Consider a photon going towards a plate with two slits.

It may be stopped by the plate, or go through the slits.

To simplify, let us assume that the case when the photon is stopped by the plate, is detected and eliminated from consideration.

The state of the electromagnetic field in each slit, is undetermined, in between the presence and the absence of the photon. The global system of both slits, is in a pure state of correlation of the slits.

And it is located "in the middle" between both states defined by (1 photon, no photon) and (no photon, 1 photon). Let us denote C the circle of points of the sphere "in the middle" (the equator) between them (taken as poles).

We have explained what are such "equatorial" points, elements of C: they are correlated states defined by an indirect isometry between both abstract spheres of presence/absence of the photon, exchanging the presence of the photon in the one, with the absence of the photon in the other.

Therefore, both equators are just following each other. Points of these equators correspond to different orientations of the electric field. Different elements of C give different correspondances between the electric fields of both slits: they say how much delay separates their oscillations (how late is one's oscillation with respect to the other). One whole way around C, makes this time difference change up to one whole period, coming back to the initial correspondence.

The photon has been sent to the slits from one specific direction, thus specifying the element of C involved (the phase difference between the slits).

After the slits, we have a screen with many points that are sensitive to the photon. So we have a measurement with many possible results (which point of the screen will detect the photon).

Each of these results consists in the pure measurement of a point of C. (The barycenter of these many points of C has to be the center of that sphere, for this to be a possible measurement.)

If we could detect which slit the photon was in (distinguish between (1 photon, no photon) and (no photon, 1 photon)), this would be a measurement along the axis of C (orthogonal in space), and would collapse the state of the system onto either (1 photon, no photon) or (no photon, 1 photon). It would no more be at its position on C. its probability of being detected by this measurement, thus as a pure measurement characterized as coming from some point of C (=whose probability cancels at the opposite point), is half the probability for this point by this measurement (=its maximum probability).

In principle, this experiment can be proceeded with any particle,
however it becomes more and more difficult (sensitive to
disturbance) as its mass increases. The biggest "particle" so far
on which it has been made and interferences have been observed, is
the fullerene (C_{60}) molecule.

So, a photon has a probability 1/2 of going through either path; if from only one path it would have a probability 1/2 of ending in either of possible final locations; but with this way of keeping both possibilities of paths, it can only reach one destination; but if a modification is done on one of these paths to inverse its phase, this operates a 180° turn of C so that the photon can only end up to the other destination. Strange conclusion: by only affecting the path of statistically half of the photons, the destination of all photons is changed !

For those who are not familiar (one might just
ignore these details in the discussions, but I did once see
someone playing on it to claim finding absurdities in the story
of the double slit experiment and its interpretation just by
complaining that these details failed to be specified and put at
their right place in the story) :

When we measure by which slit particles go,
then the result (identical with what we obtain by first letting
them go in only one slit while hiding the other, then repeating
with the other, and adding up the number of particles measured
from both cases), does rather **not** consist in 2 spots
(one spot from particles from one slit, the other from the other
slit) but only **one spot**. At least we can make it just
one spot, or if it is 2 spots (one from each slit) then they
need anyway to overlap. Let us explain this in more details.

- The result of diffraction is not many spots
with similar brightness but one big central spot where most
particles arrive (a fixed proportion like 70% or 80%, I did
not to check which precise number, it must be known
somewhere...), whose width (distance between the exact
positions of pure darkness that separate spots) is twice those
of all others.

- The diffraction phenomenon is usually considered out of subject in discussions of interference because the width of spots due to diffraction is much larger that the width of spots from interference. Precisely because these widths are inversely proportional, respectively to the width of the slits and the distance between slits : by having slits with width much smaller than the distance between slits, we get spots (and thus diffraction patterns) much larger than the pattern of interference between slits.

