sine Condition",10,"1873","Proven","n y sinθ=n' y' sinθ'","Coma-free imaging condition; confirmed")
|
||
E(205,205,"Numerical Aperture",10,"1873","Proven","NA=n sinθ; resolution d=λ/(2 NA)","Microscopy; confirmed")
|
||
E(206,206,"Fermat's Principle of Least Time",10,"1662","Proven","δ∫ n ds=0; light path minimizes optical path length","All geometric optics; exact")
|
||
E(207,207,"Huygens-Fresnel Principle",10,"1678/1818","Proven","Every point on wavefront = source of spherical wavelets","All diffraction; confirmed")
|
||
E(208,208,"Fabry-Pérot Etalon Transmission",10,"1899","Proven","T=T_max/[1+(2F/π)² sin²(δ/2)]","High-resolution spectroscopy")
|
||
E(209,209,"Critical Angle (Total Internal Reflection)",10,"17th c.","Proven","θ_c=arcsin(n₂/n₁)","Fiber optics; confirmed")
|
||
E(210,210,"Fraunhofer vs Fresnel Diffraction Condition",10,"19th c.","Proven","Fresnel number F=a²/λz; F≪1→Fraunhofer; F≫1→Fresnel","Confirmed")
|
||
|
||
# ACOUSTICS (211-217)
|
||
E(211,211,"Speed of Sound",11,"17th c.","Proven","c=√(K/ρ); c_air=√(γRT/M)≈331.3+0.606·T_°C m/s","All acoustic media; precise")
|
||
E(212,212,"Doppler Effect (Sound)",11,"1842","Proven","f'=f(c±v_o)/(c∓v_s)","All moving sources/observers")
|
||
E(213,213,"Standing Waves (String/Column)",11,"18th c.","Proven","λ_n=2L/n (fixed-fixed/open-open); λ_n=4L/n (fixed-free)","Musical instruments; confirmed")
|
||
E(214,214,"Decibel Scale (SPL)",11,"1924","Proven","L_p=10 log₁₀(p²/p₀²) dB; p₀=20 μPa","Sound pressure reference; universal")
|
||
E(215,215,"Shock Wave Rankine-Hugoniot Relations",11,"1887","Proven","Conservation eqs across shock: ρ₁v₁=ρ₂v₂; p₁+ρ₁v₁²=p₂+ρ₂v₂²; etc.","Supersonic flow; confirmed")
|
||
E(216,216,"Beat Frequency",11,"18th c.","Proven","f_beat=|f₁−f₂|","Superposition; confirmed")
|
||
E(217,217,"Helmholtz Resonator Frequency",11,"1860","Proven","f=(c/2π)√(A/VL_eff)","Bottle resonance; confirmed")
|
||
|
||
# CONDENSED MATTER (218-240)
|
||
E(218,218,"Drude Model (Electrical Conductivity)",12,"1900","Proven","σ=n e²τ/m; J=σE","Classical; qualitatively correct; quantum corrections")
|
||
E(219,219,"Bloch's Theorem",12,"1928","Proven","ψ_k(r)=e^{ik·r} u_k(r); u_k periodic","Band theory foundation; confirmed")
|
||
E(220,220,"Kronig-Penney Model (1D Band Structure)",12,"1931","Proven","cos ka=cos αa+(P/αa)sin αa","1D crystal; bands naturally emerge")
|
||
E(221,221,"Fermi-Dirac Distribution",12,"1926","Proven","f(E)=1/[e^{(E−μ)/k_B T}+1]","Fermion occupancy; all solid-state devices")
|
||
E(222,222,"Free Electron Density of States",12,"1928","Proven","g(E)=(1/2π²)(2m/ℏ²)^{3/2}√E","3D electron gas; confirmed")
|
||
E(223,223,"Sommerfeld Model (Electron Heat Capacity)",12,"1928","Proven","C_V=(π²/2)n k_B(k_B T/E_F)","Metals; linear T contribution confirmed")
|
||
E(224,224,"BCS Theory (Superconductivity)",12,"1957","Proven","T_c=1.13Θ_D e^{−1/N(0)V}; Δ(T); Cooper pairs","All conventional superconductors")
|
||
E(225,225,"BCS Gap Equation at T=0",12,"1957","Proven","Δ(0)=1.76 k_B T_c","Confirmed by tunneling spectroscopy")
|
||
E(226,226,"London Equations (Perfect Diamagnetism)",12,"1935","Proven","∂J_s/∂t=(n_s e²/m)E; ∇×J_s=−(n_s e²/m)B","Meissner effect; confirmed")
|
||
E(227,227,"Josephson Effects (DC + AC)",12,"1962","Proven","I=I_c sin φ (DC); dφ/dt=(2e/ℏ)V=(2π/Φ₀)V (AC)","Voltage standard; SQUIDs; confirmed")
|
||
E(228,228,"Curie's Law (Paramagnetism)",12,"1895","Proven","χ=C/T; C=Nμ²/(3k_B)","Paramagnetic susceptibility; confirmed")
|
||
E(229,229,"Curie-Weiss Law (Ferromagnetism)",12,"1907","Proven","χ=C/(T−T_c) above Curie point","Ferromagnetic transition; confirmed")
|
||
E(230,230,"Heisenberg Exchange Interaction",12,"1928","Proven","H=−J Σ_{⟨ij⟩} S_i·S_j","Origin of ferromagnetism; confirmed")
|
||
E(231,231,"Magnetic Hysteresis Loop",12,"1890","Proven","B−H loop; remanence B_r, coercivity H_c","All permanent magnets")
|
||
E(232,232,"Einstein Relation (Diffusion)",12,"1905","Proven","D=μ k_B T/e","Brownian motion; ionic conduction; exact")
|
||
E(233,233,"Seebeck Effect (Thermoelectricity)",12,"1821","Proven","ΔV=S ΔT; S=−(π²k_B²T/3e)(d ln σ/dE)_{E=μ}","Thermocouples; confirmed")
|
||
E(234,234,"Hall Effect",12,"1879","Proven","V_H=(I B)/(n e d); R_H=1/(n e)","Carrier density; confirmed")
|
||
E(235,235,"Quantum Hall Effect (Integer)",12,"1980","Proven","R_H=h/(ν e²); ν integer; exact quantization","Resistance standard; 10⁻⁹ precision")
|
||
E(236,236,"Wiedemann-Franz Law",12,"1853","Proven","κ/(σT)=L; L=(π²/3)(k_B/e)²≈2.44×10⁻⁸ WΩ/K²","Metals; confirmed")
|
||
E(237,237,"Debye Model (Lattice Heat Capacity)",12,"1912","Proven","C_V≈(12π⁴/5) N k_B (T/Θ_D)³ for T≪Θ_D","Phonon specific heat; confirmed")
|
||
E(238,238,"Mott Insulator Transition",12,"1949","Proven","U/t≫W→Mott insulating gap; metal-insulator transition","Strongly correlated systems")
|
||
E(239,239,"Density Functional Theory (Kohn-Sham Equations)",12,"1964–65","Proven","(−½∇²+v_eff(r))φ_i(r)=ε_i φ_i(r)","All modern materials computation; confirmed")
|
||
