SELF

10

S.B. Karavashkin and O.N. Karavashkina

However, by many reasons we cannot consider this presentation consistent with the observed revelations of EM wave, despite all temptation. We have to indicate among the reasons first of all the incorrectness of the very phenomenological model of photon. To make sure, it is sufficient to analyse the Atsukovsky's items. For example, in the item 1 he admits the photon energy rigorously corresponding to (2), but it follows from such statement that photons cannot interact, and many authors emphasise it. In particular, Feynmann writes so: "We simply see the light behaving the same as electrons: we know that it is 'wavy', and now we make certain that in addition it propagates by 'portions'. It is delivered - or scattered - by portions which we call 'photons'. Lowering the intensity of the light source, we do not change the value of photons, we change only the rate of their emanation" [4, p. 210]. "As a first approximation, we can think photons non-interacting particles. (The footnote: Further we will see that due to the photon-electron interaction there arises also a weak interaction of photons with each other). With it the energy of a system of two photons amounts the sum of the energies of photons, and their wave function satisfies the Schroedinger equation … Above this equation, the wave function has to satisfy two more conditions. First of them is the condition of transverse polarisation of each photon… Second is the condition of symmetry and follows from the photons identity. Photons obey the Bose-Einstein statistics, and so their wave function has to be symmetrical as to the particles rearrangement" [5, chapter 1, item 6, p. 36- 37].

In other words, photons can neither join nor divide. "There cannot be 3/4 of a photon. It entirely either is here or is not." [6, chapter 9, paragraph 5, p. 222]. Though this contradicts the item 7 of Atsukovsky's list. It is known that in the interference we geometrically add the amplitudes of sources of light that is proportional to the difference of distances from the sources to the point of interference. This is basically important.

If we had two coherent sources with the amplitudes

"we will record the field E   created by the summary oscillation as follows:

Denote  (r₂ - r₁)   through  . The value   is called the path difference… We can easy select in (4) the amplitude of total oscillation  2E₀ cos(k/2) . The light intensity  I  is known to be proportional to the amplitude squared, as

[7, p. 129- 130]. Or using the standard transform,

where c  is the light velocity, we yield

On the other hand, if we think the light consisting of the non-interacting and indivisible quanta, the intensity  I  at some point of the interference pattern can be presented as

where _N  is the quantity of quanta coming to the studied point from both sources. Substituting (8) into (7), we yield

We see from (9) that the total density of two beams  _N   depends nonlinearly on the path difference  , which is possible only in case if quanta interacted. This contradicts the statement of non-interacting quanta, as well as the condition that the Bose-Einstein statistics is correct in its supposition that the total energy of the quanta assemblage does not contain the term of interaction, i.e.

[8], where  N ^s   is the number of quanta in the state  s  corresponding to the frequency   ^s .