So, interference can appear only where "both spots" from both slits overlap, and with visibility that is a function of the comparison of intensities coming from both slits : where without interference one intensity is twice the other, with interference the brightest places are 34 times brighter than the darkest ones. I just got this number from calculator : ((sqrt(2)+1)/(sqrt(2)-1))^2. From a ratio of intensities of 3, we get 14, that is ((sqrt(3)+1)/(sqrt(3)-1))^2. From 4 we get 9. From 100 we get 1.5

There is nothing interesting to say about the distance between the center of the main spot from one slit and the center of the main spot from the other slit because it is a completely independent variable, that we can reduce to 0 as well by means of proper optical devices (lenses).

As an introduction to the paradoxical concepts
at play, 2 preliminary points of understanding are needed.

**1. Consider the following simpler
experiment.**

**2. Remember that the physics does not specify any "causality
order" in the "spooky action at a distance" when entangled stuff
is measured.**

I described things here : http://settheory.net/epr
pointing out that multiple interpretations for the physically
same experiments (and effectively same predictions) are
possible. And nature plays with us by its way of not having any
naturally preferred interpretation. So when someone says that
the future changes the past : well no, sorry, this might be said
about past unmeasured stuff, but you go too far when extending
this to the case of past measured stuff: it might be seen as one
possible interpretation, but most probably a wrong one.

**Let's start.**

Looking at this video https://www.youtube.com/watch?v=H6HLjpj4Nt4

Anyway, the interference pattern does not
destroy at all the "2 spots" pattern that may or may not appear
in the absence of interference; instead, it comes as a
supplementary effect (roughly as a multiplying this function by
its own function).

What I mean is that when I see the 2 spots picture at 1:27 of the video, it gives the impression that the 2 spots are clearly separate from each other. But if they were indeed separate as they are shown there, no significant interference between them would be possible.

Be careful about the risk of
over-interpretation of things in this video which seems to
exaggerate the role of the observer. I guess that by only
understanding what is said in this video as if things were a
matter of conscious observation, without any deeper technical
expertise on the subject, it would not seem clear what is wrong
with the article http://arxiv.org/abs/1009.2404

(to which I replied there)

There is a wrong claim, as well as wrong
pictures as I just explained, due to misunderstanding, in the
phrase between 8:20 and 8:25. The fact is, there is no such a
possible concept as an "observation of absence of interference"
to be testified by the presence of 2 spots, because interference
does NOT anyway remove the 2-spots pattern. Instead, it adds its
own pattern on top of it.

at 6:20 it says "if it arrives at D1 or D2
they always display an interference pattern" yes but ONLY
insofar as we make effective use of the information
distinguishing between the D1 and the D2 cases to sort out the
dots into 2 different pictures which are complementary
interference patterns.

In these conditions, there is no more physical truth in saying
that "the second photon arriving in D1 or D2 causes the
interference pattern for the first photon" than in saying that
"the precise position of the first photon on the screen changes
the probabilities of destination of the second photon between D1
or D2". Both claims are equivalent.

The experiment presented around 9:20 comes
with wrong interpretations. The fact is, it does not make direct
sense to say what affects what. Instead, things should described
as relative to the knowledge of a given observer. The video uses
the words "before" and "after" (9:45 - 9:50) but you must
understand that there is no physical role of time here, it is
only an epistemological use of time, to describe the difference
of probabilities of what you can guess about one thing "before"
and "after" you inform yourself about something else. In what I
just described before, can we say that the act of checking the
which-way path so as to reprocess an non-interference picture
into 2 complementary interference pictures, really acts on what
happens (retrospectively creates an interference that was found
to not exist) ? It doesn't. If you don't care about the fact
that the same predictions or phenomena may be described in
different ways which naively sound as if they come from distinct
realities of "what happened", but in fact they are physically
equivalent, so as to cast doubt on the question whether "what
really happened" means anything at all as opposed with specific
claims such as "it is already fixed" or "it is really changed
retrospectively by observation", then you can end up in abusive
conclusions.

Next: The EPR paradox - Quantum entropy - Quantum decoherence

Main site: Set Theory and foundations of mathematics - Foundations of physics (table of contents), with List of physics theories.