Do photons take all paths or not? There are a lot of questions about this topic on this site, none of them answer my question specifically.
I have read this question:
What does a photon emitted by an atom "look" like?

I think of the emitted photon as a point particle (but with a polarization vector) traveling in a straight line from the atom to the measuring device.

Photon description of quantum-optical interference experiments

For some people, a photon is a dimensionless point traveling on a world line (Eugene Wigner's definition of a particle).

Shooting a single photon through a double slit

The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion.

How come lenses alter the path of photons?

because photons take all paths, but since their underlying physics is "wavey" different paths can "interfere.

How do single photons travel from here to there

This calculation assumes that light simultaneously travels over all possible paths. To what extent this is just a calculational device and to what extent it reflects an underlying physical reality is a matter of opinion.

Can photons travel faster than $c$? (Feynman Lectures)

Indeed, nothing in nature moves around on all possible paths, in reality it's a field that permeates the vacuum which has quantized solutions.

There are mainly two thoughts:

*

*the photon travels in a straight line, and that explains why it only interacts with a certain atom, meaning, that the photon can only be detected once, and the photon will not interact with the other atoms because they are out of its trajectory


*the photon takes all paths, and that is why it truly goes through all possible avenues, explaining experiments like interference


Now these lead to two different propagation pictures. On the top, you can see the photon (EM wavepacket) spreading spherically in all directions. On the bottom, you can see a photon traveling from A to B, taking all possible paths.
But which picture could be experimentally proven to be correct? The picture on the top cannot explain why the photon misses all the other atoms, that is, why it is not interacting with other atoms, because all atoms are in its way basically (it spreads spherically). The picture on the bottom cannot explain diffraction, because the photons is shown not to spread like a wave (cannot interfere), but just like a billiard ball on different paths.
After the question was closed, I am editing to clarify (to reopen), that (as I understand), the question was closed due to the word "really" and what it physically means for the photon to take all paths, or whether the picture on the top (spherical spread) physically describes what is happening. I now revise these words, and the "physically" is meant here to say "experimentally provable".
Question:

*

*Do photons take all paths or not?

 A: Photons are not little balls of classical matter. In particular they have not a definite trajectory nor a position. Their description needs a suitable notion of quantum state in a suitable Hilbert space.
In some, very special, regimes states of single photons can be approximatively described as particles moving along straight paths  (para axial states). Also several paths simultaneously according to corresponding probabilities of a certain path.
Conversely, states of a very large number of photons (coherent states) can be described by classical waves to some extent.
Each such description is  quite partial and it cannot capture all facets of photon phenomenology which is fully encompassed by the complete quantum mechanical description in the Hilbert space.
The folklore picture where a photon runs all possible paths is actually a popular illustration of the  Feynman path integral method to deal with quantum particles. Actually it is a quite technical machinery  which cannot be reduced to this popular representation. Literally taken it may produce mistakes.
A: 
Do photons take all paths or not?

Yes, they take all paths. This can be seen by single photon sources and:
Double slits
Diffraction gratings
Lenses
Etc.
For me, the diffraction gratings are the most convincing.

the photon travels in a straight line,

This is clearly not correct in a myriad of experiments. Particularly where there is diffraction.
A: You could think of photon creation as 2 distinct processes: 1) let's take an excited atom with its excited electron, this electron disturbs the EM field but these forces do not involve an exchange of energy (they are said to be caused by virtual photons also known as force carriers). These forces in theory extend a great distance uniformly and effect the electrons in many atoms. Now take another electron resting in its atom, based on the laws of probability (i.e.QM) let us say they "agree" to exchange the energy. So now process 2 begins and this is what we typically refer to as the "photon wave function". This function is the one Maxwell describes (sinisoidal, straight line, wavelength etc) but its existence is based on probability.
The photon wave function changes dynamically with the environment, for example let's say a star (10 light years away) emits a photon toward an atom on the earth ... just before it arrives a water wave forms, or a mirror is placed at the location, now the photon gets reflected ... maybe back to the star or any place else.
The EM field is everywhere and is transmitting the forces of all the universes' electrons (and protons) simultaneously, the EM field is also capable of transmitting energy ... this is the photon.
A: It is a bane of small scale physics (e.g. quantum mechanics) that we have absolutely no natural intuition. By natural intuition I mean something along the lines of the following. Take this question "if a ball falls down under gravity after a meter of falling does its speed exceed 100km/h". You know the answer is no because you have seen balls falling down from tables.  We develop a theory (a model) that answers this question quantitatively (Newtonian mechanics). At the end we are very happy because our natural intuition has matched with the quantitative answer. Schematically it looks like
$$ \text{Intuition} \dashrightarrow  \text{Phenomena} \to \text{Model} \to \text{Quantitative Predictions} \to \text{Intuition} \checkmark$$
Let's take another question "which slit did photon go through in a double slit experiment?" It is not so obvious anymore because no one has seen photons go through very tiny slits. We don't even know whether this is a meaningful question. Ignoring any natural intuition we jump directly to developing a quantitative model. We can tell the intensity distribution of photons because we can detect them and count them and our model agrees with this distribution.
However, we still haven't answer the original question. We now try to interpret the theory and come up with intuition about this phenomena. Again no one has "seen" photons. We can talk about photons behaving as waves (usual interpretation Quantum mechanics) or we can talk about photons taking all paths (path integral interpretation). Note how classical these interpretations are because we only have natural intuition for classical physics. The quantitative thing (i.e. the model or if you want the math) is undisputed. However, what that math "means" is sometimes unclear, precisely because of the lack of any natural intuition. Schematically the analogous diagram looks like:
$$ \text{Phenomena} \to \text{Model} \to \text{Quantitative Predictions} \dashrightarrow \text{Intuition ??}  $$
A: Even in classical electromagnetism, Huygens' principle says that you can treat each point on a wavefront as a source of new waves traveling in all directions – or to put it another way, that you can replace the classical wave picture with one in which light is pointlike and "takes all paths", including non-straight paths.
The difference between quantum and classical light is that classical light is made of infinitely many of these particles, while quantum light is made of finitely many. Looking again at the classical case, if you consider only the infinitesimal amount of light that is absorbed at a particular point, you can think of it as spreading out from its point of emission and then "homing in" on its point of absorption (because paths outside of the past light cone of the point of absorption don't contribute). This is also a reasonable picture of a quantum photon between emission and absorption. You could also think of the photon as being in a superposition of "homing in" on every spacetime point, with the choice being made later at measurement/collapse time.
A: We don't know the path of a photon. Indeed, I wonder if the concept makes sense in quantum mechanics. We only know its wave function. The wave function is everywhere but, due to interference, far from the source you end up with the Frauhofer result.
