I understood "This is true even if the light intensity is reduced so that only one photon at a time travels through the apparatus." to mean that when the experiment is performed with individual photons, the results are as though the photon interfered with itself.
Yes, I found it, that's why I wrote "never mind" after my hasty response.
The 50% arriving at C is easy to explain. When there is no obstacle, 50% of photons go by the northern branch, 50% by the southern branch. So if an obstacle (mirror) is placed in the southern branch, they will end up at C, hence the 50%.
The numbers at A and B are more difficult to find an explanation. And right now, I don't have one. I will need to think about this. And it's late. So I'll get some sleep, and come back tomorrow.
Ok. The numbers at detectors A and B in fig4c can be explained. The northern branch photons go through the beam-spitter (bottom right-hand corner), and so half of them go to A, the other half to B.
1/2 x 50% = 25%
NOTE: the question at bottom of fig 4, "How does one single photon observed at A know about the existence of an obstacle at M?" is the wrong question to ask. Fig 4c can be explained as I did above.
What is the real troublesome, and still unexplanable to me are the numbers in fig4a (or fig4b), which read as: 0% in detector A, and 100% in detector B.
Now the explanation given: "it appears as if the wave function of each individual photon travels
both paths and engages in interference at the last beam splitter, so that only the wave to B is constructive."
This does not explain the data. Even if the photons would interfer constructively with itself at the beam-splitter(bottom right-hand corner), after that, each wave should continue along their path, and 50% should go to A, 50% to B. But we don't get that, instead we get 100% at B, none at A. That would mean the wave coming from the southern branch moving from left to right, goes 100% (of 50%)through the beam-splitter(bottom right-hand corner), IOW, doesn't split and continues to B (depicted in fig 4b), while the northern branch, which is now moving downward after reflection with the mirror(top right-hand corner), but now makes an extraordinary
90 degree turn at the beam-splitter (bottom right-hand corner), without splitting to move 100% ( of 50%) from left to right to reach B (depicted in fig 4a)!!!
So this experiment does not in anyway prove that a single photon interfers with itself. Nevertheless it is still a mystery why 100% go to B, and none to A:
(1) Why there is no splitting at the beam-splitter(lower right-hand corner) for both branches,
(2) why the northern branch, going from up to down, makes a 90 degree turn to go to the right (fig4a), and the southern branch goes straight through( fig4b).
So whether we take either the wave picture or the particle picture of the photon, we should get 50% at A , 50% at B. The result 100% at B, and none to A is definitely weird. However it does show that our classical classification of matter into two bins - one for particles, the other for waves - doesn't work at sub-atomic scale. Both picture fails to account for the data. And it doesn't prove spooky action at a distance, either.
https://en.wikipedia.org/wiki/Mach–Zehnder_interferometer#Counterfactual_measurement