The deepest pattern in physics
If you only learn three things from physics, learn the three big conservation laws. They're simpler than they sound and they constrain what can possibly happen.
- Conservation of energy. Energy isn't created or destroyed; it just changes form. The kinetic energy of a falling ball becomes heat and sound when it hits the ground. The chemical energy in food becomes the kinetic energy of your muscles becomes the heat your body radiates. Total energy in a closed system stays the same forever.
- Conservation of momentum. Momentum (mass × velocity) of a closed system stays the same. If two billiard balls collide, the total momentum before equals the total after. If a rocket pushes hot gas backward, the rocket itself moves forward by an exactly compensating momentum. Newton's third law is just conservation of momentum, said differently.
- Conservation of angular momentum. The spinning version. A spinning ice skater pulling her arms in spins faster — same angular momentum, smaller radius, higher speed. Planets orbiting the Sun keep their angular momentum because nothing torques them.
Why these matter more than F=ma
F=ma describes how things change. The conservation laws describe what's preserved through every change. They're the deeper layer. In modern physics they come from a deeper principle still — Noether's theorem, which says every conservation law corresponds to a symmetry of nature. Energy is conserved because the laws of physics don't change with time. Momentum is conserved because they don't change with location. Angular momentum because they don't change with rotation.
Sit with that. The conservation laws aren't separate facts. They're consequences of the universe having symmetries. The universe is the same everywhere, every when, every direction — and that gives us, automatically, energy/momentum/angular-momentum conservation. Symmetry → conservation. Noether published it in 1918.
Where they apply, where they don't
The conservation laws hold in classical mechanics (this track), in special and general relativity (next track), and in quantum mechanics (the track after) — with refinements. Energy at the cosmological scale is more nuanced because the universe is expanding (the symmetry is broken at that scale). At the subatomic scale, energy can briefly fluctuate by tiny amounts (uncertainty principle, quantum track). But for everyday life, the laws are airtight.
The everyday-life summary: everything you spend, you spend from somewhere; everything you do, you do by transferring momentum from somewhere. The universe is a closed accounting system in three columns.