The theories and equations that describe reality — from the smallest particles to the curve of spacetime itself. A working reference for the curious.
Energy isn't continuous — it comes in discrete packets called quanta. This single idea, proposed to solve the blackbody radiation problem, cracked classical physics open.
Everything — light, electrons, even you — behaves as both a wave and a particle. Matter has a wavelength, inversely proportional to its momentum.
The central equation of quantum mechanics. It describes how the quantum state of a system — the wavefunction ψ — evolves over time. The wavefunction encodes everything knowable about a particle.
You cannot simultaneously know a particle's exact position and exact momentum. This isn't a measurement limitation — it's how reality is built.
A quantum system exists in all possible states at once until measured. The wavefunction's squared amplitude gives the probability of finding each outcome — the universe runs on probability at its core.
Two particles can share a single quantum state — measure one, and the other responds instantly, no matter the distance. Einstein called it "spooky action at a distance." Bell's theorem proved it's real.
No two fermions (electrons, protons, neutrons) can occupy the same quantum state simultaneously. This is why atoms have structure, why matter is solid, why chemistry exists.
Particles can pass through energy barriers they classically shouldn't be able to cross. The wavefunction leaks through. This powers the sun, enables scanning tunneling microscopes — and flash memory.
Quantum mechanics meets special relativity. Dirac's equation describes relativistic electrons — and predicted the existence of antimatter before it was ever observed.
The quantum version of a mass on a spring. Its evenly-spaced energy levels underpin quantum field theory — every particle is an excitation of its field, modeled as oscillators.
Mass and energy are the same thing in different forms. A small amount of mass holds an enormous amount of energy — the principle behind nuclear power and the sun.
Gravity isn't a force — it's the curvature of spacetime caused by mass and energy. These ten equations describe how matter tells spacetime how to curve, and curved spacetime tells matter how to move.
Time slows down and lengths contract for objects moving near light speed, relative to a stationary observer. GPS satellites must correct for this daily.
Four equations that unified electricity, magnetism, and light. They predicted electromagnetic waves traveling at the speed of light — revealing that light is an electromagnetic wave.
The force on a charged particle moving through electric and magnetic fields — the basis of motors, particle accelerators, and mass spectrometers.
Zeroth: If A = B and B = C in thermal equilibrium, then A = C. Defines temperature.
First: Energy is conserved — ΔU = Q − W.
Second: Entropy always increases — S ≥ 0. Time's arrow.
Third: Absolute zero is unreachable.
Connects the microscopic world of particles to macroscopic thermodynamics. Entropy is just counting microstates.
First: Objects in motion stay in motion unless acted upon.
Second: Force equals mass times acceleration.
Third: Every action has an equal and opposite reaction.
Every mass attracts every other mass. Accurate enough to land rovers on Mars — superseded by general relativity only in extreme gravity.
Reformulations of classical mechanics in terms of energy rather than forces. The Lagrangian (L = T − V) and Hamiltonian frameworks became the language of quantum mechanics and field theory.
First: Orbits are ellipses with the central body at one focus.
Second: A line from planet to sun sweeps equal areas in equal times.
Third: The square of the orbital period is proportional to the cube of the semi-major axis.
Gives the speed of a body in orbit at any point, given its distance from the central body and the orbit's semi-major axis. Essential for Hohmann transfers and rendezvous calculations.
The tyranny of the rocket equation: the velocity a rocket can achieve depends on exhaust speed and the ratio of initial to final mass. This is why staging exists.
Our best description of fundamental particles and three of the four forces (electromagnetic, weak, strong — gravity excluded). Fermions (quarks, leptons) make up matter; bosons (photon, gluon, W/Z, Higgs) carry forces.