Do all photons really follow all available paths?

[physics pfan]

Quantum electrodynamics "states that any particle (e.g. a photon or an electron) propagates over all available, unobstructed paths and that the interference, or superposition, of its wavefunction over all those paths at the point of observation gives the probability of detecting the particle at this point." [ https://en.wikipedia.org/wiki/Fermat's_principle#Derivation ]. Feynman belabors this point in chapter two of his little QED book.
. I understand how the multiple paths are cancelling probabilities for reflection and diffraction. But what about a photon simply traveling from point A to point B with no intervening medium?

It seems that one can constrain (or select) photons so that they travel only a single linear path. The mirror cavity of a laser selects photons so that each one emitted appears to follow a single linear path. Another constraining device would be a collimating lens producing a linear beam. Does it make any sense in these cases to argue that photons follow “all available paths?” [A similar argument can be made for constrained/directed electrons.]

 

[Orodruin]

Photons are not small billiard balls. They are quantum field theoretical objects.

 

[edguy99]

Consider Landau & Lifshitz Vol. II. On page 108, the wave equation section talks about electromagnetic waves “in which the field depends only on one coordinate, say x (and on the time). Such waves are said to be plane”. Electromagnetic waves are ever changing “plane waves moving in the positive direction along the X axis”.

In volume IV, page 5, Landau & Lifshitz continue, talking about Quantization of the Free Electromagnetic Field and on page 11, introducing photons:

These formulae enable us to introduce the concept of radiation quanta or photons, which is fundamental throughout quantum electrodynamics. We may regard the free electromagnetic field as an ensemble of particles each with energy ω (= ħω) and momentum k (=nħω/c). The relationship between the photon energy and momentum is as it should be in relativistic mechanics for particles having zero rest-mass and moving with the velocity of light. … The polarization of the photon is analogous to the spin of other particles; …. It is easily seen that the whole of the mathematical formalism developed in §2 is fully in accordance with the representation of the electromagnetic field as an ensemble of photons; it is just the second quantization formalism, applied to the system of photons. …​

A photon is a plane wave traveling through space at the speed of light. Photons do travel in a straight line (subject to diffraction and reflection) but being an oscillating plane wave, you cannot say for sure where it is (uncertainty principle).

 

[physics pfan]

Photons are not small billiard balls. They are quantum field theoretical objects.

Thanks. I agree. But what about electrons, or protons that are linearly directed?

 

[Orodruin]

Thanks. I agree. But what about electrons, or protons that are linearly directed?

They too are not little billiard balls, but quantum field theoretical objects that share some properties that small billiard balls would have and therefore were called "particles".