That only works with quantum mechanics - it's a consequence of the "path integral" idea of QM. In classical optics this wouldn't work, because you'd be able to detect light on the other paths if it really did take all paths.
That only works with quantum mechanics - it's a consequence of the "path integral" idea of QM. In classical optics this wouldn't work, because you'd be able to detect light on the other paths if it really did take all paths.
I think you're confusing the distinction between classical ray optics and classical wave optics with the distinction between classical wave optics and quantum mechanics. Quantum mechanics and classical wave optics agree on the explanation for diffraction as a path interference effect. In classical optics, the reason you don't see light coming from angles away from the shortest path is because of destructive interference between the other paths.
For example, note that the Huygens principle predates quantum mechanics by over 200 years [1]. As another example, diffraction gratings (which manifestly require interference between different paths) were being made in the mid 1800s [2] but in physics documentaries you never hear of people being confused about how to explain their behavior. Because they are explained by classical wave optics. Also see this lecture which talks about diffraction in the context of ray optics [3].
Where wave optics disagrees from quantum mechanics is in the dim-light limit, when you start resolving individual photons.
[1]: https://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_princi...
[2]: https://en.wikipedia.org/wiki/Diffraction_grating
[3]: https://www.youtube.com/watch?v=5tKPLfZ9JVQ&list=PLB1A0BF14E...
Classical optics is just the limiting case of quantum optics when the path length is much longer than the wavelength. In such a case quantum optics predicts basically zero probability to detect light on any path other than the classical path--which is classical optics. So classical optics doesn't say anything that's actually contradictory to quantum optics. It's just a special case.
It's classical ray optics that fails in the path-not-longer-than-wavelength regime. Classical wave optics works in that regime. Where classical techniques fail is at low brightness (because you start resolving individual photons).
Yes, but in classical wave optics you're no longer talking about "paths" as they appear in path integrals. Classical wave optics is basically quantum wave optics without the discreteness of detections, i.e., interpreting the wave as a straightforward EM field intensity instead of as a probability amplitude for detecting a photon.