E(240,240,"Landau Fermi Liquid Theory",12,"1956","Proven","Quasiparticles with renormalized mass m*/m; same quantum numbers","Normal metals; confirmed")
|
||
|
||
# NUCLEAR PHYSICS (241-250)
|
||
E(241,241,"Radioactive Decay Law",13,"1902","Proven","N(t)=N₀ e^{−λt}; T_{1/2}=ln 2/λ; τ=1/λ","All radioactive isotopes; exact")
|
||
E(242,242,"Bethe-Weizsäcker (Semi-Empirical) Mass Formula",13,"1935","Proven","B=a_vA−a_sA^{2/3}−a_cZ²/A^{1/3}−a_a(N−Z)²/A+δ(A,Z)","Nuclear binding energies to <1% avg")
|
||
E(243,243,"Geiger-Nuttall Law (α-Decay)",13,"1911","Proven","log T_{1/2}=A+B/√E_α","Quantum tunneling explained")
|
||
E(244,244,"Nuclear Shell Model (Magic Numbers)",13,"1949","Proven","Magic no: 2,8,20,28,50,82,126; spin-orbit coupling","Nuclear energy levels confirmed")
|
||
E(245,245,"Q-Value of Nuclear Reaction",13,"1930s","Proven","Q=(m_initial−m_final)c²","All nuclear reactions; exact")
|
||
E(246,246,"Neutrino Oscillation Probability",13,"1957","Proven","P(ν_α→ν_β)=sin²(2θ) sin²(Δm² L/4E)","Super-K, SNO, KamLAND, Daya Bay")
|
||
E(247,247,"Four-Factor Formula (Nuclear Reactor)",13,"1940s","Proven","k_eff=η ε p f; criticality when k_eff=1","Nuclear chain reaction")
|
||
E(248,248,"Rutherford Scattering Cross-Section",13,"1911","Proven","dσ/dΩ=(Z₁Z₂e²/16πε₀E)² csc⁴(θ/2)","Nuclear size discovered; confirmed")
|
||
E(249,249,"Mössbauer Effect (Recoilless γ Emission)",13,"1958","Proven","Fraction f=exp(−k²⟨x²⟩)","Recoil-free fraction; Pound-Rebka-GR; confirmed")
|
||
E(250,250,"Breit-Wigner Resonance (Nuclear Reactions)",13,"1936","Proven","σ(E)=πƛ² g (Γ_a Γ_b)/[(E−E_R)²+Γ²/4]","Resonance scattering; compound nucleus")
|
||
|
||
# ASTROPHYSICS (251-268)
|
||
E(251,251,"Lane-Emden Equation (Polytropic Stars)",14,"1870","Proven","(1/ξ²)d(ξ² dθ/dξ)/dξ=−θ^n","Stellar polytropic models; confirmed")
|
||
E(252,252,"Eddington Luminosity Limit",14,"1921","Proven","L_Edd=4πGM m_p c/σ_T≈1.3×10³¹(M/M⊙) W","Radiation pressure balance; confirmed")
|
||
E(253,253,"Chandrasekhar Limit (White Dwarf)",14,"1931","Proven","M_Ch≈1.44 M⊙ (electron degeneracy pressure)","White dwarf mass limit; confirmed")
|
||
E(254,254,"TOV Limit (Neutron Star Maximum Mass)",14,"1939","Proven","M_max≈2−3 M⊙ (equation of state dependent)","GW170817; pulsar timing; confirmed")
|
||
E(255,255,"Hertzsprung-Russell Diagram + Main Sequence",14,"1910","Proven","L∝M^{3.5} (MS, M>0.5M⊙); stellar radii, T_eff","All stars; confirmed")
|
||
E(256,256,"Mass-Luminosity Relation",14,"1924","Proven","L/L⊙≈(M/M⊙)^{3.5} (MS, intermediate mass)","Binary systems; confirmed")
|
||
E(257,257,"Virial Theorem (Astrophysics)",14,"1870","Proven","2⟨T⟩+⟨U⟩=0 for gravitational systems","Galaxy clusters; dark matter evidence")
|
||
E(258,258,"Jeans Instability Criterion (Star Formation)",14,"1902","Proven","λ_J=c_s√(π/Gρ); M_J∝c_s³/√(G³ρ)","Gravitational collapse condition; confirmed")
|
||
E(259,259,"Schwarzschild Criterion (Convection)",14,"1906","Proven","|dT/dr|_rad>|dT/dr|_ad→convective instability","Stellar convection zones; confirmed")
|
||
E(260,260,"pp Chain Energy Release",14,"1939","Proven","4p→⁴He+2e⁺+2ν_e+26.73 MeV","Solar neutrino flux matches (2/3 deficit→oscillation)")
|
||
E(261,261,"CNO Cycle (Massive Stars)",14,"1938","Proven","C, N, O catalytic H fusion; dominant above ~1.3 M⊙","Solar neutrinos confirm ~1% CNO")
|
||
E(262,262,"Triple-Alpha Process (Helium Burning)",14,"1952","Proven","3 ⁴He→¹²C+7.65 MeV (Hoyle resonance at 7.65 MeV)","Carbon production in red giants; confirmed")
|
||
E(263,263,"Core-Collapse Supernova Mechanism",14,"1960s","Proven","Fe core infall→neutrino burst→explosion (delayed neutrino mechanism)","SN 1987A neutrinos detected; confirmed")
|
||
E(264,264,"Type Ia Supernova (Standardizable Candle)",14,"1990s","Proven","Chandrasekhar mass WD thermonuclear detonation; Phillips rel.","Dark energy discovery; confirmed")
|
||
E(265,265,"Neutron Star Equation of State (Various)",14,"20th c.","Proven","p(ρ) from nuclear matter theory; constraints from NS masses","GW170817 tidal deformability; confirmed")
|
||
E(266,266,"Oppenheimer-Snyder Collapse (BH Formation)",14,"1939","Proven","Dust ball collapse→BH; event horizon forms","First BH formation model; confirmed")
|
||
E(267,267,"Pulsar Spin-Down",14,"1968","Proven","Ė=−I ω ω̇; B_dipole≈3.2×10¹⁹√(P Ṗ) G","Magnetic braking; all pulsars")
|
||
E(268,268,"Olbers' Paradox Resolution",14,"1826","Proven","Dark night sky→finite age+expanding universe","Cosmological principle consequence")
|
||
|
||
# PLASMA PHYSICS (269-276)
|
||
E(269,269,"Debye Length (Plasma Screening)",15,"1923","Proven","λ_D=√(ε₀ k_B T/(n e²))","All plasmas; confirmed")
|
||
E(270,270,"Plasma Frequency",15,"1929","Proven","ω_p=√(n e²/(ε₀ m_e))≈56.4√n (rad/s)","Ionospheric reflection; confirmed")
|
||
E(271,271,"Alfvén Wave Speed",15,"1942","Proven","v_A=B₀/√(μ₀ρ)","MHD waves; solar wind, fusion; confirmed")
|
||
E(272,272,"MHD Induction Equation",15,"1940s","Proven","∂B/∂t=∇×(v×B)+η∇²B","Magnetic field evolution; dynamo theory")
