# Is light a photon or a wave? (concrete question)

• nonequilibrium
In summary, Maxwell's equations describe light as waves, and these waves can be described as excitations of normal modes. This is related to the concept of the harmonic oscillator and the quantum harmonic oscillator. In statistical mechanics, the statistics predicted by the quantum harmonic oscillator are the same as those predicted by boson statistics applied to massless particles. This leads to the idea of photons. However, it is still unclear if light should be viewed as a wave or a particle. The only way to determine this is through a theory that defines the terms used in the question, such as classical and quantum electrodynamics.

#### nonequilibrium

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?

The only thing that can answer a question about reality is a theory that defines the terms used in the question. In this case, the key term is "light". The only theories that have anything useful to say are classical electrodynamics and quantum electrodynamics. The former says that light consists of waves. The latter says that light consists of photons (and also defines the term "photon"). Quantum electrodynamics is much better at predicting results of experiments.

Light propagates as an EM wave, as described by Maxwell.
The amplitude of the wave is quantized, so its energy equals n hbar\omega.
For n=1, it describes the propagation of a photon, in the same way that Schrodinger's equation describes the propagation of an electron.

What do we mean when we call light a wave? We mean it's extended in space, it can superimpose with another light wave, giving interference, diffraction pattern etc. But all these features are inherited by quantum mechanical discription, with some additional properties that resemble particles(amplitude got discretized , so concepts of "wave" and "particle" are not mutually exclusive, and the quantum mechanical description is more complete.