Richard Feynman · Sum over paths
Which path does a particle take — if it takes all of them?
That time, that place
Quantum mechanics computed well but offered no picture. There was no way to imagine what happens as an electron goes from A to B.
Worse, precise calculations of electromagnetic interaction produced infinities. A theory whose answer is infinity is unusable.
Why this question
Feynman's idea: an electron going from A to B does not take one route. It takes every possible route at once.
Straight across, the long way round, out past the Moon and back. Compute a value for each path, add them all, and most cancel — leaving what we observe.
In plain words, nature does not choose a path. It tries all of them, and the overlap is what we see.
What was found
He also invented a way to draw the calculation: Feynman diagrams. A few lines and vertices show which particles interact and how, and you read the equation straight off the picture.
The infinities got a treatment too — renormalisation — which Feynman himself called a dippy shell game. But it worked.
How well: the electron's magnetic property, computed from this theory, agrees with measurement to more than ten decimal places. It is the most precisely verified prediction in physics.
Quantum interaction calculations gave infinities, and offered no picture
The electron's magnetic moment agreeing with experiment past ten decimal places
Particle physics became a subject you calculate by drawing