|
||
E(273,273,"Saha Ionization Equation",15,"1920","Proven","n_{i+1}n_e/n_i=(2/λ³_deB)(U_{i+1}/U_i)e^{−χ/(k_B T)}","Ionization equilibrium; stellar atmospheres")
|
||
E(274,274,"Gyro-frequency (Larmor Frequency)",15,"1897","Proven","ω_c=qB/m; r_L=v_⊥/ω_c","Particle motion in B; confirmed")
|
||
E(275,275,"Beta Parameter (Plasma Confinement)",15,"1950s","Proven","β=2μ₀ p/B²","Plasma pressure/magnetic pressure; fusion")
|
||
E(276,276,"Lawson Criterion (Fusion Ignition)",15,"1957","Proven","n T τ_E>3×10²¹ keV·s/m³ (D-T)","Fusion break-even condition; not yet achieved")
|
||
|
||
# MATHEMATICAL PHYSICS (277-295)
|
||
E(277,277,"Noether's Theorem",16,"1918","Proven","Continuous symmetry ⇔ conserved current/charge","Mathematical theorem; unfalsifiable")
|
||
E(278,278,"Stokes' Theorem",16,"1854","Proven","∫_S (∇×F)·dS=∮_C F·dl","Vector calculus; exact")
|
||
E(279,279,"Gauss's Divergence Theorem",16,"1813","Proven","∫_V ∇·F dV=∮_S F·dS","Vector calculus; exact")
|
||
E(280,280,"Green's Theorem (2D)",16,"1828","Proven","∬(∂Q/∂x−∂P/∂y)dxdy=∮ Pdx+Qdy","Special case of Stokes; exact")
|
||
E(281,281,"Fourier Transform",16,"1822","Proven","F(k)=∫ f(x)e^{−ikx}dx; f(x)=(1/2π)∫ F(k)e^{ikx}dk","All signal processing; exact")
|
||
E(282,282,"Laplace's Equation",16,"1782","Proven","∇²φ=0; harmonic functions","Potential theory: gravity, E&M, fluid")
|
||
E(283,283,"Poisson's Equation",16,"1813","Proven","∇²φ=−f(x); fundamental PDE of physics","Gravity, E&M; exact")
|
||
E(284,284,"Bessel's Equation",16,"1824","Proven","x² y''+x y'+(x²−n²)y=0","Cylindrical symmetry; exact")
|
||
E(285,285,"Legendre's Equation",16,"1785","Proven","(1−x²)y''−2xy'+n(n+1)y=0","Spherical symmetry; P_l(cosθ)")
|
||
E(286,286,"Hermite's Equation",16,"1864","Proven","y''−2xy'+2ny=0","Harmonic oscillator wavefunctions")
|
||
E(287,287,"Associated Legendre Equation",16,"19th c.","Proven","(1−x²)y''−2xy'+[n(n+1)−m²/(1−x²)]y=0","P_l^m; spherical harmonics; confirmed")
|
||
E(288,288,"Chebyshev Polynomials",16,"1853","Proven","T_n(cosθ)=cos(nθ); orthogonality","Approximation theory")
|
||
E(289,289,"Laguerre Polynomials",16,"19th c.","Proven","x y''+(1−x)y'+n y=0","Hydrogen radial wavefunction")
|
||
E(290,290,"Spherical Harmonics (Y_l^m)",16,"19th c.","Proven","Y_l^m(θ,φ)=√((2l+1)(l−m)!/4π(l+m)!) P_l^m(cosθ) e^{imφ}","Eigenfunctions of L², L_z")
|
||
E(291,291,"Gamma Function",16,"1729","Proven","Γ(z)=∫₀^∞ t^{z−1}e^{−t}dt; Γ(n+1)=n!","Factorial generalization; exact")
|
||
E(292,292,"Error Function",16,"19th c.","Proven","erf(x)=(2/√π)∫₀^x e^{−t²}dt","Diffusion, statistics; exact")
|
||
E(293,293,"Delta Function (Dirac)",16,"1927","Proven","∫ δ(x−a)f(x)dx=f(a); ∫ δ(x)dx=1","Distribution; Green's functions")
|
||
E(294,294,"Eigenvalue Equation",16,"19th c.","Proven","Âv=λv","All of QM, vibrations, linear systems; exact")
|
||
E(295,295,"Separation of Variables Method",16,"1750","Proven","ψ(x,y,z)=X(x)Y(y)Z(z); decouples PDEs","Method; exact when symmetry permits")
|
||
|
||
# STATISTICAL MECHANICS (296-308)
|
||
E(296,296,"Boltzmann Distribution",17,"1877","Proven","p_i=g_i e^{−βE_i}/Z; β=1/k_B T","Thermal equilibrium; all stat mech")
|
||
E(297,297,"Canonical Partition Function",17,"1902","Proven","Z=Σ g_i e^{−βE_i}; F=−k_B T ln Z","All thermodynamics from Z; exact")
|
||
E(298,298,"Grand Canonical Partition Function",17,"1902","Proven","Ξ=Σ_{N} Σ_{E} e^{−β(E−μN)}; Ω=−k_B T ln Ξ","Open systems; variable particle number")
|
||
E(299,299,"Boltzmann Entropy Formula",17,"1877","Proven","S=k_B ln Ω","Microstate counting; exact")
|
||
E(300,300,"Gibbs Entropy Formula",17,"1902","Proven","S=−k_B Σ p_i ln p_i","Generalized; exact")
|
||
E(301,301,"Fluctuation-Dissipation Theorem",17,"1951","Proven","⟨x²⟩_ω=(2k_B T/ω) Im χ(ω)","Linear response; confirmed")
|
||
E(302,302,"Einstein-Smoluchowski Relation (Diffusion)",17,"1905","Proven","⟨x²⟩=2Dt; D=μ k_B T","Brownian motion; confirmed")
|
||
E(303,303,"Jarzynski Equality",17,"1997","Proven","⟨e^{−W/k_B T}⟩=e^{−ΔF/k_B T}","Non-equilibrium work; exact")
|
||
E(304,304,"Crooks Fluctuation Theorem",17,"1999","Proven","P_F(W)/P_R(−W)=e^{(W−ΔF)/k_B T}","Single-molecule; confirmed")
|
||
E(305,305,"Ising Model (1D/2D Exact Solution)",17,"1925/1944","Proven","2D Onsager solution: T_c=2.269 J/k_B","Phase transitions; confirmed")
|
||
E(306,306,"Central Limit Theorem (Statistical)",17,"1901","Proven","(1/n)Σ X_i → N(μ,σ²/n)","Foundational; exact")
|
||
E(307,307,"Bose-Einstein Condensation (T_c)",17,"1925","Proven","T_c=(2πℏ²/m k_B)(n/ζ(3/2))^{2/3}","Rubidium BEC 1995; confirmed")
|
||
E(308,308,"Kramers-Kronig Relations (Dispersion)",17,"1926–27","Proven","Re χ(ω)=(1/π) P∫ Im χ(ω')/(ω'−ω)dω'","Causality; exact")
|
||
|
||
# CONTINUUM MECHANICS (309-320)
|
||
E(309,309,"Cauchy Stress Principle",18,"1822","Proven","t=σ·n; traction vector=stress tensor·normal","Foundation of continuum; exact")
|
||
E(310,310,"Generalized Hooke's Law (Linear Elasticity)",18,"19th c.","Proven","σ_{ij}=C_{ijkl} ε_{kl}; 21 independent elastic constants","All elastic solids; confirmed")
