What cannot be created or destroyed is conserved

Why this rule exists

Conservation laws turn a messy, time-varying process into a single equation: the total before equals the total after. You rarely need to follow every intermediate step. Each conservation law also reflects a symmetry of nature — energy conservation follows from the fact that the laws of physics do not change over time — which is why these rules are more fundamental than the forces they constrain.

In practice

Before solving anything, ask what is conserved: energy, momentum, charge, angular momentum. Draw a boundary around a closed system, write the conserved total on each side, and set them equal. If your answer seems to create or destroy a conserved quantity, the error is in the bookkeeping, not the universe.

Example

# A mass m dropped from height h, just before impact:

E_before = m*g*h        # all potential energy
E_after  = 1/2*m*v^2       # all kinetic energy

# Energy is conserved, so set them equal:
m*g*h = 1/2*m*v^2   ->   v = sqrt(2*g*h)

# Note: m cancels. The speed does not depend on mass.

When it doesn't apply

Conservation holds only for a closed system. An open system exchanges energy or momentum with its surroundings, so account for what crosses the boundary. Conserved is also frame- and scale-dependent — mass and energy trade places near the speed of light, and only their combined total is truly fixed.

Related rules in this book

Sources

• The Feynman Lectures on Physics, Vol. I — Feynman, R. Ch. 4: "Conservation of Energy." Addison-Wesley, 1964.
• Invariante Variationsprobleme (1918) — Noether, E. — the theorem linking each symmetry to a conserved quantity.