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FOREWORD

** **

The results of our previous scientific
investigations are colligated in the book. The general line in the development
of the classical notions concerning the microworld is preserved, and more
profound solution of some analytical tasks is given. It has required adjustment
of some provisions and the change of some outdated notions.

The attained level of comprehension of
the microworld demonstrates a close connection of physics with chemistry and
impossibility to divide the phenomena of the microworld into physical and
chemical ones in some cases. That’s why the phenomena, which take place on the
nuclei, atomic and molecular levels, are called physicochemical phenomena.

The derivation of the law of radiation of a full blackbody on the grounds of classical notions on this phenomenon proves erroneousness of the conclusion made by the scientists of the last century concerning incapability of classical physics to solve the tasks of the microworld.

Let us recall that quantum physics was
born at the beginning of the 20th century when the attempt to explain
experimental dependence of radiation of the full blackbody with the help of
wave notions concerning this radiation turned to be unsuccessful. The task was
solved when Max Planck postulated that
radiation is not constant, but it takes place in portions or in quanta of energy, that’s why the new trend in
development of physics was called quantum physics.

The level of development of classical
theoretical physics at that time did not allowed the scientists to explain many
experimental data, that’s why theoretical physics has chosen easier way: the
interpretation of the experimental results according to the new theories, which
took place at the beginning of the 20th century, were customized. There were
some attempts to describe the new experimental data on the basis of classical
laws, but these attempts failed at that time.

Now, a hundred years after it we
should accept that the directions of development of theoretical physics chosen
at that time were erroneous. Modern orthodox theoretical physics cannot explain
more experimental data than classical physics failed to explain at the end of
the 19th century.

Many
scientists are not satisfied with the state of theoretical physics and
critisize, first of all, the theories of relativity by A. Einstein considering
him the main delinquent of the existing situation. But it is not so. The
misbelief formation process was a collective one, and it started before A.
Einstein joint it. The detail analysis of this process shows that it was very
difficult to avoid it. Rapid development of exact sciences demanded system
analysis of correctness of the chosen way, but nobody could do it, because the
principles of this analysis remained closed. Now this task is solved, and we
have got an opportunity to see the background of misbelieves and the general
way of development of exact sciences. It was correct to end of the 19th
century. It is a classical way. To which we return after a century.

This book contains classical solution
of many tasks of physics and chemistry, which have not been solved by modern
orthodox physics. This book is devoted to the solution of these notions.

** **

** **

The
analysis of the estimation of theoretical physics in general and quantum
mechanics in particular performed by the most prominent physics of the 20th
century shows that fruitfulness of further development of theoretical physics
is constrained by incompleteness of exact science axiomatics. Systematization
of fundamental scientific notions (space, matter and time) and their ranking
due to a level of resumptive meaning and significance for scientific
investigations leads to the necessity to include the space-time absoluteness
axioms and the space-matter-time unity axiom into the scientific research.

The analysis of Lorentz’s transformations, the equations by Louis de
Broglie, Schroedinger, Dirac, etc. shows that they contradict the
space-matter-time unity axiom; that’s why they reflect reality incompletely and
sometimes wryly. The analysis of the existing mathematical models, which
describe behaviour of the photon within the framework of the space-matter-time
unity axiom, leads to disclosure of its electromagnetic structure, which gives
the opportunity to explain the whole spectrum of peculiarities of its
behaviour. It has been established that the law of conservation of the angular
momentum governs Planck’s constant, and due to it the electromagnetic model of
the electron is disclosed and the peculiarities of its behaviour in the atoms
are explained.

Planck’s radiation law is derived from the laws of classical physics.

The analysis of the spectra of multi-electron atoms and ions within the
framework of the notions being described leads to empirical mathematical model
of the spectrum formation, in which there is no orbital component of the
electron energy. It appears from this that there is no orbital movement of
electron in the atom. The law of conservation of the angular momentum, which
governs Planck’s constant permanency, makes the electron precess on the atomic
nucleus. It appears from this that the protons of the atomic nucleus should be
arranged on its surface. This position leads to disclosure of the principles,
which govern the formation of the nuclei, and to the structures of the atomic
nuclei, which correspond strictly to the periodic law of chemical elements.

The new scientific information opens the formation principles of the
atoms and the molecules and gives the opportunity to calculate binding energies
of the electrons with the atomic nuclei and the electrons of the neighbouring
atoms, which are united in molecules, for any energy level of the electron. It
becomes possible to build the water molecule and to analyse its behaviour in
detail during low-voltage and plasma electrolysis. In this case, one detects
the causes of occurrence of additional thermal energy during plasma
electrolysis of water as well as during the cavitation phenomena and discloses
the conditions for the reduction process control of energy consumption for
hydrogen production from water.