|
||
E(311,311,"Infinitesimal Strain Tensor",18,"19th c.","Proven","ε_{ij}=(1/2)(∂_j u_i+∂_i u_j)","Small deformations; exact in limit")
|
||
E(312,312,"Young's Modulus / Elastic Modulus",18,"1807","Proven","E=σ/ε (uniaxial); stress-strain ratio","Tensile testing; confirmed")
|
||
E(313,313,"Shear Modulus",18,"19th c.","Proven","G=τ/γ; G=E/[2(1+ν)] (isotropic)","Torsion testing; confirmed")
|
||
E(314,314,"Bulk Modulus",18,"19th c.","Proven","K=−V dp/dV; K=E/[3(1−2ν)] (isotropic)","Hydrostatic compression")
|
||
E(315,315,"Poisson's Ratio",18,"1827","Proven","ν=−ε_transvers/ε_axial; −1<ν<0.5","All materials; confirmed")
|
||
E(316,316,"Euler-Bernoulli Beam Equation",18,"1750","Proven","EI d⁴w/dx⁴=q(x); deflection","Structural engineering; confirmed")
|
||
E(317,317,"Timoshenko Beam Theory",18,"1921","Proven","Shear deformation included; more accurate for short beams","Confirmed; higher-order corrections")
|
||
E(318,318,"Elastic Wave Speeds (P and S waves)",18,"19th c.","Proven","v_P=√((K+4G/3)/ρ); v_S=√(G/ρ)","Seismology; confirmed")
|
||
E(319,319,"Creep / Viscoelastic Maxwell Model",18,"1867","Proven","dε/dt=(1/E) dσ/dt + σ/η","Polymer, metal creep; qualitative")
|
||
E(320,320,"Plastic Yield (Von Mises Criterion)",18,"1913","Proven","σ_v=√(½[(σ₁−σ₂)²+(σ₂−σ₃)²+(σ₃−σ₁)²])≥σ_y","Ductile failure; confirmed")
|
||
|
||
# INFORMATION THEORY (321-326)
|
||
E(321,321,"Shannon Entropy",19,"1948","Proven","H=−Σ p_i log₂ p_i (bits)","Information theory; exact")
|
||
E(322,322,"Shannon-Hartley Channel Capacity",19,"1948","Proven","C=B log₂(1+S/N)","All digital communication; exact")
|
||
E(323,323,"Nyquist-Shannon Sampling Theorem",19,"1949","Proven","f_s≥2 f_max to perfectly reconstruct","DSP everywhere")
|
||
E(324,324,"Landauer's Principle",19,"1961","Proven","Erasure of 1 bit dissipates ≥k_B T ln 2 heat","Confirmed experimentally 2012")
|
||
E(325,325,"Kolmogorov Complexity (Algorithmic Info)",19,"1965","Proven","K_U(x)=min{|p|:U(p)=x}","Theoretical; non-computable but defined")
|
||
E(326,326,"Maximum Entropy Principle (Jaynes)",19,"1957","Proven","Maximize S subject to constraints→least biased distribution","Inference; confirmed")
|
||
|
||
# METROLOGY / EXTRA (327-333)
|
||
E(327,327,"Speed of Light Defines Meter",20,"1983","Proven","c=299792458 m/s EXACT","1m=c·(1/299792458)s")
|
||
E(328,328,"Planck Constant Defines Kilogram",20,"2019","Proven","h=6.62607015e-34 J·s EXACT","Kibble balance")
|
||
E(329,329,"Elementary Charge Defines Ampere",20,"2019","Proven","e=1.602176634e-19 C EXACT","1A=e·(1/1.602176634e-19)s⁻¹")
|
||
E(330,330,"Boltzmann Constant Defines Kelvin",20,"2019","Proven","k_B=1.380649e-23 J/K EXACT","Acoustic gas thermometry")
|
||
E(331,331,"Avogadro Number Defines Mole",20,"2019","Proven","N_A=6.02214076e23 EXACT","XRCD; silicon sphere")
|
||
E(332,332,"Josephson Voltage Standard",12,"1962–90","Proven","V=n f/K_J; K_J=2e/h=483597.9 GHz/V EXACT","Voltage metrology")
|
||
E(333,333,"Quantum Hall Resistance Standard",12,"1980","Proven","R_H=h/(i e²); R_K=h/e²=25812.80745... Ω","Resistance metrology")
|
||
|
||
cur.executemany("INSERT INTO equations VALUES (?,?,?,?,?,?,?,?)", eq)
|
||
|
||
# ================================================================
|
||
# SUB-EQUATIONS (detailed formulas)
|
||
# ================================================================
|
||
subs = []
|
||
def add_sub(rid, sub, name, latex, desc, cond=""):
|
||
subs.append((rid, sub, name, latex, desc, cond))
|
||
|
||
add_sub(1,"1st","Inertia","\\Sigma \\vec{F}=0\\Rightarrow \\vec{v}=\\text{const}","No net force → constant velocity","Inertial frames")
|
||
add_sub(1,"2nd","F=dp/dt","\\vec{F}=\\frac{d\\vec{p}}{dt}=m\\vec{a}","Constant mass; relativistic: F^\\mu=dp^\\mu/d\\tau","")
|
||
add_sub(1,"3rd","Action-Reaction","\\vec{F}_{A\\to B}=-\\vec{F}_{B\\to A}","Equal and opposite in Newtonian mechanics","")
|
||
add_sub(2,"EL","Euler-Lagrange","\\frac{d}{dt}\\frac{\\partial L}{\\partial \\dot{q}_i}-\\frac{\\partial L}{\\partial q_i}=0","From \\delta S=0; S=\\int L dt","Generalized coordinates")
|
||
add_sub(3,"Hamilton","Hamilton's Canonical Equations","\\dot{q}_i=\\frac{\\partial H}{\\partial p_i},\\; \\dot{p}_i=-\\frac{\\partial H}{\\partial q_i}","Phase space, symplectic; H=T+V for conservative","Exact")
|
||
add_sub(4,"HJ","Hamilton-Jacobi","\\frac{\\partial S}{\\partial t}+H\\left(q,\\frac{\\partial S}{\\partial q},t\\right)=0","S action as function of endpoint; classical→quantum bridge","")
|
||
add_sub(7,"Euler","Euler's Rigid Body Rotation","I_1\\dot{\\omega}_1-(I_2-I_3)\\omega_2\\omega_3=\\tau_1","Principal axes; torque-free precession","")
|
||
add_sub(14,"Hooke","Hooke's Law","\\sigma=E\\varepsilon,\\; F=-kx","Linear elastic; valid below yield","")
|
||
add_sub(16,"Coriolis","Coriolis Force","\\vec{F}_{\\text{cor}}=-2m\\,\\vec{\\omega}\\times\\vec{v}'","Rotating frame fictitious force","Weather, Foucault pendulum")
|
||
