4 ms·

I'm being a bit cheeky; I have a physics degree. And I love Feynman's take on magnetism if you look up that video. He makes a strong distinction between "why" a

I'm being a bit cheeky; I have a physics degree. And I love Feynman's take on magnetism if you look up that video. He makes a strong distinction between "why" and "how" noting that physics doesn't really know why. It's a needed dose of humility for those who need to be reminded that humans are NOT the masters of the universe, and our understanding of physics has profound limits (and is poorly distributed throughout the human population). Why is the principle of least action a thing? Why does entropy only ever increase? What is actually doing all that computation behind quantum effects? No-one knows.

Cleonis 3y ago
About Hamilton's stationary action (which you refer to as 'least action'). I have created an educational resource in which I address the question of how it comes about that F=ma can be recovered from Hamilton's stationary action. This resource gives a two-pronged approach: the concepts are illustrated with interactive diagrams, and parallel to that a full presentation of the mathematics. I start with a discussion of the nature of Calculus of Variations. I use the problem of a soap film stretching between two parallel concentric rings as motivating example. This leads to a derivation of the Euler-Lagrange equation. Then I move to the Catenary problem. Interestingly, with the catenary problem both approaches are possible; you can solve for the catenary with differential calculus (as Leibniz did) or you can apply calculus of variations. What that means is that the catenary problem can serve as a Rosetta stone, offering a bridge between differential calculus and calculus of variations. http://cleonis.nl/physics/phys256/calculus_variations.php http://cleonis.nl/physics/phys256/calculus_variations.php The discussion specifically for Hamilton's stationary action is in an article of its own: http://cleonis.nl/physics/phys256/energy_position_equation.php http://cleonis.nl/physics/phys256/energy_position_equation.p...

Cleonis 3y ago

About Hamilton's stationary action (which you refer to as 'least action'). I have created an educational resource in which I address the question of how it comes about that F=ma can be recovered from Hamilton's stationary action. This resource gives a two-pronged approach: the concepts are illustrated with interactive diagrams, and parallel to that a full presentation of the mathematics. I start with a discussion of the nature of Calculus of Variations. I use the problem of a soap film stretching between two parallel concentric rings as motivating example. This leads to a derivation of the Euler-Lagrange equation. Then I move to the Catenary problem. Interestingly, with the catenary problem both approaches are possible; you can solve for the catenary with differential calculus (as Leibniz did) or you can apply calculus of variations. What that means is that the catenary problem can serve as a Rosetta stone, offering a bridge between differential calculus and calculus of variations. http://cleonis.nl/physics/phys256/calculus_variations.php http://cleonis.nl/physics/phys256/calculus_variations.php The discussion specifically for Hamilton's stationary action is in an article of its own: http://cleonis.nl/physics/phys256/energy_position_equation.php http://cleonis.nl/physics/phys256/energy_position_equation.p...