| > Because photons are massless you have to use quantum field theory, simple quantum mechanics does not apply Photons themselves are quantum objects; they do not appear in classical theories of light. They have several physical attributes which are quantized: spin (+/- 1), helicity (+/- \hbar), chirality (+/- \hbar), charge (0). The masslessness is what makes chirality == helicity as massless particles spin in the same direction along the axis of motion for any observer seeing such an axis. Frequency is not quantized. A monochromatic light source at frequency f will emit individual photons with energy hf, but the frequency is observer dependent (e.g. one observer may decide that the photons are all hf_{lower} and another may decide that the photons are all hf_{higher}, and an accelerated observer may see the photons arriving from the source with different frequencies at different times; and in all cases each photon will have some hf_{observer} energy). Photon number is also not conserved -- they can be freely emitted or absorbed. They also always move relativistically (even "slow light" in media does). These features conspire such that the wave-function of a photon only makes sense as long as the photon is neither emitted nor absorbed, and only in a fully relativistic quantum theory. That's what drives your "... you have to use [relativistic] quantum field theory". [0] You can however devise an (effective) single-photon wave function, and this is done for single-photon experiments, e.g. in studies of single-photon spatial structure, as in the Bialynicki-Birula paper you link to (see eqn 42, and note the point about non-renormalizability). World-lines are attached to all objects in a relativistic theory (i.e., one where there is Poincaré invariance in the infinitesimal neighbourhood around every point in spacetime), whether those objects are classical or quantum. Extended objects technically have worldlines attached to each of their microscopic components, but one can usually consider such objects as having a single worldline in some limit; as in fully classical Newtonian mechanics, this would usually be attached to the centre of mass. (In special relativity, which is the theory of flat spacetime, you just use the Schrödinger equation. In very weakly curved spacetime you'd use the Schrödinger-Newton equation, and progress from there as necessary). [0] It's not strictly the masslessness. Neutrinos have a tiny positive mass and almost always move relativistically. (The exceptions form the cosmic neutrino background, the elements of which have lost momentum in the expansion of space). |