Conservation of Energy
Energy is conserved: in any isolated system, the total amount of energy stays constant. It can change form — kinetic to potential, heat to mechanical work, mass to radiant energy — but it cannot be created or destroyed. This is one of the most powerful and most carefully validated principles in physics.
Feynman's treatment is unusual in its philosophical honesty. Most textbooks present energy conservation as a fact about the world. Feynman emphasizes that we have no idea what energy is. It is not a substance, not a fluid, not a mechanism. It is an abstract numerical quantity that, when we compute it for any isolated system, always comes out the same before and after any process. The law tells us the number is invariant; it does not tell us what the number refers to.
The Blocks Analogy
Feynman illustrates with "Dennis the Menace" — a child with indestructible blocks. His mother counts the blocks each day and always gets 28. One day she gets 25 — but discovers three are under the rug. Another day she gets 30 — but realizes some blocks arrived from outside. The conservation law is like counting blocks. We've learned to account for all the hiding places: kinetic energy, gravitational potential energy, heat, chemical energy, nuclear energy, mass itself. When we inventory them correctly, the total is always constant. But we don't know what the blocks are.
Forms of Energy
The main categories that must be tracked:
- Kinetic energy — energy of motion: $KE = \fracmv^2$ (classical)
- Gravitational potential energy — energy stored by height: $PE = mgh$
- Elastic potential energy — energy in compressed or stretched springs
- Chemical energy — stored in molecular bonds; released in combustion, metabolism
- Nuclear energy — stored in nuclear binding; released in fission and fusion
- Thermal energy (heat) — the kinetic energy of atoms in disordered motion
- Radiant energy — carried by electromagnetic radiation (photons)
- Rest-mass energy — E = mc²; mass itself is a form of energy
Why Perpetual Motion Is Impossible
Feynman derives the formula for gravitational potential energy not from force laws but from a simpler argument: perpetual motion machines cannot exist. If PE = mgh were not exact — if the energy of raising an object by height h depended on the path taken — you could design a machine that returned more energy than you put in. The impossibility of perpetual motion forces the formula to be exact. This is the kind of reasoning that gives conservation laws their power: they constrain what formulas can look like, not just what numbers come out.
The Connection to Symmetry
Noether's theorem (1915) shows that conservation of energy is not an independent axiom — it follows from time-translation symmetry: the laws of physics are the same today as they were yesterday and will be tomorrow. If the laws changed with time, energy would not be conserved. Conversely, if you found energy being created or destroyed, you would have evidence that the laws of physics are time-dependent. The six major conservation laws (energy, momentum, angular momentum, charge, baryon number, lepton number) each correspond to a symmetry — see symmetry-conservation-laws.
Connections
- symmetry-conservation-laws — conservation of energy as a consequence of time-translation symmetry
- e-equals-mc-squared — mass is a form of energy; the conversion factor is c²
- available-energy — not all conserved energy can do useful work; entropy governs this
- heat-as-atomic-motion — heat is conserved energy in disordered form