Classical physics derived from quantum mechanics: Feynman Path Integral

Classical Mechanics and Relativity: Lecture 5
0:00 Introduction
2:35 Fermat's Principle
9:57 Variational principles
17:16 Double slit experiment
21:38 Quantum interference
25:08 Feynman Path Integral
31:12 Quantum trajectories
38:26 Classical Action of quantum paths
42:36 Path integral representation of wavefunction
44:17 Classical path from quantum interference

Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete and self-contained course in which everything is derived from scratch.

In this lecture I make the connection between classical mechanics and quantum mechanics. By analogy to Fermat's principle of least time in the theory of optics, and by considering a generalization of the double slit experiment, I introduce Feynman's Path Integral formulation of quantum mechanics. From it, I derive the principle of least action, and hence all of classical mechanics.

Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler

[Hecatonicosachoron]

This idea of breaking down wave propagation in free space as multiple-slit diffraction but increasing the number of barriers and slits is really great!

[patb]

the best simple explanation of path integrals I have seen.

[sankatmochan]

Fist time i have understood something…its mind blowing just like Feynman.Thanks❤❤❤❤

[a.c.e]

Best...explanation...ever. I cannot express how much this helped me in both understanding the math and being able to now understand the more complex formulations with normalization in them. I cannot thank you enough. This video deserves to have at least 10 million views, there is literally no other source that explains it this well. I with all of my being, significant or little, thank you for the time and passion sir.

[iliavarnaseri]

I am amazed by how you are able to articulate these complex subjects so clearly! I am loving these lectures!

[shrd]

Excellent and ground up explanation of Feynman path integral. Thank you.

[stauffap]

I've been looking for this type of mathematical discription of what feynman was talking about in his lectures for a couple of years now, so this is very exciting to me. Now, i can finally tackle some problems quantitatively :)

Your explanations were very clear and understandable, thank you!

[irtazaazim]

each word you speak is full of wisdom.... loved it

[camac]

Beautiful lectures, always so clear. Love from italy

[andiware]

Thank you very much. This was great review on a tricky topic.

[stevenschilizzi]

Very clear introduction to Feynman’s PI. Many thanks for your effort.
This has raised my curiosity, however, and I’m interested to know how one goes from this introductory exposition to the more standard form of FPIs that have an integral in the exponent of e. Could you do a video on that? Thanks again!

[realdarthplagueis]

Great video! Probably the best explanation I have ever seen of these ideas.

I have one (perhaps stupid) question: If the paths around the path of least action creates constructive interference, why can't paths around (very near) other paths do the same? In your example you drew 3 vectors whose sum was nearly zero, and therefore had destructive interference, but would one not see constructive interference for vectors near (similar) any of the individual paths in that example? So I guess I don't understand why the sum of these vectors _around_ the path of least action is so special, given the argument about the sum of the vectors in your example.

[quantumwormholes]

I'm certain that anything in the universe comes into being from interference. All phenomena seem to slide through the rifts of spacetime left untouched by other phenomena.

[xjuhox]

Nicely done! But the choice of quantum phase, ϕ = kx - ωt, is not an obvious step.

[faizahmed]

these lectures are very helpful. Pleas upload if passible mathematical physics from scratches to advanced level

[louis]

the intensity should be proportional to A^2, but you said it equals to A^2?

[gibbs-]

The lecture was very nice, sir. I have a question. Why action S should have the same dimension as phase (precisely, S/ħ)? Is this by coincidence? Or any interpretation?