If photon doesn't have probability to be in dark (destructive interference) area, what will be the effect of adding obstacles (walls) in the dark (destructive interference) area for the double slit experiment?
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$\begingroup$ In theory you should be able to sneak them in if they are very thin BUT there will be a sub diffraction effect at the wall tips AND adding this material will change the net index of refraction. ... the pattern should narrow a bit. $\endgroup$– PhysicsDaveCommented May 18 at 21:02
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$\begingroup$ It probably would get additional interference effect. Remember that a slit or a thin wall have the same effect if they're small enough! So the particles on the side of each light beam could diffract on these walls as well. That'd be an interesting experiment to run! $\endgroup$– Chris Ze ThirdCommented May 18 at 21:11
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$\begingroup$ I think fundamental double-slit interference still be produced at the slits at least because in principle this does not deny for the photon to go and bump into the walls and be absorbed or scattered by them. I.e. walls does not eliminate photon "path to try". $\endgroup$– Agnius VasiliauskasCommented May 20 at 7:42
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On wikimedia commons the description of the image that you used as illustration is described as: Simulation of the double-slit experiment with electron
Of course, that doesn't detract from your question. The illustration serves your purpose.
Still, it is worth mentioning that the image is generated. It's a simulation; it is not a camera picture of an actual experiment.
To obtain a picture like that in a real world experiment you would have to introduce some sort of smoke, so that the electromagnetic radiation has something to interact with.
With those preliminaries out of the way:
Your opening sentence says "If photon doesn't have probability to be in dark (destructive interference) area (...)"
I recommend against thinking that way.
In a double slit experiment each slit acts as a point source of radiation. Think of each slit as the source of a diverging beam of radiation. In the space where that radiation propagates we know there is a superposition of those beams.
I now turn to discussing how probability comes in.
In general (not specific to interference effect):
Radiation interacting with matter has a probability. For instance: if the space is filled with a smoke then most of the radiation makes it through, but some of the radiation interacts, and is then scattered. That is, if we shine a beam of light through a smoke, then what we see from the side is the small percentage of the light that is scattered.
Now the way that interference effect comes in:
When you have an interference pattern: in the dark areas the electromagnetic radiation is just as present as in the light areas, it's just that in the dark areas the phase relation is such that the probability of interaction with matter is zero.
The introduction of the walls as depicted in the image that you provided will have significant effect.
The propagation of the radiation from each slit is not parallel to the "beams" of area of constructive interference.
At every point in space the propagation from slit 1 and the propagation of slit 2 are at angle with respect to each other. Let me refer to that as the 'separation angle'. The areas of constructive interference are along a line that bisects the separation angle.
That is:
The propagation from slit 1 is at a slight angle to the walls that you introduced, and likewise the propagation from slit 2 is at a slight angle to the walls.
Pretty soon all of the radiation will have come in contact with the walls, and presumably those walls will either absorb or scatter the radiation.
(As mentioned in a comment: there will also be diffraction effects at the wall tips. I'm not sure how large those diffraction effects will be.)
The point that I want to emphasize: it's not that in the areas of destructive interference the radiation has a lower probability of being present. On the contrary: the radiation is equally present everywhere. There is no obstruction to propagation.
It is the probability to interact with matter that is lower in the areas of destructive interference.
The geometry of the double slit setup as a whole sets up a phase relation. That phase relation is what gives the interference effects.
Later edit:
Let me address the notion of photons.
The vivid demonstration of that is when a double slit setup has been created with such low luminosity that an interference pattern is seen to build up one speck at a time.
(Detecting single events is actually very, very challenging. It requires a device that acts as a photomultiplier tube. That is: in order to detect single events you have to create some form of avalanche. When the gain is cranked up too high you end up with many false positive detections.)
As the pattern of specks build up there is no predicting where the next speck will appear. With a double slit setup: over time an interference pattern forms.
In the history of physics the photo-electric effect is seen as a vivid demonstration that there is something about electromagnetic radiation that cannot be described with the classical theory of electromagnetic radiation.
If the frequency of the incoming light is such that the corresponding energy is below the threshold to knock electrons loose then not a single electron is knocked loose. If the corresponding energy exceeds the threshold then the maximum kinetic energy that the released electrons can have is that energy surplus.
What is happening is that there is something about the interaction of light and matter that makes it an all-or-nothing process. The energy that the radiation can transfer to matter must transfer in a single event.
In physics the information that you have access to is the outcome of measurements. We try to infer how radiation propagates, but there is no way of measuring directly how radiation propagates. The thing that is accessible to measurement is the event of transfer of energy from light to matter.
The concept of 'photon' refers to the all-or-nothing nature of transfer of energy from light to matter. It is an over-interpretation to suppose that light is propagating in the form of photons. How light propagates is not accessible to measurement, so we should not speculate as to how light propagates. The proper attitude, I believe, is to grant the minimum that is necessary to formulate a theory.
We have the quantum theory of the electromagnetic field, Quantum Electrodynamics, abbreviated to QED. QED is used to describe propagation of electrodynamics waves. QED gives as results of computation: probability of interaction with matter. In terms of QED the propagation is distributed in space. The propagation is so similar to the wave nature of classical wave propagation that Maxwell's theory of electromagnetism appeared to be adaquate to describe all properties of electromagnetic waves.
However, as demonstrated by the photo-electric effect (and many other phenomena), the transfer of energy from light to matter occurs in a single event, at a specific location.
Generally, when people move towards over-interpretation they are painting themselves into a corner.
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$\begingroup$ Thanks Cleonis for this elaboration, your answer is convincing. I'm just curious to know if there is any interference pattern in optics where the dark (destructive interference) lines pattern is perpendicular to the direction of wave/ photon propagation? I searched but I couldn't find. One physicist told me that this pattern cant be exist because it violates locality. Is this statement correct? $\endgroup$ Commented May 19 at 19:02
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$\begingroup$ @WaelKhatib I would say this is answer wrong, based old historical principles. The reason being "radiation" is defined as the photon energy and there's none in the dark areas. What is is the dark areas (as well as the bright areas) is the EM field, the EM field guides the photons/energy. To say the radiation is out of phase and cancels is a violation of conservation of energy .... furthermore this poor type of explanation typically somehow tries to infer that the out of phase photons somehow end up in the bright bands. $\endgroup$ Commented May 19 at 23:31
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$\begingroup$ I recommend that you submit your follow-up question as a new question. (Stackexchange is designed to work as a one question - one answer format.) That said: I expect no such pattern can occur. I googled the following query: "diffraction grating simulation" Among the search results was a video of a 37-second simulation sine-wave grating For about 2 or three cycles there is a checkerboard pattern. The checkerboard pattern is aligned with the diffraction grating. I expect that further away from the grating the pattern becomes increasingly blurred. $\endgroup$– CleonisCommented May 20 at 5:26
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$\begingroup$ @PhysicsDave you are attributing a point of view to me that isn't mine. It appears you are seeing ghosts. You are talking in terms of photons; I have consistently avoided the word 'photon', for a reason. My goal was to steer the OP away from thinking in terms of photons. About the definition of radiation: I checked: the general concept of 'radiation' is 'release of energy from a source in a form with a wave-character'. Your personal definition of 'radiation' is significantly narrower than the definition that the community uses. Your personal definition of 'radiation' is untenable. $\endgroup$– CleonisCommented May 20 at 5:45
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$\begingroup$ @Cleonis, thanks for your advise. I will ask this question as a new question. Thanks all for your comments. $\endgroup$ Commented May 21 at 17:49