This is the link to the Veritasium YouTube video where Derek and his friend show that light indeed explores all the paths. A laser beam is made to fall on a point say $P$ on a reflecting surface at an angle $i$. It gets reflected by angle $r$, where $i=r$ and they observe it with a camera. They then cover the point P with a black sheet so that the classical path $i=r$ is blocked. Then they place a translucent sheet with about $5000$ lines/mm vertically below the laser and show that light indeed went from directly below the laser to the camera. My question is, isn't it simply scattering of light? Because we are able to see the laser source all the time, even the laser path, which means light is being scattered in all directions and to our eyes too. Same is true for the reflecting surface. Then isn't it just the scattered light being seen on the camera after interference due to the lines on the translucent sheet?
1 Answers
There is a sense in which the experiment does show the light is travelling by multiple paths, but we need to be careful here as the light does not take multiple trajectories in real space - it takes multiple trajectories in an abstract space called configuration space.
The experiment just shows diffraction. It is effectively light passing through two diffraction gratings because the light passes through a diffraction grating, reflects off the mirror and passes back through the diffraction grating again. Unsurprisingly the two passes through the diffraction grating generate multiple maxima and that is what the camera is recording.
On the face of it this may seem completely unconnected with the idea of a path integral, but in fact it's not so different. We know that the propagation of light can be described by the Huygens-Fresnel principle, and indeed Feynman (allegedly) came up with his idea by considering light passing through a diffraction grating and gradually removing all the parts of the grating that blocked the light i.e. considering the limiting case of a grating consisting only only of the slits with nothing between them.
The experiment is a nice way of explaining the basic idea, but you are quite correct that it does not show that the light takes multiple trajectories in real space i.e. the 3D space in which the experiment is being done. It shows that light takes multiple trajectories in configuration space.
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