The Action Principle

Creator

Creator

Seonglae Cho

Created

Created

2024 Mar 30 15:59

Editor

Editor

Seonglae Cho

Edited

Edited

2025 Apr 17 22:45

Refs

Refs

Principle of Least Action, Hamilton’s Principle

The physical system moves along a path that minimizes or maximizes a certain quantity called action.

Planck constant is a unit of Action; Quantum of Action. This explains why electron angular momentum is quantized and explains the photoelectric effect. This physical quantity is fundamental to the quantization of the universe and applies to all matter. As it maintains as a

Standing wave, having wave characteristics means it explores all possible paths rather than a single path.

Action

Action is defined by the integral of the Lagrangian, which describes the state of the system over time using either the

Lagrangian or

Hamiltonian.

The action principle leads to different Lagrangians: for

Classical Mechanics, for

Special Relativity, for

Electromagnetism, and for

General Relativity, all of which are derived from Action.

is

Kinetic energy and is

Potential Energy

Stationary Action Principle

Euler–Lagrange equation

Hamilton's principle

In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the differential equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories.

Hamilton's principle

https://en.wikipedia.org/wiki/Hamilton's_principle

Hamilton's principle

Action principles

Action principles lie at the heart of fundamental physics, from classical mechanics through quantum mechanics, particle physics, and general relativity.[1] Action principles start with an energy function called a Lagrangian describing the physical system. The accumulated value of this energy function between two states of the system is called the action. Action principles apply the calculus of variation to the action. The action depends on the energy function and the energy function depends on the position, motion, and interactions in the system: variation of the action allows the derivation of the equations of motion without vector or forces.

Action principles

https://en.wikipedia.org/wiki/Action_principles

양자역학 (영상 마지막 실험 소름...)

싸늘하다. 양자역학이 가슴에 와서 꽂힌다. 하지만 걱정하지 마라. 모든 건 파동이자 입자니까. 조은규, Wun Ho Lee, 코카펩시 님 멤버십 회원 가입 감사합니다. ▀▀▀ 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 ▀▀▀ 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 ▀▀▀ Sign up to our Patreon to watch the Q&A for free: / veritasium Try Snatoms! A molecular modelling kit I invented where the atoms snap together. https://ve42.co/SnatomsV ▀▀▀ 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 ▀▀▀ Special thanks to our Patreon supporters: Adam Foreman, Albert Wenger, Alex Porter, Alexander Tamas, Anton Ragin, Autodidactic Studios, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, Gnare, gpoly, Greg Scopel, Juan Benet, Keith England, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, qiaohui wei, Richard Sundvall, Sam Lutfi, Tj Steyn, TTST, Ubiquity Ventures, wolfee ▀▀▀ 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 Strong, Geeta Thakur, Emilia Gyles, Zoe Heron, Emily Zhang and Tori Brittain Thumbnail contributions by Ignat Berbeci, Ben Powell, Jakub Misiek, Ren Hurley, and Peter Sheppard Additional video/photos supplied by Getty Images and Storyblocks Music from Epidemic Sound Translated by Mingi Kwon, GivernyAI Dubbed by Mingi Kwon

양자역학 (영상 마지막 실험 소름...)

https://www.youtube.com/watch?v=MfPhiRxnfRA

양자역학 (영상 마지막 실험 소름...)

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