Hamilton’s principle

Does light take all possible paths at the same time? 🌏 Get exclusive NordVPN deal here ➵ https://NordVPN.com/veritasium It’s risk free with Nord’s 30 day money-back guarantee!✌

A massive thank you to Dr. Andrew Mitchell for all his help and expertise. If you want to delve further into this topic then we highly recommend his lecture on Classical physics derived from quantum mechanics: https://www.youtube.com/watch?v=2iuLwWDYC4U&t=1s

We’re incredibly grateful to Prof. David Kaiser, Prof. Steven Strogatz, Prof. Geraint F. Lewis, Elba Alonso-Monsalve, Prof. Christopher S. Baird, Prof. Anthony Bloch, and Prof. Stephen Bartlett for their invaluable contributions to this video.

A special thanks to Mahesh Shenoy from FloatHeadPhysics for his help with this video. Check out his excellent intuitive video on the UV Catastrophe here (Sep 2024): https://www.youtube.com/watch?v=ALEDjjAVZSY

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0:00 What path does light travel?
2:40 Black Body Radiation
6:47 How did Planck solve the ultraviolet catastrophe?
9:42 The Quantum of Action
13:25 De Broglie’s Hypothesis
15:16 The Double Slit Experiment
20:00 How Feynman Did Quantum Mechanics
25:01 Proof That Light Takes Every Path
31:16 The Theory of Everything

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Try Snatoms! A molecular modelling kit I invented where the atoms snap together.
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References:
Armin Hermann (Nov 1974). The Genesis of Quantum Theory (1899-1913). – https://ve42.co/genquanttheor
Richard P. Feynman (1985). QED The Strange Theory of Light and Matter. – https://ve42.co/qed
A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The
Principle of Least Action: History and Physics. – https://ve42.co/Bloch2018
Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. – https://ve42.co/LazyU
PBS Space Time. (Nov 2021) – https://www.youtube.com/watch?v=Q_CQDSlmboA
Sabine Hossenfelder. (May 2022) – https://www.youtube.com/watch?v=A0da8TEeaeE
Max Planck (1901). On the Law of Distribution of Energy in the Normal Spectrum. Annalen der Physik – https://ve42.co/lawdistenergy
Paul Ehrenfest (1911). Welche Züge der Lichtquantenhypothese spielen in der Theorie der Wärmestrahlung eine wesentliche Rolle?. Wiley Online Library – https://ve42.co/quantthermrad
Nils-Erik Bomark and Reidun Renstrøm (Aug 2023). The Ultraviolet myth. Proceedings of Science – https://ve42.co/uvmyth
Planck’s law. In Wikipedia – https://ve42.co/planckslaw
PBS Space Time. (Jul 2017). – https://www.youtube.com/watch?v=vSFRN-ymfgE&t=10s
Einstein and The Photoelectric Effect. (Jan 2005) via APS News – https://ve42.co/einsteinphotoelec
Louis de Broglie (1924). On the Theory of Quanta. – https://ve42.co/theoryquanta
Larry Sorensen (2012). Path Integrals 1. University of Washington – https://ve42.co/pathintegrals
Feynman’s Method of “A Particle Exploring All Possible Paths”. (Mar 2018) via Pure Dhamma – https://ve42.co/allposspaths
A great intuitive video on the Feynman path integral approach – https://www.youtube.com/watch?v=Sp5SvdDh2u8&t=1253s
Origins of Quantum Theory. via University of Pittsburgh – https://ve42.co/origquanttheor

Images & Video:
Nobistor Altona 1880 via NDR – https://ve42.co/streetlight
Edison incandescent lights by William J. Hammer via Wikimedia Commons – https://ve42.co/edinclights
The full expanded form of the Standard Model Lagrangian by Chen Ning Yang et al. via Wikipedia – https://ve42.co/stmodellang
Muon Ray. (2011). https://www.youtube.com/watch?v=-QUj2ZRUa7c
Muon Ray. (2011). https://www.youtube.com/watch?v=1C7abO7LtV0
Bohrs Atomic Model via EEEGUIDE.COM – https://ve42.co/bohrmodel

