I understand why treating light as particle-like photon packets leads to the observed results. I seek to understand why one would expect different results if light were treated as a wave (and thus why these results imply particle-like behaviour).
Experiment 1: Increasing the intensity. I imagine a light wave incident on the surface as Ψ = Asin(kx-ωt). I imagine increasing the intensity of light as adding multiple parallel waves incident on the surface. If each wave deposited enough energy to kick out 1 electron per second, wouldn’t adding multiple waves kick out more electrons per second without changing the energy per electron?
Is treating increased intensity as more parallel rays too much like particles? If I instead treat increased intensity as increased amplitude squared, then I think of the wave as pouring energy into the metal surface at a faster rate, like a thicker stream of water from a spout. In this case, wouldn’t the light have deposited enough energy to free an electron more quickly, and thus still eject more electrons per second?
As a corollary here, is it right to equate A² ∝ number of photons?
Experiment 2: Increased frequency. I do understand why a continuous stream of energy from a wave is inconsistent with a threshold frequency to elicit a current.
Why would increasing the frequency (and therefore energy) of a wave not increase the kinetic energy of the most energetic ejected electrons?
Wouldn’t a single, particle-like wave-packet, also have energy proportional to its amplitude² as well as its frequency, and thus kick off more energetic electrons?