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"Brilliance and poverty" of quantum mechanics

Nikolay Noskov
Translated from Russian by Jury Sarychev

The exciting pleasure of victories in discovery and becoming of a quantum mechanics has passed. On the basis of research of radiation spectrums and absorption of photons there was a powerful math-physical formalism abounding with principles, guesses, postulates, interpretations, models and mysterious formulas, which one, strangely enough, work.

All development of quantum mechanics and its broadest application in practice displays, that the researchers have found out the very relevant correlations of a material world, and also have learned to use them.

The quantum mechanics was formed as empirical science – on the basis of observations, facts, experiments. Hardly we can assume other way of development of science, as: observation, fact, experiment, empirical law, check and refinement of the law, creation of the theory, check and refinement of the theory.

However quantum mechanics was not lucky. It formed at once after a special relativity theory and simultaneously with a general theory of relativity. That was accompanied by a rebuff from ideals of a classic mechanics, from its invariants, from ether, from the mechanical program, which one most precisely was expressed by the Helmholtz [1]. "The problem of physical sciences is to reduce all physical phenomena to forces of attraction and repulsion, the value which one should depend on distance between interacting points". This program was stated by Newton, Huygens, Euler, Laplace,... Faraday, Maxwell, Hertz. But, taking into account fallacy of the Helmholtz concerning the theory of a delayed potential of Gauss, Weber, Gerber etc, it is possible now to see, that the mechanical program of the Helmholtz requires of principle additions. It should look so: "The problem of physical sciences is, that all physical phenomena to reduce to attraction forces, repulsion and to radiation, the value which one should depend on distance between interacting bodies, from their charge, mass, velocity and acceleration".

Having refused from the mechanical program, the developers of a quantum mechanics have appeared in a very unpleasant situation, when, using the language, methods and analogies of a classic mechanics, they persistently convinced themselves and other in impossibility of fulfillment of its requirements. All hopes in creation any acceptable theory was connected with a mathematical formalism, the program of which most brightly was expressed by Feynman [2]: "...Probably, the best way of creation of the new theory is to guess equations, not paying attention to physical analogs or physical explanation". (Nobel lecture).

Thus, in development of a quantum mechanics the first part is made only: creation of the empirical laws. The second part – creation of the theory – has appeared simply impracticable, as the empirical laws are not related to a physical reality and their causal essence is not detected.

The approach of Bohr [3] has appeared most successful, as he used the mechanism theory of a classic mechanics based on outcomes of experiments of the Rutherford, and it was the most exact path. Why it was not a success?

Five illogicalities are evident at the first acquaintance to the theory of Bohr:

1) Deviation from classic principles in definition of a total energy of an electron on orbit.

2) Error judgement that the electron at motion on orbit in accordance with the laws of a classic electrodynamics should emit energy.

3) Allocation of steady stationary orbits of an electron not as a problem of a mechanics, but as a problem of no emitted electron.

4) The frequency of radiation correlate with ΔE (not with E + ΔE), i.e. only with additional disturbance, not with full energy of an electron.

5) Steady orbits are considered equivalent, while the electron always, eventually, returns to steady basic orbit.

How it can chow oneself, these illogicalities are connected with Nils Bohr's bad knowledge of a classic mechanics. It (classic mechanics) has failed in connection with conceiving of a relativity theory as it was represented to everybody in that time. Probably, so it is possible to explain a reason that he did not begin to coordinate advanced postulates with mechanics of Galileo – Newton – Euler.

But, the reader will disagree, you see there is still common sense based on logic, analysis, comparisons, analogies, approximating etc. To confuse a common sense, relativists have added to it an epithet "narrow – minded" and have declared war against it. And Bohr was among them.

Having ignored ideals of a classic mechanics and, first of all the internal logic of nature and mechanical principle, Bohr has suffered a defeat. His model hardly has described atom of hydrogen only. But he was on right way, and all subsequent generations of the researchers, if do not understand it, feel. The constant reference to Bohr's model at researches of equations of Schrodinger and Dirac is the proof of this.

