Feynman's Path Integral: The Most Elegant Idea in Physics

How does a particle get from A to B? According to Feynman, it takes every possible path simultaneously—straight lines, loops,
zigzags, all of them. The classical world we see emerges because most paths cancel out, leaving only the one where nature
finds its optimum.

This is the path integral formulation of quantum mechanics.

TIMESTAMPS
0:00 - The Three Pillars of Quantum Mechanics
0:17 - Classical Action and the Lagrangian
0:35 - The Quantum Problem: No Definite Paths
0:54 - Feynman's Sum Over Histories
1:15 - Quantum Amplitudes: Complex Numbers, Not Probabilities
1:32 - The Path Integral Formula
1:50 - Interference: Why Some Paths Survive
2:08 - The Classical Limit: Newton from Feynman
2:28 - Computing the Free Particle Propagator
2:52 - Connection to Schrödinger's Equation
3:10 - Why Path Integrals Matter for Modern Physics
3:31 - The Profound Lesson

WHAT YOU'LL LEARN
• Why quantum particles explore all possible trajectories
• How each path contributes amplitude e^(iS/ℏ)
• The stationary phase principle and constructive interference
• How classical mechanics emerges as ℏ → 0
• The exact solution for the free particle propagator
• Why path integrals are the language of quantum field theory

This video is aimed at physics undergraduates and anyone who wants the real explanation—not analogies, but the actual
physics.

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