add_sub(24,"Newton-G","Newton's Law of Universal Gravitation","\\vec{F}=-\\frac{G m_1 m_2}{r^2}\\hat{r}","Inverse-square; weak-field GR limit","G=6.67430e-11")
|
||
add_sub(28,"Kepler3","Kepler's 3rd Law","T^2=\\frac{4\\pi^2}{GM}a^3","For elliptical orbits, a=semi-major axis","Two-body")
|
||
add_sub(33,"Redshift-GR","Gravitational Redshift","\\frac{\\Delta\\nu}{\\nu}=-\\frac{GM}{rc^2}","Pound-Rebka; GPS ~38μs/day correction","Static weak field")
|
||
add_sub(36,"Coulomb","Coulomb's Law","\\vec{F}=\\frac{1}{4\\pi\\varepsilon_0}\\frac{q_1 q_2}{r^2}\\hat{r}","Force between point charges","1/r^{2+\\delta}, \\delta<10^{-16}")
|
||
add_sub(37,"Lorentz","Lorentz Force","\\vec{F}=q(\\vec{E}+\\vec{v}\\times\\vec{B})","EM force on moving charge","All particle accelerators")
|
||
add_sub(38,"ME1","Gauss (Electric)","\\nabla\\cdot\\vec{E}=\\rho/\\varepsilon_0","Electric charge is source of E-field","SI units")
|
||
add_sub(38,"ME2","Gauss (Magnetic)","\\nabla\\cdot\\vec{B}=0","No magnetic monopoles; m_\\gamma<10^{-18} eV/c²","")
|
||
add_sub(38,"ME3","Faraday-Lenz","\\nabla\\times\\vec{E}=-\\frac{\\partial\\vec{B}}{\\partial t}","Changing B creates circulating E","Generators, MRI, induction")
|
||
add_sub(38,"ME4","Ampère-Maxwell","\\nabla\\times\\vec{B}=\\mu_0\\vec{J}+\\mu_0\\varepsilon_0\\frac{\\partial\\vec{E}}{\\partial t}","Currents+changing E create circulating B; displacement current predicted EM waves","")
|
||
add_sub(50,"Poynting","Poynting Vector","\\vec{S}=\\frac{1}{\\mu_0}\\vec{E}\\times\\vec{B}","EM energy flux (W/m²); u=½ε₀E²+½B²/μ₀","")
|
||
add_sub(51,"Wave-eq","EM Wave Equation","\\Box\\vec{E}=0,\\;\\Box\\vec{B}=0,\\; \\Box=-\\frac{1}{c^2}\\frac{\\partial^2}{\\partial t^2}+\\nabla^2","c=1/√(μ₀ε₀); Light=EM wave","Maxwell→Hertz 1887")
|
||
add_sub(54,"Larmor","Larmor Radiation Formula","P=\\frac{q^2 a^2}{6\\pi\\varepsilon_0 c^3}","Non-relativistic accelerated charge radiation","Synchrotron confirmed")
|
||
add_sub(70,"IdealGas","Ideal Gas Law","pV=nRT=N k_B T","p in Pa, V in m³, n in mol, T in K","R=8.314462618")
|
||
add_sub(75,"Carnot","Carnot Efficiency","\\eta_{\\max}=1-\\frac{T_c}{T_h}","Maximum possible heat engine efficiency","Irreversible: η<Carnot")
|
||
add_sub(86,"Planck","Planck's Blackbody Law","B_\\nu(\\nu,T)=\\frac{2h\\nu^3}{c^2}\\frac{1}{e^{h\\nu/k_B T}-1}","Spectral radiance [W/(sr·m²·Hz)]","Energy/mode: hν/(e^{hν/kT}−1)")
|
||
add_sub(91,"Compton","Compton Scattering","\\lambda'-\\lambda=\\frac{h}{m_e c}(1-\\cos\\theta)","Photon scatters from free electron; Δλ_max=0.00486 nm","Kinematic derivation")
|
||
add_sub(92,"deBroglie","de Broglie Wavelength","\\lambda=\\frac{h}{p}=\\frac{h}{\\gamma mv}","Matter waves; Davisson-Germer 1927","All particles")
|
||
add_sub(93,"TDSE","Time-Dependent Schrödinger Eq.","i\\hbar\\frac{\\partial}{\\partial t}|\\psi\\rangle=\\hat{H}|\\psi\\rangle","Unitary evolution; fundamental","Non-relativistic QM")
|
||
add_sub(93,"TISE","Time-Independent Schrödinger Eq.","\\hat{H}\\psi=E\\psi","Stationary states; eigenvalue eq.","")
|
||
add_sub(95,"Born","Born Rule","\\rho(\\vec{r},t)=|\\psi(\\vec{r},t)|^2","Probability density; normalized to 1","All quantum measurements")
|
||
add_sub(98,"HUP","Heisenberg Uncertainty","\\Delta x\\Delta p\\geq\\frac{\\hbar}{2},\\; \\Delta A\\Delta B\\geq\\frac{1}{2}|\\langle[A,B]\\rangle|","From non-commuting operators","General Robertson-Schrödinger")
|
||
add_sub(99,"HO","Harmonic Oscillator Levels","E_n=\\hbar\\omega(n+\\tfrac{1}{2}),\\; n=0,1,2,\\dots","Zero-point E₀=½ℏω; ladder ops â,â†","Casimir effect, quantum optics")
|
||
add_sub(100,"Hatom","Hydrogen Energy Levels","E_n=-\\frac{R_y}{n^2},\\; R_y=\\frac{m_e e^4}{8\\varepsilon_0^2 h^2}=13.605693\\,\\text{eV}","Non-relativistic; Bohr model energy","Degeneracy: 2n² including spin")
|
||
add_sub(102,"Pauli","Pauli Spin Matrices","S_i=\\frac{\\hbar}{2}\\sigma_i,\\; \\sigma_x=\\begin{pmatrix}0&1\\\\1&0\\end{pmatrix},\\; \\sigma_y=\\begin{pmatrix}0&-i\\\\i&0\\end{pmatrix},\\; \\sigma_z=\\begin{pmatrix}1&0\\\\0&-1\\end{pmatrix}","Spin-½ operators","[σ_i,σ_j]=2iε_{ijk}σ_k")
|
||
add_sub(104,"Dirac","Dirac Equation","(i\\hbar\\gamma^\\mu\\partial_\\mu-mc)\\psi=0","Relativistic spin-½; {γ^μ,γ^ν}=2g^{μν}I₄","Predicted positron; g=2")
|
||
add_sub(109,"PauliExc","Pauli Exclusion Principle","\\psi(\\vec{r}_1,\\dots,\\vec{r}_i,\\dots,\\vec{r}_j,\\dots)=-\\psi(\\vec{r}_1,\\dots,\\vec{r}_j,\\dots,\\vec{r}_i,\\dots)","Fermion antisymmetry","Violation prob<4.5×10^{-29}")
|
||
add_sub(116,"Optical","Optical Theorem","\\operatorname{Im}f(0)=\\frac{k}{4\\pi}\\sigma_{\\text{total}}","Unitarity of S-matrix; exact","Forward scattering amplitude")
|
||
add_sub(117,"PathInt","Feynman Path Integral","\\langle x_f,t_f|x_i,t_i\\rangle=\\int\\mathcal{D}[x(t)]\\, e^{iS[x]/\\hbar}","Sum over all possible paths","Equivalent to Schrödinger")
|
||
add_sub(121,"Lorentz-Boost","Lorentz Boost","x'=\\gamma(x-vt),\\; t'=\\gamma\\left(t-\\frac{vx}{c^2}\\right),\\; \\gamma=\\frac{1}{\\sqrt{1-v^2/c^2}}","Boost along x; SR","c invariant in all frames")
