Photons are bosons so they do not annihilate, they just pass through each other.

A photon is its own anti-particle, so it does not annihilate with another photon. A fermion and an anti-fermion do annihilate into a photon, which can then spontaneously annihilate into a fermion and an anti-fermion pair. Photons can interact with each other, but they do not annihilate with each other.

When two photons cancel each other, due to their opposite phase, what this process is called and what is the result?

The process is called interference and it applies to a single photon travelling over two different paths, not two photons. There will be a location some distance away where the waves are in phase. The amplitude determines the probability of detecting the photon at each location so it just means it will probably be detected "elsewhere".

Is the energy of the photon resulting to the destructive interference of R1+R2 just the heating of reflection surface? or are R1and R2 participating by transfering energy to ... (nowhere)?

If the interference on path R is destructive, it is constructive on path T therefore by applying a coating that cancels reflection, all the energy is transmitted.

- But ray 1 is reflected before the second reflection(R2) takes place. Hence, R1 transfers some energy that later is canceled by R2. Does R2 carries negative energy??? (it seems strange that covering the ns-surface will increase the amount of incoming energy).

- for the second figure: If the angle of incidence is 0 degrees and the distance of the emitter to the mirror is just the right one for the incident ray (lazer beam) to destructively interfere with reflected ray where does the energy of the photons go?

Thank you George for your time (so far).

IH: But ray 1 is reflected before the second reflection(R2) takes place.

R1 and R2 are two possible routes that a photon might take but the difference in path length produces a half wave shift hence the phases would cancel. The consequence is that each single photon has a low probability of going in that direction but a high probability of following the T path. Energy isn't "cancelled", it just doen't travel in that direction at all. You are writing as if there were two particles but is is only one that we are discussing.

IH: for the second figure: If the angle of incidence is 0 degrees and the distance of the emitter to the mirror is just the right one for the incident ray (lazer beam) to destructively interfere with reflected ray where does the energy of the photons go?

All the energy returns to the laser and the amplitude would increase until other losses equal the input power (nothing is perfect). Since the rays are travelling in opposite directions, interference would create a standing wave, this is simply what happens inside any laser between the mirrors. The laser frequency then gets 'tuned' such that a whole number of waves fit into the cavity.

- In the first case how many of the possible routes a photon might take?

a) T

b) R1

c) R2

d) R1+R2

e) R1+T

f) R2+T or

g) R1+R2+T ?

QM seems to say that g) is the case (all possible routes) although the probability for R1 or R2 is practically zero or to be precise the result of R1+R2 is zero (am I right?). I still doubt that transparency(T) of membrane increases when its thickness increases from λ/8 (no destructive interference) to λ/4 (destructive interference).

- I have tried to perform the second experiment with a pocket-laser beam in front of a glass mirror and a phenomenon similar to the concentration of light rays of the sun, by using a lens, is obtained. Even tiny flame with smoke coming from nowhere (air?) is observed at mirror's proximity.

Two photons moving co-linearly in opposite directions and then colliding could simply pass through each other, but if they are energetic enough they could transform into, say, an electron-positron pair. This is usually construed as the opposite of annihilation. An electron-positron pair reacting to form two photons moving co-linearly in opposite directions is usually construed as annihilation.

Dear Ioan,

IH: In the first case how many of the possible routes a photon might take?

Look up Feynmann's "sum over histories", you calculate over every possible path then sum at each possible eventual detection point to get the relative probability of the photon being detected there. You can think of a photon in that sense being like an expanding sphere centred initially on the source point but when detected it acts like an indivisible particle so can only be seen at one location. This is where what is called "wave/particle duality" is counter-intuitive and very hard to understand.

You may have a look at: https://physics.stackexchange.com/questions/23930/what-happens-to-the-energy-when-waves-perfectly-cancel-each-other

There's a lot there but this part succinctly summarises what I said:

• "The field landing on detector 1 is the interference between two waves, one from the lower path, and one from the upper path. Let's suppose the field in each arm is a collimated beam of coherent light, well-approximated as a plane wave, and the interferometer is well-aligned, so the two outputs are almost perfectly overlapped. By changing the thickness of the sample, we can change the relative phase between the two waves, changing our interference from destructive (less energy on detector 1) to constructive (more energy on detector 1). Where did this energy come from? If the beams are nicely matched, this interference can even be completely destructive, and detector 1 will register zero signal. Where does the energy go?
• The short answer is: detector 2. The total energy hitting the two detectors is constant, as you vary the phase shift caused by the sample. Constructive interference at detector 1 goes hand-in-hand with destructive interference at detector 2.
• If you only look at one detector or the other, it might seem like energy is created or destroyed by interference, but as other answers mention, we must consider the whole system."

I feel that this strange behaviour is another indication that none phenomenon is spontaneous but instead is expressed by the average "primitive" properties that appear on a short time-interval that could be from some Planck time-lengths (for quantum phenomena) to some femtoseconds or even nanoseconds (for biological systems). This "short" spacetime space/period is more than enough to settle a detectable result that may not be rationally explicable by a route of sequential spontaneous events.