The Equations That Define Physics

From Newton's laws to the frontiers of neutrinovoltaic technology — the 16 most important formulas in physics, explained.

#1 1687 Matter

Newton's Second Law

F = ma

The fundamental relationship between force, mass, and acceleration.

Isaac Newton
#2 1687 Universe

Law of Universal Gravitation

F = G·m₁m₂/r²

The force of gravity between two masses.

Isaac Newton
#3 1877 Matter

Boltzmann Entropy

S = k_B · ln(W)

The bridge between microscopic states and macroscopic thermodynamics.

Ludwig Boltzmann
#4 1865 Technology

Maxwell's Equations

∇·E = ρ/ε₀ , ∇×B = μ₀J + μ₀ε₀ ∂E/∂t

The four equations that unify electricity, magnetism, and light.

James Clerk Maxwell
#5 1905 Particles

Mass–Energy Equivalence

E = mc²

The most famous equation in physics — energy equals mass times the speed of light squared.

Albert Einstein
#6 1915 Universe

Einstein Field Equations

G_μν + Λg_μν = (8πG/c⁴)T_μν

How matter and energy curve spacetime — the foundation of general relativity.

Albert Einstein
#7 1900/1905 Particles

Planck–Einstein Relation

E = hf

Energy is quantized — the birth of quantum mechanics.

Max Planck / Albert Einstein
#8 1926 Particles

Schrödinger Equation

iℏ ∂Ψ/∂t = ĤΨ

The fundamental equation governing quantum systems.

Erwin Schrödinger
#9 1927 Particles

Heisenberg Uncertainty Principle

Δx · Δp ≥ ℏ/2

The fundamental limit of precision in quantum measurements.

Werner Heisenberg
#10 1928 Particles

Dirac Equation

(iγ^μ ∂_μ − m)ψ = 0

Unifying quantum mechanics and special relativity — predicting antimatter.

Paul Dirac
#11 1967–1973 Particles

Standard Model Lagrangian

ℒ = ℒ_gauge + ℒ_fermion + ℒ_Higgs + ℒ_Yukawa

The complete mathematical description of all known fundamental particles and forces.

Various
#12 1900 Particles

Radioactive Decay Law

N(t) = N₀ · e^(−λt)

The exponential decay of unstable atomic nuclei.

Ernest Rutherford
#13 1929 Universe

Hubble's Law

v = H₀ · d

The expansion of the universe — galaxies recede proportionally to their distance.

Edwin Hubble
#14 1922 Universe

Friedmann Equations

(ȧ/a)² = 8πGρ/3 − k/a² + Λ/3

The equations governing the expansion of the universe from general relativity.

Alexander Friedmann
#15 1974 Universe

Hawking Radiation Temperature

T = ℏc³ / (8πGMk_B)

Black holes emit thermal radiation — connecting gravity, quantum mechanics, and thermodynamics.

Stephen Hawking
#16 2024 Technology

Schubart–NEG Master Equation

P(t) = η · ∫V Φeff(r,t) · σeff(E) dV

The master equation for neutrinovoltaic energy conversion — turning invisible radiation into electrical power.

Holger Thorsten Schubart