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Shine a torch into a swimming pool and the beam bends at the water. Light takes the quickest route Pierre de Fermat said so in 1662. But how could light know which route is quickest before it sets off? Richard Feynman's answer is one of the strangest ideas in physics: it doesn't choose a path at all. Every possible path gets an arrow of the same length; the arrows turn with the "action" along each path; add them all up, and almost everything cancels except the path we actually see. This is the story of that idea. A bored teenager and his physics teacher, Mr Bader. A beer party in the Nassau Tavern in Princeton, where Herbert Jehle pointed Feynman to a forgotten 1933 paper by Paul Dirac, and the next morning the word "analogous" turned into an equals sign and the Schrödinger equation fell out. Feynman's arrows, the double-slit stripes, why a thrown ball follows just one path, and his favourite example: a mirror that reflects from its edges once you scrape the right strips away the rainbow on the back of a CD. The 1948 meeting where Bohr said a path had no meaning, Dyson, Schwinger and Tomonaga, and Wheeler trying the idea on Einstein. Then the test. In August 2026, a team at South China Normal University measured the arrows for single photons, step by step, and checked Feynman's two rules on all 1,419,857 paths through their experiment. The sum matched where the photons landed to about 95%. What it did not prove and why is in the last chapter. CHAPTERS 0:00 How does light know the quickest route? 1:04 Hero, Fermat and the lifeguard 2:32 A teacher, a tavern and a forgotten paper 4:31 Feynman's arrows 6:12 Why the world takes one path 8:02 Nobody understood him 9:29 Feynman's paths are everywhere 10:09 Checking the rules: 1,419,857 paths 12:31 Did they prove it? MORE FROM ARTHUR'S PHYSICS The Double-Slit Experiment: 225 Years, and Nobody Can Explain It The Mystery of 1/137: The Number That Haunted Richard Feynman Why Can't Anything Sit Perfectly Still? The Rule Even Einstein Couldn't Break Why Do You Weigh Anything? 99% of Your Mass Isn't Matter SOURCES • Y.-L. Wen, L.-M. Tian et al., "Direct experimental test of Feynman's path integral postulates with single photons", Science Advances (26 August 2026), doi:10.1126/sciadv.aeh1011 • Y. Wen et al., "Demonstration of the quantum principle of least action with single photons", Nature Photonics 17, 717 (2023) • O. S. Magaña-Loaiza et al., "Exotic looped trajectories of photons in three-slit interference", Nature Communications 7, 13987 (2016) • R. P. Feynman, "Space-Time Approach to Non-Relativistic Quantum Mechanics", Reviews of Modern Physics 20, 367 (1948) • R. P. Feynman, Nobel Lecture, 11 December 1965 (nobelprize.org) • R. P. Feynman, The Feynman Lectures on Physics, vol. II, ch. 19, "The Principle of Least Action" • R. P. Feynman, QED: The Strange Theory of Light and Matter (1985) • R. P. Feynman, The Character of Physical Law (1965) • P. A. M. Dirac, "The Lagrangian in Quantum Mechanics", Physikalische Zeitschrift der Sowjetunion 3, 64 (1933) • F. J. Dyson, Physical Review 75, 486 (1949) • J. A. Wheeler, Physics Today 42, 24 (1989); T. Sauer, "Remarks on the Origin of Path Integration: Einstein and Feynman" (arXiv:0801.1654) • "On the interpretation of Feynman diagrams" (arXiv:1901.02233) — Bohr at the Pocono meeting • D. Bohm, Physical Review 85, 166 and 180 (1952) • S. Dürr et al., Science 322, 1224 (2008) IMAGE CREDITS All photographs are from Wikimedia Commons and are shown cropped and tinted. • Richard Feynman, 1959 — public domain • Richard Feynman's Los Alamos ID badge, c. 1943 — United States Army, public domain • Pierre de Fermat, 17th century — public domain • Pierre-Louis Maupertuis, c. 1740 — Robert Tournières, public domain • John Wheeler, Copenhagen 1963 — GFHund, CC BY 3.0 • Paul Dirac, 1933 — Nobel Foundation, public domain • Edward Teller, 1958 — Lawrence Livermore National Laboratory, public domain • Niels Bohr, c. 1922 — AB Lagrelius & Westphal, public domain • Freeman Dyson, 2005 — ioerror, CC BY-SA 2.0 • Julian Schwinger, 1965 — Nobel Foundation, public domain • Sin-Itiro Tomonaga, 1965 — Nobel Foundation, public domain • Albert Einstein, 1921 — Ferdinand Schmutzer, public domain • Rainbow on a CD-ROM — Yann Droneaud, CC BY-SA 2.0 Music: "Science Documentary" by leberch (Pixabay Content License). Everything else is drawn; none of the visuals are AI-generated.

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