My second argument is from Richard Feynman:
What's he saying here? Two things actually. The first is an experiment that doesn't make sense from a wave interpretation. You launch a bunch of photons at a detector, which works as follows: the photons hit a metal plate and knock off some electrons, which are then attracted to a charged plate nearby, so they go smash into that plate and knock off even more electrons, which are attracted to an oppositely charged plate also nearby, so they go smash into that and knock off even more electrons...and so on until there's enough electrons to signal a beeping circuit. So the experimental question is: if I send a lot of photons ("strong wave intensity"), how many electrons do I smash off the first plate and what is the energy of each individual electron? A wave interpretation would suggest that the number of electrons you smash off remains roughly constant, but as you weaken the wave you weaken the total energy that each electron takes, so the energy per electron goes down, and perhaps at some point when your wave is so weak it won't disturb any electrons. A particle interpretation, on the other hand, reverses that. A single photon smashes off a single electron once in a while, and that electron has some energy E. A bunch of photons smash off a bunch of electrons, and each electron has the same energy E as in the single case. So to recap: waves suggest as you weaken the light, you still get the same bunch of electrons out but at weaker energies. Particles suggest that as you weaken the light (fewer photon particles), you get fewer electrons out each with the same energy. What happens in reality? The particle version happens, not the wave version. Go home, wave theorists! Some other experiments seem to permit both wave and particle interpretations, but apparently not all. Particles win, Newton's conclusion (though not his method) was right.
The second thing Feynman says notes that the mathematics of waves as commonly understood don't really work at higher dimensions. With one photon, yeah, psi(photon_position, time)=psi(pp, t) looks like a wave. psi(pp1, pp2, t) does not, however. How would one visualize psi(pp1, pp2, pp3, pp4, pp5, t)? It only makes sense as a high-dimensional probability distribution, which looks like a wave in the 2D case but doesn't really look like a higher-order wave for higher orders.
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