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[NEW VIDEO!] The REAL Three Body Problem in Physics (Patreon)

Published:
2024-07-15 11:37:15
Imported:
2026-06
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Content

Hello! I know I'm super late to the party with this video but it took me way longer than expected to understand! Thank you for your patience and I hope you enjoy the explanation :)

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The REAL Three Body Problem in Physics

👉 To try everything Brilliant has to offer for free for a full 30 days, visit https://brilliant.org/upandatom or click on the link in the description. You’ll also get 20% off an annual premium subscription. Thank you to Dr. Shane Ross for all of your help and consultation with this video. It wouldn't have been possible without you. For a deep dive into chaos theory and nonlinear dynamics, visit Dr. Shane Ross's youtube channel @ProfessorRoss and check out this playlist about the three body problem! https://youtu.be/ZE299fDuPjc Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collections/up-and-atom Subscribe to Up and Atom for physics, math and computer science videos https://www.youtube.com/c/upandatom For a one time donation, head over to my PayPal :) https://www.paypal.me/upandatomshows *A big thank you to my AMAZING PATRONS!* Michael Seydel, Thorsten Auth, Chris Flynn, Izzy Ca, Tate Lyles, Richard O McEwen Jr, Scott Ready, John H. Austin, Jr., Brian Wilkins, David Johnston, Thomas Krause, Lynn Shackelford, Ave Eva Thornton, Andrew Pann, Anne Tan, Jeffrey Dutt, Joseph Lamoree, Francisco, Marc-Antoine, Thomas Urech, chuck zegar, David Tuman, Ben Mitchell, Tyler Simms, James Mahoney, Jim Felich, Jeremy, Robin High, KiYun Roe, DONALD McLeod, Ron Hochsprung, Andi B, James Matheson, Kevin Anderson, Alexander230, Tim Ludwig, Alexander Del Toro Barba, Justin Smith, A. Duncan, Mark Littlehale, Tony T Flores, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, bpatb, Joel Becane, Cy 'kkm' K'Nelson, eris esoteric, Paul Barclay, 12tone, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Louis Mashado, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Susan Jones, Jonathan Rayback, geek1027, Smarter Every Day, Nick McKay, Miles Freeman, Bunny Lushington, Jake!, Motty Porat, Yaw Mintah, Carlos Escolar, Anthony Docimo, robert lalonde, Julian Nagel, Cassandra Durnord, Paul Bunbury, Richard Rensman, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, James N Smith, Roland Gibson, Piotr Klos, Joe McTee, Oleg Dats, John Spalding, Simon J. Dodd, Tang Chun, Michelle, William Toffey, Fabio Manzini, James Horsley, Craig Tumblison, Cameron Tacklind, Lance Ahmu, Steve Watson, Potch, Thomas P Taft, Indrajeet Sagar, Markus Herrmann, Pablo de Caffe, Taylor Hornby, Colin Byrne, Jesper de Jong, Sofia Fredriksson, Phat Hoang, Spuddy, Sascha Bohemia, tesseract, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, James Palermo, Chris Teubert, Fran, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Louis M, ROBERT C PAYNE, Moose Thompson, Rick DeWitt, Pedro Paulo Vezza Campos, S, Garrett Chomka, Rebecca Lashua, Pat Gunn, George Fletcher, RobF, Vincent Seguin, Michael Brunolli, Shawn, Jesse Clark, Steven Wheeler, Philip Freeman, Armin Quast, Jareth Arnold, Simon Barker, amcnea and Simon Dargaville. Creator - Jade Tan-Holmes Script - Jade Tan-Holmes Animations - Tom Groenestyn Music - epidemicsound.com Chapters 0:00-1:02 What is The Three Body Problem? 1:02-5:41 Newton's Dilemma 5:41- 7:00 A worthy contestant 7:00-8:22 Fixed Points 8:22-9:39 Saddle Points 9:39-11:07 Chaos is deterministic, but unpredictable 11:07-13:04 The Three Body Problem is unsolvable 13:04 Think like a scientist

Comments

Tim Ludwig

Hi Jade! Great to see a new video from you! Thanks for the very nice explanation of the three body problem and the origin of chaos 😃

Armin Quast

This is a really great video. What I like most about it is that you've used history, maths and phyics to explain the problem.

Martin S

Lovely animations in this one, well done!

Scott Ready

Three body problems come in many guises. Poincare gave birth to modern Optimal Control Theory in which a controlling function effects a system simplified as two bodies. The controlling operator can be a matrix of functions that interacts with a pair of matrices representing a system. The linear operator mechanics nested within Dirac brackets has a higher Cantor aleph rating than the continuum. The manifolds within which the dynamics plays out can have a Riemannian curvature with saddle points and aspects of negative or positive curvature spread through out. A control function can change the pattern for geodesics, however it will have physical limits and everything obeys the conservation of energy and momentum. In going from the 2-body quantized angular momentum model of hydrogen given by Niels Bohr in 1911 to a 3-body model with one more electron or a compound nucleus, one has to grasp the multi-body difficulties that underlie fermions, those mass-endowed particles that refuse to occupy the same place at the same time, unless they have diametrically opposing spins. The atomic science may seem to be abstract and complicated, and yet, we deal with many aspects of 3-body problems in our daily frustrations in trying to find certain objects. An object (or creature) can hide by slipping behind another object. Herein we have the birth of the three dimensional world. Entangled fermions map out the geometry of a room and create the third dimension. When looking for a missing key, we have a 3-body problem in the form of the looker, the key, and everything else which is not of immediate interest. With a Dirac comb you search the landscape, sweep away distractions and hopefully pull off a sequence of steps to form an operator that acts on a state, and if you are lucky, gives it right back as the key in your hand. To wit, you solve an eigenvalue problem in a complicated three dimensional world with a history and a perpetual desire to try out every possible arrangement or mapping of a room. Feynman says sum over all of the possible sequences of steps in going from A to B as though they were quantum amplitudes. When a 3-body problem gets parsed into more components and greater detail, a Law of Large Numbers takes over and one sees the familiar classical world that minimizes the action S at a saddle point (in a space of functions). Variations of sequences (paths) away from the minimum paths tend to cancel each other out. A first order shift away from a saddle point introduces no more than a second order change in the action S for a path close to satisfying dS = 0. This tiny power-packed equation comes from Euler and Lagrange, after the time of Newton, and long before Poincare. The little d for an infinitesimal shift from one alternative to another usually gets written as the delta of Variational Calculus (a predecessor of Optimal Control Theory). The S stands for the action cost of a sequence of steps. Elsewhere in mathematical physics, S stands for entropy, which has its own tally depending on how many entangled bodies one happens to have. Each fermion brings its own space so when we start to accumulate them, we do not add them like dots into an already given space. Instead each particle adds to the number of cross-products of a full 3-dimensional space we have to manage. The dynamics lives in the cross-product of as many Hilbert spaces as we have particles. The number of particles and cross products, the number of dynamical dimensions can expand or collapse down to a point, a singularity. A tremendous amount of sophisticated mathematics (and computer programming) comes into play.