3 ms·

The Lazy Universe: An Introduction to the Principle of Least Action

20 points by lagrange77 5y ago

lagrange77 5y ago
Just wanted to share this wonderful book with you. Interesting review: https://aapt.scitation.org/doi/10.1119/1.5024210 https://aapt.scitation.org/doi/10.1119/1.5024210
nh23423fefe 5y ago
after going through https://www.youtube.com/playlist?list=PL2ym2L69yzkamORF9DGWRhE9qUnb0_-6H https://www.youtube.com/playlist?list=PL2ym2L69yzkamORF9DGWR... i found i understood action much better. i kept thinking why the hell are the units "phase space" what does this even mean. How is that even connected to h_bar? But then following along the derivations to define the action and then the mystery kind of goes away. Understanding the machinery makes the magic real, but also evaporates the confusion. Like minimizing the action is interesting, but the real a-ha for me, was the derivation of the euler-lagrange and see how the functional equation actually works. Following the types, and compiling in my mind, gave the understanding.
- lagrange77 5y ago
  > Understanding the machinery makes the magic real, but also evaporates the confusion. Physics and Mathematics in one sentence. Nicely said. Thanks for the playlist, will definitely look into it, good lectures on variational calculus are rare.
  - nh23423fefe 5y ago
    Yeah I wanted to finally understand QM better so I needed to understand how basic wavefunctions are actually solved for. After this playlist, I can't solve for simple potentials myself, but I can follow along with proofs much better now and my intuition is building
Cleonis 5y ago
I have created an exposition of Hamilton's stationary action that is visualization based. The visualizations consist of interactive diagrams. Each diagram represents a case where the visitor can sweep out a range of trial trajectories (using a slider), to home in on the true trajectory. The three main diagrams have multiple sliders, allowing the visitor to make a local adjustment to the trial trajectory. The diagrams display how the kinetic energy and the potential energy respond to change of the trial trajectory. http://www.cleonis.nl/physics/phys256/energy_position_equation.php http://www.cleonis.nl/physics/phys256/energy_position_equati... The objective of the exposition is to make Hamilton's stationary action entirely transparent.
- lagrange77 5y ago
  That's wonderful. Dank u well!

20 points by lagrange77 5y ago

Just wanted to share this wonderful book with you. Interesting review: https://aapt.scitation.org/doi/10.1119/1.5024210 https://aapt.scitation.org/doi/10.1119/1.5024210

nh23423fefe 5y ago

after going through https://www.youtube.com/playlist?list=PL2ym2L69yzkamORF9DGWRhE9qUnb0_-6H https://www.youtube.com/playlist?list=PL2ym2L69yzkamORF9DGWR... i found i understood action much better. i kept thinking why the hell are the units "phase space" what does this even mean. How is that even connected to h_bar? But then following along the derivations to define the action and then the mystery kind of goes away. Understanding the machinery makes the magic real, but also evaporates the confusion. Like minimizing the action is interesting, but the real a-ha for me, was the derivation of the euler-lagrange and see how the functional equation actually works. Following the types, and compiling in my mind, gave the understanding.

lagrange77 5y ago
> Understanding the machinery makes the magic real, but also evaporates the confusion. Physics and Mathematics in one sentence. Nicely said. Thanks for the playlist, will definitely look into it, good lectures on variational calculus are rare.
- nh23423fefe 5y ago
  Yeah I wanted to finally understand QM better so I needed to understand how basic wavefunctions are actually solved for. After this playlist, I can't solve for simple potentials myself, but I can follow along with proofs much better now and my intuition is building

Cleonis 5y ago

I have created an exposition of Hamilton's stationary action that is visualization based. The visualizations consist of interactive diagrams. Each diagram represents a case where the visitor can sweep out a range of trial trajectories (using a slider), to home in on the true trajectory. The three main diagrams have multiple sliders, allowing the visitor to make a local adjustment to the trial trajectory. The diagrams display how the kinetic energy and the potential energy respond to change of the trial trajectory. http://www.cleonis.nl/physics/phys256/energy_position_equation.php http://www.cleonis.nl/physics/phys256/energy_position_equati... The objective of the exposition is to make Hamilton's stationary action entirely transparent.

lagrange77 5y ago
That's wonderful. Dank u well!