The Closest We’ve Come to a Theory of Everything

Summary by Krater

This video explores the principle of least action in physics, tracing its history from Fermat and Bernoulli to Maupertuis, Euler, and Hamilton, and showing how it unifies mechanics and optics.

From the video

Answers: What is the principle of least action and how does it work?

• principle of least action
• Fermat's principle of least time
• Snell's law
• Maupertuis' principle
• Hamilton's principle
• Euler-Lagrange equation
• calculus of variations

What it concludes

• The path of fastest descent between two points is an arc of a cycloid, not a straight line.
• Snell's law of refraction can be derived by finding the path that minimizes travel time rather than distance.
• Maupertuis' principle states that nature minimizes action, defined as mass times velocity times distance.
• Euler and Lagrange added mathematical rigor to the principle of least action, proving energy conservation and fixed energy between paths.
• Hamilton's principle reformulates the principle of least action using the Lagrangian (kinetic minus potential energy) integrated over time.
• The principle of least action is equivalent to Newton's second law F = ma but applies more broadly across mechanics and optics.