Seonglae ChoPrinciple 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.
Stationary Action Principle
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.
https://en.wikipedia.org/wiki/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.
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.
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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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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.
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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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Written by Casper Mebius and Derek Muller
Edited by Trenton Oliver and Peter Nelson
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https://www.youtube.com/watch?v=MfPhiRxnfRA
