• Richard Feynman QED pixel-art physics sticker, 3" × 3" / White

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Richard Feynman Sticker

Quantum? It’s Complicated. | Physics

\[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]
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Doodles that became the working language of particle physics. Feynman shared the 1965 Nobel Prize for quantum electrodynamics and gave physics the Feynman diagram. A pixel-art portrait on a 3" × 3" sticker; the physics panel below has the equation, every symbol and the sources.

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3″ × 3″ kiss-cut sticker.

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The physics

Feynman's rule: to get from a to b, a quantum particle takes every possible path, and each path contributes a phase set by its action. You add all those amplitudes and square the total to get the probability.

The sticker says Quantum? It's Complicated. Feynman's own view was that the rule is simple and you will not like it.

In 1948 Richard Feynman published a new way to do quantum mechanics. To find the chance that a particle gets from a to b, do not follow one path. Follow all of them, even those looping past the Moon. Give each path a little arrow, a complex number of fixed length, turned through an angle equal to the path's action S divided by ħ. Add every arrow. The first formula on this page is that sum. Square the length of the total, the second formula, and that is the probability.

Why, then, does a ball follow one curve? ħ is tiny. For paths far from the classical one, the angle swings wildly between neighbouring paths, their arrows point every which way and cancel. Only near the path of stationary action do neighbours share nearly the same angle, so their arrows line up and add. Classical mechanics is what remains after everything else cancels.

Applied to electrons and light, this thinking gave quantum electrodynamics and the diagrams named for him. He shared the 1965 Nobel Prize with Sin-Itiro Tomonaga and Julian Schwinger, who had reached the same theory by other routes.

The line on the live page comes from his lectures published as The Character of Physical Law: "I think I can safely say that nobody understands quantum mechanics." He meant the rules work perfectly and explain nothing about themselves.

On the commission investigating the 1986 Challenger disaster, at a televised hearing, he dropped a piece of the booster's rubber seal into a glass of ice water to show how badly it behaved in the cold.

The rule is one line. The complicated part is that every path counts.

Equations

\[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]
\[P = \left\lvert\sum_k \phi_k\right\rvert^{2}\]
SymbolMeaningUnit
\(K(b,a)\) amplitude to go from a to b (propagator), in d spatial dimensions \(\mathrm{m^{-d}}\)
\(S\) classical action along a path \(\mathrm{J·s}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(\phi_k\) amplitude for alternative k \(\mathrm{1}\)
\(P\) probability \(\mathrm{1}\)

Sources

  1. Feynman (1948) Space-Time Approach to Non-Relativistic Quantum Mechanics, Rev. Mod. Phys. 20, 367
  2. Feynman (1949) The Theory of Positrons, Phys. Rev. 76, 749
  3. NobelPrize.org — The Nobel Prize in Physics 1965 (Tomonaga, Schwinger, Feynman)
  4. Encyclopaedia Britannica — Richard Feynman
  5. Feynman Lectures on Physics Vol. III Ch. 3: Probability Amplitudes

Source Feynman, R. P. (1948). Space-Time Approach to Non-Relativistic Quantum Mechanics. Reviews of Modern Physics 20, 367–387.doi.org/10.1103/RevModPhys.20.367

Field notes

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