|
||
add_sub(126,"Emc2","Mass-Energy Equivalence","E^2=(pc)^2+(mc^2)^2","p=0 → E=mc²","Every nuclear reaction confirms")
|
||
add_sub(129,"EFE","Einstein Field Equations","G_{\\mu\\nu}+\\Lambda g_{\\mu\\nu}=\\frac{8\\pi G}{c^4}T_{\\mu\\nu}","G_{\\mu\\nu}=R_{\\mu\\nu}-½R g_{\\mu\\nu}","Gravity=spacetime curvature")
|
||
add_sub(136,"BH-Entropy","Bekenstein-Hawking Entropy","S_{\\text{BH}}=\\frac{k_B A}{4\\ell_P^2}=\\frac{k_B c^3 A}{4G\\hbar}","Entropy∝horizon area; 4 laws of BH mechanics","T_H=κ/2π")
|
||
add_sub(137,"HawkingT","Hawking Temperature","T_H=\\frac{\\hbar c^3}{8\\pi GM k_B}","Schwarzschild BH; T_H(M_⊙)≈6.2×10^{-8}K","Radiation too faint for astro. BH")
|
||
add_sub(139,"SM-Lagrangian","Standard Model Lagrangian","\\mathcal{L}_{\\text{SM}}=-\\frac{1}{4}G_a^{\\mu\\nu}G^a_{\\mu\\nu}-\\frac{1}{4}W_i^{\\mu\\nu}W^i_{\\mu\\nu}-\\frac{1}{4}B^{\\mu\\nu}B_{\\mu\\nu}+i\\sum\\bar\\psi\\cancel{D}\\psi+|D_\\mu\\Phi|^2-V(\\Phi)+\\mathcal{L}_{\\text{Yukawa}}","SU(3)×SU(2)×U(1); 3 generations","Most precise physical theory")
|
||
add_sub(140,"YM","Yang-Mills Field Strength","F_{\\mu\\nu}^a=\\partial_\\mu A_\\nu^a-\\partial_\\nu A_\\mu^a+gf^{abc}A_\\mu^b A_\\nu^c","Non-abelian gauge; self-interactions","Basis of QCD+EW theory")
|
||
add_sub(142,"QCD-Lag","QCD Lagrangian","\\mathcal{L}_{\\text{QCD}}=\\sum_{f=1}^6\\bar\\psi_f(i\\cancel{D}-m_f)\\psi_f-\\frac{1}{4}G_a^{\\mu\\nu}G^a_{\\mu\\nu}","D_\\mu=\\partial_\\mu-ig_s A_\\mu^a T^a","Asymptotic freedom+confinement")
|
||
add_sub(144,"Beta-QCD","QCD 1-loop Beta Function","\\beta(\\alpha_s)=-\\frac{\\alpha_s^2}{2\\pi}\\left(11-\\frac{2}{3}n_f\\right)","β<0 for n_f≤16 → asymptotic freedom","α_s running 4 decades confirmed")
|
||
add_sub(148,"GMOR","Gell-Mann–Oakes–Renner","m_\\pi^2=-\\frac{(m_u+m_d)\\langle\\bar\\psi\\psi\\rangle}{f_\\pi^2}","Pion mass from quark masses+condensate","f_π≈92.2 MeV")
|
||
add_sub(149,"Higgs-Mech","Higgs Mechanism","M_W=\\frac{gv}{2},\\; M_Z=\\frac{v}{2}\\sqrt{g^2+g'^2},\\; v=\\frac{1}{\\sqrt{\\sqrt{2}G_F}}\\approx 246\\,\\text{GeV}","SSB gives gauge boson masses","m_H=125.25 GeV")
|
||
add_sub(159,"Fried1","First Friedmann Equation","H^2=\\left(\\frac{\\dot{a}}{a}\\right)^2=\\frac{8\\pi G}{3}\\rho-\\frac{kc^2}{a^2}+\\frac{\\Lambda c^2}{3}","H(t)=Hubble parameter; a(t)=scale factor","H₀=67.4 km/s/Mpc")
|
||
add_sub(160,"Fried2","Second Friedmann Equation","\\frac{\\ddot{a}}{a}=-\\frac{4\\pi G}{3}\\left(\\rho+\\frac{3p}{c^2}\\right)+\\frac{\\Lambda c^2}{3}","Acceleration from Λ; SN 1998 Nobel","q₀=−0.53")
|
||
add_sub(176,"N-S","Navier-Stokes (Incompressible)","\\frac{\\partial\\vec{v}}{\\partial t}+(\\vec{v}\\cdot\\nabla)\\vec{v}=-\\frac{1}{\\rho}\\nabla p+\\nu\\nabla^2\\vec{v}+\\vec{g}","ν=μ/ρ kinematic viscosity; ∇·v=0","Re=UL/ν")
|
||
add_sub(183,"Kolmo","Kolmogorov Spectrum","E(k)=C_K\\varepsilon^{2/3}k^{-5/3}","Turbulence inertial range; C_K≈1.5","~5 decades confirmed")
|
||
add_sub(191,"Snell","Snell's Law","n_1\\sin\\theta_1=n_2\\sin\\theta_2","Fermat's principle; refraction","Isotropic media")
|
||
add_sub(196,"DoubleSlit","Young's Double-Slit","\\Delta y=\\frac{\\lambda L}{d}","Fringe spacing on screen at distance L","d=slit separation")
|
||
add_sub(199,"Bragg","Bragg's Law","n\\lambda=2d\\sin\\theta","X-ray diffraction from crystal planes","All crystallography")
|
||
add_sub(241,"Decay","Radioactive Decay Law","N(t)=N_0 e^{-\\lambda t},\\; T_{1/2}=\\frac{\\ln 2}{\\lambda},\\; \\tau=\\frac{1}{\\lambda}","Exponential decay","All radioactive isotopes")
|
||
add_sub(242,"BetheW","Bethe-Weizsäcker Mass Formula","B=a_v A-a_s A^{2/3}-a_c\\frac{Z^2}{A^{1/3}}-a_a\\frac{(N-Z)^2}{A}+\\delta","a_v≈15.75,a_s≈17.8,a_c≈0.711,a_a≈23.7 MeV","±δ=±34A^{-3/4} MeV (pairing)")
|
||
add_sub(246,"NueOsc","Neutrino Oscillation Probability","P(\\nu_\\alpha\\to\\nu_\\beta)=\\sin^2(2\\theta)\\,\\sin^2\\!\\left(\\frac{\\Delta m^2 L}{4E}\\right)","2-flavor approximation","Super-K, SNO, Daya Bay confirmed")
|
||
add_sub(277,"Noether","Noether Current","J^\\mu=\\frac{\\partial\\mathcal{L}}{\\partial(\\partial_\\mu\\phi)}\\Delta\\phi-T^{\\mu}_{\\;\\nu}\\epsilon^\\nu,\\; \\partial_\\mu J^\\mu=0","Symmetry → conserved current","Mathematical theorem")
|
||
add_sub(297,"Partition","Canonical Partition Function","Z=\\sum_i g_i e^{-\\beta E_i},\\; F=-k_B T\\ln Z","All thermo. from Z","β=1/k_B T")
|
||
|
||
cur.executemany("INSERT INTO sub_equations (equation_id, subsection, name, latex_formula, description, conditions) VALUES (?,?,?,?,?,?)", subs)
|
||
|
||
# ================================================================
|
||
# VERIFICATIONS
|
||
# ================================================================
|
||
v_list = []
|
||
def add_v(eid, test, expt, yr, prec, st="Confirmed"):
|
||
v_list.append((eid, test, expt, yr, prec, st))
|
||
|
||
# Maxwell
|
||
add_v(38,"Hertz Radio Wave Detection","Hertz 1887",1887,"Qualitative→confirmed","Confirmed")
|
||
add_v(38,"Photon mass limit","Various electromagnetic tests",2000,"m_γ<10^{-18} eV/c²","Confirmed")
