# Must a photon ever be thought of as 3-dimensional

I am still (ref. my previous questions) trying to understand the nature of photons, so here goes: It seems most physicists imagine the photon as a wave packet, which can be mathematically constructed by superimposing (infinitely) many plane waves of slightly different frequencies to obtain its wave function. This packet (its center) travels at the speed of light in a straight line with constant momentum (inherent energy) proportional to its frequency.

Further, the photon frequency or speed (or both - its momentum) must have a spread. If not, the uncertainty principle would make it impossible to determine the position of the photon (one could not write $x=ct$).

Maxwell says an E-field (electric) can not propagate without being associated with its corresponding H-field (magnetic), the cross product representing the Poyinting vector as a measure of the fields inherent energy/momentum. Now this vector can not have any component parts besides the one in line with the path of the photon, or else a magnetic field detector should register the photon as it passes sufficiently close and thus interact with it without colliding. The same goes for an electric field detector. Hence, if the spatial path of the photon is absolutely straight, its momentum in all other directions should be exactly zero. Now this requires that the cross sectional diameter of the photon, if compared to a particle, should be zero, otherwise there would have to be radiation (from its associated 3-dimensional wave packet representation) propagating radially from the photon, so the question is:

Are there any experiments/theories that need to be explained by the photon having E and H field components that are not entirely normal to the path or that require the photon to have a "diameter" in the normal plane, and, if so, how would this not contradict the reasoning above?

One further question. Can an individual photon be circularly polarized ( yes - in wave packet theory) and thus not be blocked by any filter or does this only apply in practise to photon beams.

• EM fields and photons are mutually exclusive concepts. If you want to consider photons then you are using QFT where there are no EM fields. If you want to consider EM fields then you are using classical mechanics where there are no photons. Mixing both concepts into the same picture makes no sense. Also, photons do not have EM fields (whatever that means). Moreover, photons do not have a well defined path. Sorry, but the question makes little sense to me. – AccidentalFourierTransform Jan 16 '17 at 9:43
• So a light beam can not be described as elecromagnetic radiation, which seems to obliviate most of what I have read? – Jens Jan 16 '17 at 9:55
• What @AccidentalFourierTransform says is only half way true. In the classical limit of quantum electrodynamics you can describe light rays as (complicated) superpositions of photons. – Mikael Fremling Jan 16 '17 at 9:58
• @Jens a light beam can be described as either EM radiation or photons. Not both. Also, your "one further question" makes no sense: circularly polarised waves are blocked by filters. Why do you think they are not? – AccidentalFourierTransform Jan 16 '17 at 10:02
• Related/possible duplicates: physics.stackexchange.com/q/90646/50583, physics.stackexchange.com/q/269077/50583 and their linked questions – ACuriousMind Jan 16 '17 at 12:25