Laws as Approximations
Every physical law is an approximation. It holds within some regime of scale, speed, energy, or precision — and breaks down when you push outside that regime. This is not a flaw in physics; it is the honest structure of scientific knowledge.
Newton's law of gravity is a spectacularly accurate approximation for objects moving slowly relative to the speed of light and for gravitational fields that are not too strong. It fails at high speeds (where special relativity matters), near very massive objects (where general relativity matters), and at the scale of single atoms (where quantum mechanics takes over). Einstein's general relativity is a better approximation in those regimes — but it too is expected to fail at the Planck scale, where quantum gravity would take over, and we do not yet have that theory.
Why "Approximation" Is Not a Weakness
Calling laws approximations might sound like they're untrustworthy. The opposite is true. Knowing the domain of validity of an approximation is knowing when it is safe to use it. Newtonian mechanics is so accurate within its domain that it still sends spacecraft to Jupiter. The approximation is exact enough for any practical purpose within that regime.
The weakness comes only when you forget the domain. Engineers who designed early particle accelerators discovered this: at the speeds needed, the particles gained mass in ways Newtonian mechanics could not predict, and the machines didn't work. The fix was relativistic corrections — a better approximation for that regime.
The Hierarchy
Physics has a layered structure of increasingly accurate approximations, each valid in its domain:
- Classical mechanics (Newtonian): objects much larger than atoms, speeds much less than light
- Special relativity: fast-moving objects, flat spacetime
- General relativity: strong gravitational fields, curved spacetime
- Quantum mechanics: atomic and subatomic scale
- Quantum field theory / QED: particles, fields, and their interactions at high energy
- (Open) Quantum gravity: unknown regime where quantum mechanics and general relativity must both apply
Each layer contains the previous one as a limiting case: Newton follows from Einstein when speeds are small; classical mechanics follows from quantum mechanics when objects are large.
The Implication for Truth Claims
Feynman is careful about what "the laws of physics" means. He does not say they are false; he says they are descriptions that happen to work within a domain, and we should always be suspicious that there is a deeper or more accurate description waiting to be discovered. The method is not to seek final truths but to continuously improve approximations and extend their reach.
Connections
- experiment-as-sole-judge — the mechanism by which we discover that an approximation has failed
- epistemic-humility — approximations are an institutionalized form of intellectual humility
- general-relativity-gravity — Einstein's correction of Newton is the paradigmatic example