Don't worry, my question is not as vague or typical as the title might suggest: We know Mawell's equations describe light as waves. Waves can be described as excitations of normal modes (for reasons that are not yet entirely clear to me; references are welcome). This is described by the harmonic oscillator. Actually, this needs to be described by a quantum harmonic oscillator. It turns out, in statistical mechanics, that the statistics predicted by the quantum harmonic oscillator are the same as those predicted by boson statistics as applied to massless particles (under certain conditions). This motivates how the classical idea leads to the idea of photons. Good. Of course, the above result can be interpreted in two ways: either it's really a wave but the math coincides with that of a particle. Or it is really a photon but the math coincides with that of a wave. Is one view preferred above the other? I predict some will say "but how can we tell the difference if we've just proven that the two ideas are indistinguishable", but then I ask: aren't there certain conditions for the above argument? I expect that some conditions will break the equivalence, in which case we can experimentally prefer one above the other. Has such a thing happened? EDIT: maybe I can rephrase it succintly: is either the excitation (the wave view) or the photon (the particle view) an approximation for the other?