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On the virial theorem and its physical meaning

We know physics and chemistry are based on the laws and rules called - either the principles, or the postulates, or the initial entities. The most striking examples of the axioms in physics are the laws of motion and equivalence principle of Newton, the Bohr postulates and Heisenberg uncertainty principle, Einstein's GTR and STR, the Big Bang theory, etc.

In chemistry, this approach is demonstrated by Lewis's rules, periodic law, resonance theory, etc. Such a way of promotion of scientific thought has a common feature - a lack of cause-effect relationships described in the above mentioned titles. At present, the formation of such rules, laws and theories is considered to be the ultimate goal (achievement) of physics and chemistry by an overwhelming mass of research scientists, as well as people outside science.

According to the history of science, this situation has been existing since the time of formation of science.

Along with the overwhelming number of people who believe that these achievements are final result of science, there have always been people who were deeply interested in science and trying to find the cause-effect relationships between phenomena. For us, only the search for the causes and consequences is a truly scientific approach, and fortune favored us. In previous works, we found out the cause-effect relationships in a variety of physical and chemical phenomena (for more details, see the sites

Currently, the correctness of the virial theorem is not in doubt either in printed publications or on the Internet. Both in physics and chemistry, both in classical science, and quantum one, the theorem is considered to be proved. Consequently, it is widely used, for example, in describing the hydrogen atom.

In our book (How Chemical Bonds Form and Chemical Reactions Proceed... p. 29 ), we wrote:

"Electrons are attracted to the nucleus because of electrostatic interaction forces. However, the electrons do not fall to the nucleus because they revolve around it with a certain velocity, i.e. have a certain kinetic energy. In its simplest form, the proof of the virial theorem is derived from the stationary condition of the orbit (see which is stated follows: the electron is at a certain distance from the nucleus because both forces - the centripetal Fcp connecting the charged particles and the centrifugal Fcf tending to tear an electron from the nucleus - balance each other, i.e.

Fcp = Fcf.                                                             (1)

The centrifugal force was calculated by the equation

F cf = me v2/rH = 9,1*10-31 *(2,2*106)2/0,53*10-10 = 0.83*10-7Н                             (2)

where Fcf , me  ,v and rH  is the centrifugal force, the Newtonian mass of the electron, the electron's velocity in orbit and the orbital radius of the hydrogen atom, respectively.

The centripetal force (or, in the case of the hydrogen atom, the Coulomb force) is described by the equation: 

1- engl                                            (3)

where Fcoul, ε0  and q is the Coulomb force, the electrical constant and the charge of electron and proton, respectively".

We substitute the following numerical values ​​in the formula: 8.99*109 Н*m2/s2 as the electrical constant, 0.16*10-18 C as the charge of the electron and proton, 0.529*10-10 m as the radius of the hydrogen atom. We find that the Coulomb force (centripetal force) in the hydrogen atom is 0.82*10 -7Н.

Fcoul  =8.99*109* (0.16*10-18)2/(0.529*10-10)2 =0.82*10 -7Н

The centrifugal force was calculated by the equation

F cf = me v2/R,                                                              (4)

where me ,and are the Newtonian mass of the electron, the velocity of the electron in the orbit and the orbital radius of an electron in a hydrogen atom (the radius of a hydrogen atom).

Similarly, substituting numerical values, we obtain the value of the centrifugal force:

F cf = 9,1*10-31 *(2,2*106)2/0,529*10-10 = 0.83*10-7Н.

In addition, we calculated the numerical value of the accelerations under the action of Coulomb forces and the value of the centrifugal acceleration.

The calculation made ​​by us (in the first approximation, it was assumed that the atomic nucleus was motionless), gave the following values: the acceleration acquired under the influence of the Coulomb force is equal to

2-engl                                                    (5)

Centrifugal acceleration, calculated according to the formula

аcf= v2/RH   (6)

is equal to: 

4 engl

In these formulas, q, m, v, RH are the charge (of electron and proton), the inertial electromagnetic mass of electron, the velocity of the electron in the orbit and the radius of a hydrogen atom, respectively.

In the calculations we didn't use the value of the electron mass but we took another value, which was measured more than 100 years ago: q/m= -1.76×10-11 C/kg.  Different sources give different values ​​for the electron velocity: from 2.22×106m/s to 2,18×106m/s. This is the reason for the inexact equality of the calculated values ​​of accelerations.

Further, the calculation of centrifugal forces and the centrifugal acceleration through Newtonian mass (matter which has no charge) will be called the first calculation, and the calculation via the mass, the inertial properties of which are conditioned by the charge and are described by the laws of electrodynamics, will be called the second calculation.

Let's examine in greater details the physical meaning of mass in both cases.

In terms of the physical meaning the first calculation is understood as a magic postulate, the  physical meaning of which (cause-effect relationship) is not clear.

Before the discovery of the atomic-molecular structure of matter and the laws of electromagnetic phenomena (particulary Faraday laws), the physical reasons which reveal such coincidences could not be determined. Indeed, before these discoveries it was impossible to suggest, even in the form of hypotheses, the existence of a cause-effect relationship between the Newtonian mass and the Coulomb forces, not to mention anything about the numerical coincidence.