1. The correct definition of full, kinetic and potential energies of an electron on orbit has the important significance for understanding of essence of a phenomenon of radiation and quantitative solution of equations of a quantum mechanics. I shall not set up reasoning and proof that the potential energy can not be negative, since it is a scalar quantity. It has only theoretical meaning, and for two bodies having a volume, the full potential energy can be determined only by two integrals: from infinity up to a contact of bodies and from a contact of bodies to combination of centers of their gravity. The difference of potential energies from infinity into given orbit, or from one orbit on other and kinetic energy, which one is equal to half of full energy of an electron on orbit and half of difference of potential energies from infinity into given orbit have practical meaning.

2. Erroneous judgement that under the laws of a classic electrodynamics the revolving electron should emit energy move from the monography to the monography, from the tutorial to the tutorial, starting from Bohr and Born, finishing modern transactions. The thoughtless copying of errors in physics has resulted in pitiable outcomes. Physics has wallowed in "guessing of equations".

Even such sensible reasoning that an electron moves on an equipotential surface, not changing the energy, results in a conclusion that the electron should not emit. However take a classic equation of an electrodynamics of Weber and you will see that the second derivative of distance between an electron and proton on a circular orbit in a term of equation, accountable for radiation, is equal to zero. On what basis have Bohr and Born declared, that there should be a radiation?!

3. And now we came to the most important illogicality in theory of Bohr. This is the statement of existence of steady discrete orbits, connected with non-emitting of an electron and not justified by mechanical reasons. At first, obviously, that nonemitting of an electron can not cause stability. Secondly, what does prevent an electron to fall on a core, even discretely emitting?

Scarecrow from a fairy tale by Volkov "the Wizard of emerald city", would reason so: "If I was a Newton or Laplace, I would think, that the electron has steady discrete orbits due to a resonance of two oscillations having different reasons. One of them is the cyclical frequency that can be found from equilibrium of centrifugal and centripetal forces. But other... Where to take other?"

Still Newton has noted that it is impossible to explain motion of planets with existing laws of a classic mechanics, when a central body (Sun) is in one of focal points of an ellipse. So, if the planet moved on orbit under the already known laws of a mechanics, the central body would be not in focal point, but in center of an ellipse. However he could not find an answer to problem, and for the subsequent generations of the researchers this problem has dropped out from a field of vision and as though has ceased to exist.

Such motion of planets, and also electrons in atom, is explained only in the event that a planet and electron experience longitudinal oscillations, length which one is equal to length of orbit. However Born in one of the philosophical articles has told approximately so: "the quantum mechanics could be explained with longitudinal vibrations of moving bodies, however laws of such motion do not follow from anywhere..." But we see such motion of bodies on orbits, therefore, such laws should exist.

The laws of such motion of bodies are obtained due to research of a delayed potential [4]. Modeling process of arrival of a delayed potential to a moving trial body in a field of forces, I have found out, that the delayed potential reaches to a body non-uniformly, now it delays more, now it delays less. It means, that the trial body moves with longitudinal oscillations. Thus, the longitudinal oscillations of moving bodies in fields of forces are the general law of the nature, and this law has appeared possible to derive with the help of three variables: distance, force of interaction and phase velocity. It looks so: length of longitudinal oscillation of a moving body is directly proportional phase velocity and is inversely proportional to distance between interacting bodies and force of interaction. The derived law results in two interesting formulas, which one already exist in physics, but are obtained by a heuristic way, intuitively. First of them is law of radiation energy of the Planck – Einstein; second is correlation of de Broglie lengths of waves.

It is not necessary to explain the reader, that the derived formulas in comparison with already existing have brand new sense. They describe longitudinal – oscillatory (pulsatory) motion of bodies.

Thus, we can note, that de Broglie intuitively, by mysterious mode has found that indispensable second oscillation, which one, adding with cycle oscillation, will form stable motion of bodies on orbit at the moment of a resonance with it.

So far as de Broglie [5] has found the law "by guessing of an equation", naturally, it comprises discrepancies, which one have resulted in its fancy explanation, such as "wave – particle". After a fifty years' rough controversy in a scientific press and on conferences it "sounds" in the modern reference books on physics as follows: "...According to statistical interpretation the de Broglie's waves have the special physical sense "of waves of probability". It were good, if the authors of such formulation have explained: how does that "the statistical interpretation" really diffract on crystal lattice?!

The de Broglie's is inaccurate because wave law should include a phase velocity, instead of linear. By the way, physicists, transforming with the help of the de Broglie formula frequency of oscillation of light in length and on the contrary, use for this purpose by velocity of light as phase. The inference of the de Broglie formula as outcome of delay of a potential has shown, that the non-linear factor amending on velocity (such as relativistic) should include in it. This factor has very significance for exact finding of "a defect of mass" in nuclear physics.

