SELF

40

S.B. Karavashkin and O.N. Karavashkina

As it is known, the postulate of existence of stable stationary states of oscillators is a necessary premise to conclude the correct formula of black body radiation. "It is Nielse Bohr's merit (1913) of clear formulation of this point and its generalisation for any atomic systems" [1, p. 293].

When this quantization postulate was introduced, the majority of scientists admitted the viewpoint that in this way "the classical physics has been fully clear shown inapplicable to the within-atomic motion" [1, p. 295].

At the same time, Niels Bohr in his basic paper [2], when solving the problem of electron radiation in the atom, operated with quite particular concepts of classical mechanics - such as trajectory of electron, point material body etc. And the statement that "classical electrodynamic was insufficient to explain the properties of atom on the basis of Rutherford-like model is clearly revealed in consideration of simplest system consisting of very small positively charged nucleus and electron moving in the closed orbit around the nucleus" [3, p. 86] is grounded on the fact that Bohr, as well as all following scientists, has not succeeded in getting over the paradox of stable orbit of electrons in atom and electron's strongly discrete radiation of the energy in going from one orbit to another. "In accordance with the electromagnetic theory of light we could expect that, like radio waves evidence of electric oscillations taking place in radio stations, the frequencies of particular lines of natural spectrum of elements inform of electrons moving in atoms. But mechanics does not give sufficient grounds to interpret this information; due to the above possibility of change in mechanical state, we are not in position to grasp the appeared sharp spectral lines" [2, p. 64].

At the same time, merely formal postulating the quantum nature of radiation has not lifted the phenomenological difficulty in describing the processes in atom, but only allowed at a definite stage to calculate the frequencies of atomic systems, well consistent with the experimental data. With it the statement that quantum theory "not only has explained (with the help of Relativity) all niceties in the structure of hydrogen atom, but is successfully applied also to describe multi-electron atoms, molecules, particle scattering etc." [4, p. 81] is quite inaccurate. Quantum theory does not explain the phenomenology of quantization, just as Bohr's theory, which was criticised as inconsistent in frames of quantum theory. Even more, quantum hypotheses of wave nature of particle and corpuscles of light - photons cannot stand a least scientific criticism.

Take for our consideration the shape of wave function of free particle. "It will be natural to think that to a free particle moving evenly and directly with the constant pulse p and energy E corresponds a plane monochromatic wave. We can write down the wave function , describing such wave, in the complex form, some more general in comparison with the plane light wave:

(1)

Here p is the pulse of particle directed not in the axis OX but arbitrarily, r₀ is the distance from the origin of coordinates to the equiphase surface, a is the wave amplitude" [, p. 38]

Having written similarly the wave function (only without delay phase), E. Fermi [5, p. 21] derived the Schroedinger equation as

(2)

and further in the same second lecture considered different models, in that number for a free particle. But the concept of monochromatic wave does not relate to some particular point of space at some particular moment of time. "Monochromatic light is the light radiation with a definite frequency… Each time-limited radiation covers some interval of frequencies" [6, p. 325]. Thus, if we represent a particle as the monochromatic wave, its extent (or probability of location) has to have the size far from quantum. And if we suppose a particle having quantum size ( 10 ^-19 m), the spectrum of its wave function has to be very wide. Consequently, the Schroedinger equation will take basically other form.

Again, if we suppose that the particle is determined by the wave function as a chain of waves, there arises the difficulty with stability of this particle in time. Actually, "at first stages of development of quantum mechanics, there was undertook an alluring attempt to solve the wave-particle contradiction, thinking the particles as wave packets … However attaractive this simple idea can seem, in the nearest consideration it appears absolutely wrong. Decisive argument is the following. The favourable properties of packet …, just its stability and motion as the whole with the group velocity, do not give us the complete pattern of the packet properties. As the matter, we yielded them only as the first-range approach, since, considering the motion of packet, we used the approximative relation between v and k:

(3)

discarding all the rest terms of expansion. But if we calculate precisely, we will yield some other result - it appears, though the maximum of packet moves with the velocity dv/dk equal v   for the De Broglie waves, the very packet in moving in the disperging medium does not retain its shape and size but gradually expands - spreads … Quite cumbersome calculation which we do not show here proves, if we form a packet of De Broglie waves having at the moment t=0 the shape of Gaussian probability curve …, the extension of packet doubles in the time interval which is expressed by the formula

(4)

where m is the mass of particle, h is the Planck constant, and b is the hemi-width of packet. For a particle having the mass m=1 g and length 2 mm (b=0,1 cm), the corresponding packet doubles in 6*10 ¹⁷ years. But for the particle having the electron's mass (m = 0,9*10 ^-27 g ) with b 10 ^-12 cm , time will be t 1,6*10 ^-26 s, i.e. the packet corresponding to electron would spread immediately - of course, this contradicts the most elementary observations" [1, p. 462- 465].

The probabilistic interpretation of De Broglie waves also does not solve the arisen problem, as in this case the probability to find an electron at some region of space in t 1,6*10 ^-26 s   will twice diminish, which also does not correspond to the most elementary observations. Simpler speaking, with such abrupt change in time of the probability to reveal the particle in space, it would be possible to design no one betatron or electronic microscope; nothing to say that the size of electron indicated by Shpolsky can be well less, and so the uncertainty to detect the electron in a limited region of space would disable us even to detect its trajectory in the bubble chamber. But if we interpret   in (1) as the probability to detect the particle in some region, from this it will follow immediately that the particle can be detected with a periodic probability in the infinite region of space, which also contradicts the observations.

Finally, if we suppose that the density of probability can be matched only to some assemblage of electrons, in this case we would have no right to apply this conception to atomic structures, and the more to the hydrogen atom, in which only one electron revolves around the nucleus.

Thus we see, pure formal postulating that the energy is quantified does not clear the phenomenology of process in atomic structures but only creates a whole spectrum of additional unsolvable contradictions.

So in this paper we return again to the classical statement of problem of electron's motion in the field of nucleus, in order to try to establish the cause stabilising the electron's orbit. We will show that in reality the orbits stability is quite explainable in frames of classical phenomenology, if we note the factors to which the researchers still paid insufficient attention. Developing this study, it will be not difficult to show that the revealed factors determine not only the stability of atomic structures but also formation of the specific structures of macro bodies - such as galaxies.