|
||
add_v(38,"1/r² Coulomb deviation","Cavendish-type electrostatics",2000,"δ<10^{-16}","Confirmed")
|
||
# GR
|
||
add_v(129,"Eddington Solar Eclipse (Light Deflection)","Eddington 1919",1919,"~10% precision","Confirmed")
|
||
add_v(129,"Gravitational Redshift (Pound-Rebka)","Pound & Rebka 1960",1960,"~10^{-5}","Confirmed")
|
||
add_v(129,"Shapiro Time Delay","Viking, Cassini",1970,"10^{-5}","Confirmed")
|
||
add_v(129,"Frame-Dragging (Gravity Probe B)","GP-B 2011",2011,"~10%","Confirmed")
|
||
add_v(129,"LIGO GW150914 (Binary BH Merger)","LIGO 2015",2015,"SNR>20; ringdown matches GR","Confirmed")
|
||
add_v(129,"EHT M87* Shadow","EHT 2019",2019,"40 μas; GR prediction","Confirmed")
|
||
add_v(129,"PSR B1913+16 Orbit Decay","Hulse-Taylor 1974",1974,"<0.2% agreement with GR quadrupole","Confirmed")
|
||
add_v(129,"Double Pulsar PSR J0737-3039","Kramer et al. 2006",2006,"5 independent GR tests passed","Confirmed")
|
||
# QM
|
||
add_v(93,"Hydrogen 1S-2S Spectroscopy","Hänsch group",2005,"10^{-10}","Confirmed")
|
||
add_v(104,"Positron Discovery (Anderson)","Anderson 1932",1932,"Prediction→discovery","Confirmed")
|
||
add_v(108,"Electron g-2","Hanneke et al. 2008",2008,"1 part in 10^{12}","Confirmed")
|
||
add_v(109,"VIP Pauli Violation Search","Gran Sasso",2015,"Violation prob<4.5×10^{-29}","Confirmed")
|
||
add_v(109,"Borexino Pauli Violation","Borexino",2016,"β²/2<2.6×10^{-37}","Confirmed")
|
||
add_v(120,"Loophole-free Bell Test","Hensen et al. 2015",2015,">40σ violation of local realism","Confirmed")
|
||
# SM
|
||
add_v(139,"Higgs Boson Discovery","ATLAS+CMS 2012",2012,"m_H=125.25±0.17 GeV; >5σ","Confirmed")
|
||
add_v(139,"LEP Electroweak Precision Fit","LEP/SLD",2001,"χ²/ndf≈22/15","Confirmed")
|
||
add_v(139,"W Boson Mass","CDF II/ATLAS",2022,"Tensions being resolved","Tension/Confirmed")
|
||
add_v(142,"α_s running 4 decades","HERA, LHC, SLD",2020,"Confirmed","Confirmed")
|
||
add_v(142,"Lattice QCD Hadron Spectrum","BMW/MILC/FLAG",2020,"<1% light hadrons","Confirmed")
|
||
add_v(142,"Tetraquark Z_c(3900)","BESIII/Belle 2013",2013,">5σ","Confirmed")
|
||
add_v(142,"Pentaquark P_c(4380)","LHCb 2015",2015,">5σ","Confirmed")
|
||
# Cosmology
|
||
add_v(159,"CMB Power Spectrum (Planck 2018)","Planck",2018,"ΛCDM at <1%","Confirmed")
|
||
add_v(159,"Supernova Ia Accelerating Universe","Riess/Perlmutter 1998",1998,"Nobel 2011; confirmed","Confirmed")
|
||
add_v(159,"BAO Standard Ruler","SDSS/BOSS/DESI",2015,"147 Mpc comoving sound horizon","Confirmed")
|
||
add_v(164,"CMB Temperature","COBE/FIRAS 1990",1990,"T₀=2.72548 K; ΔT<50 ppm","Confirmed")
|
||
add_v(165,"Primordial Deuterium Abundance","Quasar Absorption",2010,"D/H=(2.53±0.03)×10^{-5}","Confirmed")
|
||
add_v(165,"Primordial ⁴He Abundance","Extragalactic HII Regions",2018,"Y_p=0.24709±0.00025","Confirmed")
|
||
# Nuclear
|
||
add_v(241,"α-Decay Half-lives (Geiger-Nuttall)","Geiger+Nuttall 1911",1911,"Quantum tunneling explains range","Confirmed")
|
||
add_v(246,"Solar ν Deficit→Oscillation","Super-K + SNO 2001",2001,"ν_e→ν_{μ,τ} confirmed","Confirmed")
|
||
add_v(246,"Reactor ν Disappearance (θ₁₃)","Daya Bay/RENO 2012",2012,"θ₁₃≈8.5°; >5σ","Confirmed")
|
||
# Fluids
|
||
add_v(176,"Poiseuille Flow Viscometry","Standard viscometers",1900,"R⁴ dependence confirmed","Confirmed")
|
||
add_v(176,"Kolmogorov Spectrum","Wind tunnels, ocean, atmosphere",1980,"k^{-5/3} over ~5 decades","Confirmed")
|
||
add_v(179,"Bernoulli in Wind Tunnels","Aeronautical engineering",1900,"Lift+pipe flow confirmed","Confirmed")
|
||
# Optics
|
||
add_v(191,"Snell's Law Verification","Refractive index metrology",1900,"Confirmed to high precision","Confirmed")
|
||
add_v(199,"DNA Structure from X-ray Diffraction","Franklin/Watson/Crick 1953",1953,"Bragg's law applied","Confirmed")
|
||
# Condensed Matter
|
||
add_v(224,"BCS Isotope Effect","Various 1950",1950,"T_c∝M^{-1/2}","Confirmed")
|
||
add_v(227,"Josephson Voltage Standard","NIST",1980,"K_J=2e/h=483597.9 GHz/V; exact","Confirmed")
|
||
add_v(235,"Quantum Hall Resistance Standard","Klitzing 1980",1980,"R_K=h/e²=25812.807 Ω","Standard; 10^{-9} precision")
|
||
# Stat Mech
|
||
add_v(303,"Jarzynski Equality (RNA pulling)","Bustamante group",2005,"RNA hairpin unfolding","Confirmed")
|
||
add_v(304,"Crooks FT (DNA hairpin)","Collin et al. 2005",2005,"Single-molecule","Confirmed")
|
||
# Landauer
|
||
add_v(324,"Landauer Bit Erasure Heat","Bérut et al. 2012",2012,"k_B T ln 2 confirmed","Confirmed")
|
||
# Astro
|
||
add_v(252,"Eddington Limit in X-ray Binaries","X-ray telescopes",2000,"ULX confirmed","Confirmed")
|
||
add_v(260,"Solar pp Chain (Borexino)","Borexino",2014,"Solar ν flux matched","Confirmed")
|
||
# Exoplanet
|
||
add_v(28,"Exoplanet Mass via Radial Velocity","Kepler/TESS/HARPS",2015,"Kepler's 3rd law used for masses","Confirmed")
|
||
|
||
cur.executemany("INSERT INTO verifications (equation_id, test_name, experiment, year, precision_level, status) VALUES (?,?,?,?,?,?)", v_list)