What has taken place further? And further incredible events have begun. Schroedinger [6] has written a not clear equation – riddle which one for some reason scientists have begun assiduously to guess and to attempt to find its solutions. It is unknown event in science.

If, as they assert in all books on a quantum mechanics "it is impossible to deduce a wave equation strictly logically, then the formal steps carrying on to it, are, as a matter of fact, only witty guesses" (Born). What was his confidence in correctness grounded on?

Max Born [7] has found the solutions of the Schroedinger wave equation with the help of statistical interpretation of a wave function, but thus the quantum mechanics finally has gained a mystical view. Practically simultaneously with Schroedinger Heisenberg [8] has opened new version of a formalism of a quantum mechanics: with the help of a matrix analysis and so-called "indeterminacy relations". Around of latter one have inflamed philosophical passions, not calming down to this day.

If the researchers did not accuse continually classic mechanics in insolvency, and have looked in it for analogies, at once they would see that at any real oscillation of a rigid body there are same problems, as in "indeterminacy relation" of Heisenberg. So if to define in some instant, velocity and impulse of an oscillating body, then it is impossible to define a full energy of oscillation. If we define energy, then instantaneous velocity and impulse loses sense.

Nevertheless, Russian physicists Ternov and Sokolov [9] in 1969 have found the logical inference of a Schroedinger equations. It turned out that the Schroedinger equations are a system of three known equations. One of them is ratio for lengths of de Broglie's waves. Second is energy conservation law on orbit of Hamilton. Third one is general wave equation of oscillation of medium deduced for a sound by Helmholtz and for light in ether by Maxwell.

For a mathematical formalism there is no difference what equations are joint in a system. But for physicists of a classic mechanics it is completely unacceptable to solve a joint set of equations, one of which is the law of motion of a rigid body and other is law of oscillation of medium. Therefore equations of Schroedinger and Dirac cannot be considered as physical. Any paradoxes, statistical solutions, "vagueness" of an electron etc. occur from here.

From all above said follows, that the stable states of electrons on orbit can be found from a resonance of two oscillations: cyclical, defined from a balance of power on orbit and longitudinal, defined by the formula, having form of de Broglie's expression. So far as the resonance of these frequencies is possible only at total length of longitudinal oscillation, from here the integer sequence of steady discrete orbits follows.

At definition of cyclical oscillation from a Newton's law of a balance of power on orbit, at least, two fundamental conclusions follow some more. At first, the constant of quantization (Planck) for an electrodynamics (in atom) is less than a constant of quantization in gravitation (for planetary systems) approximately in 1040 times. Secondly, the centripetal force, especially in atom, depends on quantity of bodies (electrons) on orbit and, the laws of delay of a potential can interfere with their laws of motion.

The quantum mechanics can and should find the determined form of a classic mechanics; for all that classic mechanics should include a delayed potential.


The literature:

  1. H. Helmholtz. Über die Erhaltung der Kraft. Leipzig, 1907, s. 6.
  2. R. Feynman. The Nobel lectures.
  3. N. Bohr. The quantum mechanical description of a physical reality.
  4. N. Noskov. To a problem on limitation of a field of application of a classic mechanics. SPE "Print" Institute of high-energy physics, Academy of Sciences; Kaz. SSR, Alma-Ata, 1991.
  5. L. de Broglie. The substantiation of quantum conditions of the Bohr. Thesis. Ann. de Phys., v. 10, 1925, p. 22.
  6. E. Schroedinger. Ann. Phys., Bd. 79, 1926, s.361, 489; Bd. 80, 1926, s. 437; Bd. 81, 1926, s. 109.
  7. M. Born. Probabilistic interpretation of a wave function. Zs. Phys., Bd. 37, 1926, s. 563; Bd. 38, 1926, s. 803.
  8. W. Heisenberg. Zs. Phys., Bd. 33, 1925, s. 879
  9. A.A. Sokolov, I.M. Ternov. A quantum mechanics and nuclear physics. M.: Prosveshchenie, 1970, p. 39...40.

Is published earlier:

"Science of Kazakhstan", 1 (85), January 1...15, 1997.

Date of the publication:

May 10, 2000

Electronic version:

© NiT. Current publications, 1997

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