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Special thanks to our Patreon supporters:
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Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver and Peter Nelson
Animated by Fabio Albertelli, Mike Radjabov, Ivy Tello, Andrew Neet and Emma Wright
Illustrations by Jakub Misiek, Tommy A. Steven and Cainejan Esperanza
Filmed by Derek Muller and Casper Mebius
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Bean, Geeta Thakur, Emilia Gyles, Zoe Heron, Emily Zhang and Tori Brittain

Thumbnail contributions by Ben Powell, Jakub Misiek, Ren Hurley, and Peter Sheppard

Additional video/photos supplied by Getty Images and Storyblocks
Music from Epidemic Sound

The single principle that underpins all of physics. Head to https://brilliant.org/veritasium to start your free 30-day trial and get 20% off an annual premium subscription.

A massive thank you to Prof. Steven Strogatz for his expertise and enthusiasm.

A huge thank you to Prof. Haithem Taha, Prof. Anthony Bloch, Dr. Carl-Fredrik Nyberg Brodda, Dr. Sarah Millholland, and Dr. Andrew Mitchell for all their help with finding the story and getting it right.

A special thanks to Dr. Aurèle Adam, Ron Haaksman, Marc Serra Peralta, and everyone at the Delft Makerspace for their help with preparing and performing experiments.

00:00 One rule that replaces all of physics
00:51 The problem of fastest descent
05:09 Fermat’s principle
07:17 Bernoulli’s solution
10:38 Maupertuis’ principle
12:28 Maupertuis attacked and ridiculed
14:01 Euler & Lagrange to the rescue
17:22 The general approach to solving these problems
19:32 Writing the principle into its modern form
23:17 Why the principle works
27:08 Another way to do mechanics
30:19 A “spooky” breakthrough

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Join us on Patreon for early access videos and exclusive bonus content https://ve42.co/PatreonDE

Patrons: Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Burt Humburg, Chris Harper, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, I. H., John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Martin, Matthias Wrobel, Max Paladino, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, Toni , TTST, Ubiquity Ventures, wolfee

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically – https://ve42.co/SnatomsV

▀▀▀
Key references:

A fantastic book on the history of the Principle of Least Action: Rojo, A. and Bloch, A. The
Principle of Least Action: History and Physics. – https://ve42.co/Bloch2018
Coopersmith, J. (2017). The lazy universe: an introduction to the principle of least action. Oxford University Press. – https://ve42.co/LazyU
3Blue1Brown. The Brachistochrone, with Steven Strogatz via Youtube – https://ve42.co/Brach3B1B
Vsauce. The Brachistochrone via Youtube – https://ve42.co/BrachV
PBS Space Time. Is ACTION The Most Fundamental Property in Physics? via Youtube – https://ve42.co/PBSAction

Full list of references: https://ve42.co/T

Images & Video:
Voltaire. (1753). Diatribe du Docteur Akakia. – https://ve42.co/DiatribeAkakia
Philosophical Transactions cover. via Wikimedia Commons – https://ve42.co/PhilTransImage
Kids Fun Science. (Jun 28, 2017). Refraction of Light with a arrow experiment via Youtube – https://ve42.co/RefractionFunSci
Physics with Simon Poliakoff. Refraction demonstration with water and laser via Youtube – https://ve42.co/SimonPoliakoff
Mercury Transit Across Sun. via Nasa.gov – https://ve42.co/MercTransit

▀▀▀
Directed by Casper Mebius
Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Mike Radjabov, Gregor Čavlović, Emma Wright, James Finnemore and David Szakaly
Illustrated by Jakub Misiek, Emma Wright, and Maria Gusakovich
Filmed by Derek Muller and Casper Mebius
Additional research by Gabe Bean, Gregor Čavlović, and Geeta Thakur
Produced by Casper Mebius, Derek Muller, Rob Beasley Spence, Gabe Bean, Gregor Čavlović, and Tori Brittain
Thumbnail contributions by Jakub Misiek, Ren Hurley and Peter Sheppard
Additional video/photos supplied by Getty Images, Storyblocks, and NASA SVS
Music from Epidemic Sound

Hamilton’s principle

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This Single Rule Underpins All Of Physics