If you like the double slit experiment, you'll probably like Feynmann's "motivation" of the path integral in quantum field theory:
Suppose you take the double slit (plate with two holes in it), and you start adding more holes. Of course the particle will go through all of them, but with less probability the further they are off-axis. We can also add more than one plate, and the particle will go through all possible combinations of holes with some probability. Now suppose we let the number of plates go to infinity, and then let the number of holes in each plate go to infinity. The particle still goes through all of the infinite combinations of holes, with less probability if the path is unlikely. But really, there is nothing left anymore between the particle source and the screen! There is just free space! So this path integral with the particle going sort-of-everyhere weighted by probability actually describes propagation through free space.
That connection between slits in the infinite limit and path integrals is really fascinating. I've read of lot of Feynman, but never that. Where does he talk about it?
I'm actually not sure, off the top of my head, but I think it's from his book "Quantum Mechanics and Path Integrals"; he also used it in lectures IIRC.
Suppose you take the double slit (plate with two holes in it), and you start adding more holes. Of course the particle will go through all of them, but with less probability the further they are off-axis. We can also add more than one plate, and the particle will go through all possible combinations of holes with some probability. Now suppose we let the number of plates go to infinity, and then let the number of holes in each plate go to infinity. The particle still goes through all of the infinite combinations of holes, with less probability if the path is unlikely. But really, there is nothing left anymore between the particle source and the screen! There is just free space! So this path integral with the particle going sort-of-everyhere weighted by probability actually describes propagation through free space.