Planck has pointed out the following paradox connected with registration of electromagnetic radiation by the quantum detector.

Let's assume that for observation the photo multiplier with potential of an exit of photocathode

A limit of sensitivity of modern quantum detectors is about

But experimental average time interval between two photocounts by such intensity of radiation is on 14 degrees lower.

So-called «reduction of wave function» at the moment of registration, according to Copenhagen treatment of quantum mechanics, occurs not in reality but only in consciousness of the observer and this mental reduction in any way does not explain how the energy of radiation distributed on great space can be concentrated in the volume of individual atom.

Now we will show, that all this reasoning is based on incorrect preconditions and completely loses force in the modern theory of interaction of radiation with atom.

Under the action of monochromatic external radiation field the two-level system begins to oscillate with Rabi frequency

where

Population of top level (under condition of an exact resonance of an external field with a difference of frequencies between levels) is defined as (see, e.g.

By these transitions atom exchanges energy with an external field: in the first half-cycle atom takes away energy from a field, in the second – gives it back. It occurs because by transition from top to down, the induced radiation is in phase with external radiation, and by transition from below upwards – in an antiphase with it (Fig. 1). Any "instant jumps" of electronic density thus does not occur, contrary to those notions which have used in the first stages of development of quantum theory. Transitions of electronic density between stationary states are gradual and continuous.

Transitions downwards occur not only under the influence of external field, but under the influence of fields of surrounding atoms (collision) or vacuum field (spontaneous transitions). Overwhelming part of such transitions are thermal relaxation when energy of top level has been transferring nonradiatively to surrounding atoms. Registration of radiation by the detector can take place only in those infrequent cases, when transition downwards occurs with radiation of photon (wave train) incoherent to external field, or with separation of an electronic cloud from atom (photoeffect).

Let's consider the «Planck's paradox» from these positions.

When the front of radiation reaches the detector surface, simultaneous oscillation of all atoms begins with Rabi frequency. Owing to emerging of the exited states, there arises a certain probability of registration acts which is proportional to product of average density of population of top level

Planck considers a case when

where

Thus, by small intensity of external radiation, top levels have time (the time of thermal relaxation) to get population only of insignificant small value.

According to (2), average density of population of top level can be estimated as

Thus, in each individual act of registration the electron or photon train of very small integral intensity participates, in comparison with integral from