Hey, so I just watched the Veritasium video "Something Strange Happens When You Trust Quantum Mechanics" (https://www.youtube.com/watch?v=qJZ1Ez28C-A), and it got me thinking.
The video talks about how light takes every possible path and ends up following the one with the least action. Super cool concept. But then, around the 30-minute mark, there’s this wild experiment where a laser is aimed at one side of a mirror, and there's a diffraction grating placed on the other side. Even though the laser isn’t hitting the grating directly, you still see light coming out from that side. That part really tripped me up.
So here’s my question: Where is the energy for that “other path” coming from?
My gut says energy has to be conserved, so if light is somehow taking a new path via the grating, does that mean the original laser beam is losing energy? Maybe it just gets dimmer?
But then I thought… what if you could make a really clever diffraction setup that always pulls light along some super-efficient path? Could you, in theory, siphon off light energy from a bulb on the other side of the planet without anyone near the bulb noticing?
And if the original beam's intensity is not lowered, then we would have generated free energy!
So is this really about energy moving along a new path, or are we just bending scattered light in a clever way to make it look like something more mysterious is going on?
Cool video. Doing the double-slit experiment in my freshman physics class is a favorite memory from college. Seeing it in person blew everyone's minds, even the kids who had learned about the experiment before.
If you google "is energy conserved in the double-slit experiment" you'll find some physics forums with decent answers. Basically, the total energy emitted by the light source does not change. Energy is conserved. Don't think of the laser light as a discrete beam that is being split off onto a second path. Instead, imagine that the laser light is constantly shining all over that foil and card. The dark regions appear dark because the light waves there are canceled out by interference from adjacent light waves. Similarly, the red areas are illuminated because in those areas the adjacent waves did not cancel each other out. The bright spots visible on the polarized foil occur because the polarizer blocks thin regions of the light, preventing them from canceling out adjacent light that wasn't blocked. So light wasn't redirected there, but was always there and was simply made visible to us by the effect of the polarizer.
Light, quantum mechanics, and the probabilistic nature of the universe are all real head trips. I still struggle to wrap my mind around them. As such, there's a good chance my simplistic paragraph above is incorrect or misleading, so take my answer with a grain of salt.
I don’t think this fully answers OP’s question, though (at least as I understand it): while a photon’s wave function spreads out everywhere including the diffraction grating and card, what counts for conservation of energy is where the photon is actually observed. So if we manipulate the interference pattern of the wave function to cause a photon to be observed where the probability would normally cancel to zero—and if the probability of observing the photon somewhere remains one—does that accordingly reduce the probability of observing the photon where we would otherwise have expected to see it?
At this point I have to admit that I am out of my depth. We need a real physics major to chime in.