On the other hand, already after the discovery of the nuclear-atomic-molecular structure of matter and the laws of electromagnetic phenomena the usage of the above-mentioned first calculation and the preservation of the Newtonian physical meaning of the parameter m can be explained only by the inertia of thinking and belief in figures of authority (especially in the indisputable authority of Newton).

As contrasted with the first calculation, the second calculation is a fine demonstration of the need to exclude a mechanical Newtonian mass from the initial entities, as was done with calorie and phlogiston in the course of development of chemistry and physics.

The second calculation can beexplained by using the physical mechanism. According to the laws of electrodynamics, when charged particles move with the acceleration EMF occurs, which causes the emergence of a force equal in magnitude to the force that caushed the charge motion with  acceleration (in this case, the Coulomb force) and  opposite to this force in direction (in this case, the centrifugal force).

The electron acquires a linear acceleration under the influence of Coulomb forces.

The equality of centrifugal and centripetal accelerations is a demonstration that the laws of electrodynamics do not depend on the type of acceleration. That is, it does not depend on the sign of the acceleration (whether it is positive or negative), or on the type of motion (translational-linear or centripetal-curvilinear), or on what force exactly led to the accelerated motion.

After the cessation of the exposure of the force causing the accelerated motion of the body, the action of the force caused by the EMF also gradually stops, and the body continues to move with the acquired velocity.

In previous works, in the process of determinating the cause of inertial properties of the electron, we concluded that the inertial properties of matter are conditioned by the charge and, therefore, the inertial mass is of electromagnetic origin. On the other hand, in subsequent studies (primarily in the article "Mass" and in this article), we are inclined to conclude that m is a factor which is, most likely, depends on the structure of the charge. For electrons it is 1837 times smaller than for nucleons.

Such a significant difference in the inertial properties of electrons and nucleons suggests that the inertial properties of matter are primarily conditioned by the nucleons.

The equation   M = 1,00732 · Z +1,0087 · N

which is cited in the article "The equivalence principle" and which calculates the atomic weight of element,  and where Z is the number of protons, N is the number of neutrons, and the coefficients 1,00732 and 1,0087 take into account the intranuclear interactions, and the equation fromn the article "The mass" for the calculation of inertial mass

m = qH2R / v = qH1H2R / E

prove that the mass is proportional to the charge. There is no postulated Newtonian mass.

The exception of the Newtonian mass from the fundamental physical entities is identical to the change in definition of the Periodic law after the discovery of H. Moseley. Before the Moseley's discovery the Periodic Law was formulated by Mendeleev in the following manner: the properties of chemical elements are not arbitrary but are in periodic dependence on atomic mass. After the Moseley's discovery the Periodic Law was formulated in the following manner: the nuclear charge is the most important property of the element that determines its chemical properties.

Now we can say that the inertial properties of matter are conditioned by the charge!

An important result of this work is following:

1. the additional evidence that the Newtonian mass does not exist and therefore there is no gravitational attraction in the view of Newton. The combining of the Newtonian gravity with the electrodynamic interactions was one of the unsolvable problems in the process of development of the unified field theory.
2. the regular contribution to the substantiation of the electrodynamic nature of the mass.
3. the detailed demonstration (in addition to our previous works) of that the centrifugal forces are not fictitious forces but they are electromagnetic forces caused by the EMF which appears in case of the charge motion with acceleration.

Although it is believed that the virial theorem is proved, and the solar system is described by the virial theorem, but still well-known problem which is 300 years old on the stability of this system does not have a unique analytic solution. Newton considered that the stability of the solar system is ultimately provided by supernatural forces. The instability of the model of the hydrogen atom of Bohr-Rutherford became one of the main reasons that led Bohr to the recognition of the quantum-mechanical description of the atom and the acknowledgment of the ideas of Heisenberg and Schrödinger. Hitherto existing evidence, unlike ours, did not give a physical explanation for these phenomena.

What is the main difference between this article and the preceding ones.

In most of articles from our books and articles placed on websites and (except for the articles "The mass", "The equivalence principle, "The calculation of the covalent radius of an hydrogen atom") give a phenomenological explanation of the inertial mass based on the laws of electrodynamics (mainly on Faraday's law).

In order to verify the correctness of this explanation, in our time, it was necessary for us to understand and believe (to overcome the inertia of thinking)
1) in the correctness of our explanation of electrical conductivity (see the article "General Chemistry XXI Century", the chapter "Phenomenological explanation of electrical conductivity");
2) that the laws of Faraday discovered by him as the result of the experiments with the conductors and magnets, also apply to the convection currents;
3) that a moving single charge is a convection current;
4) that a single charge moving with an acceleration is an alternating current, and that the AC possesses a self-induction, as well as any other current (see "How chemical bonds form and chemical reactions proceed", p. 244).

And even after the overcoming of the inertia of thinking in all these mentioned problems we have had only a phenomenological qualitative explanation because the coefficient of self-induction of the convection current could not be calculated quantitatively.

In contrast to this multi-layered overcoming of the inertia of thinking, in this article it is proving quantitatively that the charge moving with an acceleration causes the emergence of the emf. As a result, the force appears acting on the charge. The action of this force is equal in magnitude to the force that caused the motion of the charge with acceleration, and is the opposite to it in direction.

On the virial theorem and its physical meaning
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