|
||
|
||
# ================================================================
|
||
# OPEN PROBLEMS
|
||
# ================================================================
|
||
op_list = []
|
||
def add_op(pid, name, desc, rel):
|
||
op_list.append((pid, name, desc, rel))
|
||
|
||
add_op(1,"Quantum Gravity","GR+QM inconsistent at Planck scale (10^{-35}m). String theory, LQG, CDT, asymptotic safety — none confirmed.","129,93,104")
|
||
add_op(2,"Dark Matter","Overwhelming gravitational evidence (rotation curves, CMB, lensing, Bullet Cluster). No particle ID. WIMPs, axions, sterile ν — unconfirmed.","129,159")
|
||
add_op(3,"Dark Energy / CC Problem","Observed ρ_Λ≈(2.3×10^{-3}eV)⁴ vs QFT prediction ~(10^{18}GeV)⁴. Factor 10^{-120}. Why so small but nonzero?","129,159,168")
|
||
add_op(4,"Baryon Asymmetry","η=(n_B−n_B̄)/n_γ≈6×10^{-10}. Sakharov conditions satisfied but SM CP violation too small by factor ~10^{-9}.","139,146")
|
||
add_op(5,"Neutrino Masses","Oscillations prove m_ν≠0. Dirac? Majorana? Seesaw? 0νββ-decay not yet observed. Absolute scale unknown.","104,147,246")
|
||
add_op(6,"Strong CP Problem","Why is QCD θ-angle <10^{-10}? PQ mechanism→axion. ADMX, CAST searches ongoing.","142,144")
|
||
add_op(7,"Hierarchy Problem","Why is m_H(125 GeV)≪M_Pl(10^{19} GeV)? No SUSY, extra dims, or compositeness seen at LHC up to ~few TeV.","139,149")
|
||
add_op(8,"Inflation Mechanism","Inflation fits data (flatness, horizon, structure), but inflaton field unknown. No direct detection. Eternal inflation? Multiverse?","172")
|
||
add_op(9,"Quantum Measurement Problem","Why does observation collapse wavefunction? Copenhagen, Many-Worlds, de Broglie-Bohm, QBism — no experimental discrimination.","93,95,120")
|
||
add_op(10,"Arrow of Time","Why was Big Bang entropy so low? Past Hypothesis. Boltzmann brain problem.","68,299,300")
|
||
add_op(11,"Hubble Tension","H₀(CMB)=67.4±0.5 vs H₀(local)=73.0±1.0. ~5σ. New physics or systematics?","159,163,173")
|
||
add_op(12,"Lithium Problem (BBN)","Predicted ⁷Li/H~5×10^{-10} vs observed ~1.6×10^{-10} in metal-poor halo stars. Factor ~3.","165")
|
||
add_op(13,"Nature of Dark Energy","Is w exactly −1 (Λ) or evolving? DESI, Euclid, Roman Space Telescope.","168")
|
||
add_op(14,"Black Hole Information Paradox","Does info escape during BH evaporation? Island formula, replica wormholes — apparent resolution but exact mechanism unclear.","136,137,138")
|
||
add_op(15,"Proton Decay","τ_p>10^{34} yr (Super-K). No decay observed. Simple SU(5) GUT ruled out. Larger GUTs or no unification?","155,156")
|
||
add_op(16,"Muon g-2 Anomaly","a_μ(exp)−a_μ(SM)=251(59)×10^{-11} (4.2σ). New physics or underestimated hadronic contributions?","108,158")
|
||
add_op(17,"CKM Unitarity Tension","First-row unitarity: |V_ud|²+|V_us|²+|V_ub|²=0.9985±0.0007 (2σ low).","146")
|
||
add_op(18,"Gallium Neutrino Anomaly","Deficit in ⁵¹Cr/³⁷Ar calibration. Possible sterile ν.","246")
|
||
add_op(19,"Existence of Magnetic Monopoles","None detected. Dirac condition requires charge quantization if they exist.","38,36")
|
||
add_op(20,"Cosmic Lithium Problem","⁷Li from BBN higher than observations. Possible solution: astration, new physics, or stellar depletion.","165")
|
||
|
||
cur.executemany("INSERT INTO open_problems VALUES (?,?,?,?)", op_list)
|
||
|
||
# ================================================================
|
||
# POPULATE FTS
|
||
# ================================================================
|
||
cur.execute("INSERT INTO eq_fts(rowid, title, description) SELECT id, title, significance FROM equations")
|
||
|
||
# ================================================================
|
||
# USEFUL VIEWS
|
||
# ================================================================
|
||
cur.executescript("""
|
||
CREATE VIEW v_all AS
|
||
SELECT e.eq_number, e.title, e.year_range, d.name as domain, e.status, e.significance
|
||
FROM equations e JOIN domains d ON e.domain_id=d.id ORDER BY e.eq_number;
|
||
|
||
CREATE VIEW v_by_domain AS
|
||
SELECT d.name, COUNT(e.id) as num_eqs
|
||
FROM domains d LEFT JOIN equations e ON e.domain_id=d.id
|
||
GROUP BY d.id ORDER BY d.name;
|
||
|
||
CREATE VIEW v_verified AS
|
||
SELECT e.eq_number, e.title, v.test_name, v.experiment, v.year, v.precision_level, v.status
|
||
FROM equations e JOIN verifications v ON v.equation_id=e.id ORDER BY e.eq_number, v.year;
|
||
|
||
CREATE VIEW v_all_formulas AS
|
||
SELECT e.eq_number, e.title, se.subsection, se.name, se.latex_formula
|
||
FROM sub_equations se LEFT JOIN equations e ON se.equation_id=e.id
|
||
ORDER BY e.eq_number, se.id;
|
||
""")
|
||
|
||
conn.commit()
|
||
conn.close()
|
||
|
||
print(f"Database: {DB} ({os.path.getsize(DB)} bytes)")
|
||
print(f"Equations: {len(eq)}")
|
||
print(f"Sub-sections: {len(subs)}")
|
||
print(f"Verifications: {len(v_list)}")
|
||
print(f"Constants: {len(constants)}")
|
||
print(f"Open Problems: {len(op_list)}")
|
||
print(f"Domains: {len(domains)}")
|