The transmutation process of the atomic nuclei of alkaline metals and
the cathode material becomes clear, and the control methods of this process
take place.

The
monograph is finished with the analysis of the control of the law of
conservation of angular momentum of the formation processes of the atoms,
molecules, biological systems and the formation process of the Vector
cosmological potential, which has been discovered recently.

**1. ****EXACT SCIENCES BETWEEN TWO CENTURIES**

** **

It is known that the end of the 19th
century was marked by the crisis on classical physics. Many experimental data
were accumulated, especially in the field of optics. Its results failed to
explain the physical theories existing at those days [31], [102].

As the theories were based on axioms, they were analyzed carefully. Most of them are based on the fifth axiom by Euclid concerning parallel straight lines [6], [171]. The controversy was finished by the concept that the situations can take place in the Nature when these parallel straight lines intersect in infinity. This statement was given a status of an axiom without any experimental proof of its reliability [6]. From this axiom, the non-Euclidean geometries by Lobachevsky, Minkovsky, Riemann, etc., originated as well as the theories based on these geometries [6], [80], [119], [135], [147], [149]. First of all, both theories of relativity by Einstein originated from it.

Emergence of several alternative
geometries caused agitation among the mathematicians. This situation was
described by M. Kline, the American historian, in the following way [6]:
“Existence of several alternative geometries was a shock for mathematicians;
they were astonished to greater degree when they understood that it was
impossible to deny the application of the non-Euclidean geometries to physical
space”.

The ambiguities connected with
emergence of the non-Euclidean geometries took place in the second half of the last
centuries, but only now they begin to attract attention. Neither physicists,
nor mathematicians paid much attention to this ambiguity. “Curiously enough,
mathematicians “turned their backs on the God”, the all-mighty geometer did not
wish to tell them, which geometry he selected during the creation of the
universe”, - writes M. Kline [6].

It is an exact and simple description
of the essence of the existing situation. Now it is difficult to determine why
the mathematicians have behaved in such a way; it is more difficult to
understand the physicians who were eager to use the non-Euclidean geometries
for their theoretical investigations [70].

Academician A.A. Logunov
convincingly demonstrated in his lectures on the theory of relativity and
gravitation (published by the Moscow State University) that GTR fails to
observe the laws of conservation of energy and impulse and that inertial mass
as determined by GTR does not make physical sense. Logunov considers that these
facts cast doubt on the existence of black holes and on the Big Bang
Hypothesis, which originates from GTR [145]. According to him, it discredits
the existence of such objects as black holes and such phenomena as the Big
Bang, due to which the Universe was formed as GRT adherents think.

L. Brilluen, the French scientist,
noted: “General theory of relativity is a shining example of an excellent
mathematical theory, which is built on sand and leads to a gorge of mathematics
in cosmology (typical example of science fiction)” [131].

Here is the statement made by
Academician Hannes Alven, the astrophysicist and the laureate of the Nobel
Prize. He calls the cosmological theory of expanding Universe, which originates
from GTR, a myth and proceeds: “the less the evidence, the more phrenetic the
faith in this myth becomes. As you know, this cosmological theory is the
perfection of nonsense. It states that the Universe has originated at a certain
definite moment like an exploded bomb, which has (more or less) a pin head
size. It looks like that in the present intellectual situation the Big Bang
theory has an advantage of common sense contempt: “I believe, because it is an
absurd!”. When the scientists struggle against astrological drivels outside the
temple of science, one should bear in mind that inside this temple large
nonsense is cultivated sometimes” [82].

It is clear from these statements
that mathematics can play a part of not only the truth cognition instrument,
but it can be a guide to the world of delusion and to block the exit from this
world with its authority for those who happened to be there. It explains
indifference of the majority of the scientists, first of all, of the physicists
to vivid ambiguities, which take place in science. Earlier, these ambiguities
served as a powerful pulse for the analysis of ambiguities. Now only some of
them are brave enough to speak about their doubts. These statements are very
valuable for science, because they belong to people, who have understood the
essence of difficulties, which arise on
the cognition way, better than others. That’s why we should treat these
statements as pearls of human thought and try to understand the essence of
doubts, which disquieted these great thinkers.

The part of physics, in which the
behaviour of elementary particles is studies, is called quantum physics. As we
have already noted, it is a branch of physics, which was born at the beginning
of the 20th century in the day when Max Planck made his report concerning black
body radiation at the sitting of the German physical society. In this report he
introduced his famous constant, which served as a foundation of quantum physics
and with which the majority of secrets of behaviour of elementary particles is
connected as it has turned out. This constant was called the Planck’s constant
later on. It had mechanical dimensionality of moment of momentum or angular
impulse, as physicists call it. It proved availability of angular motion in the
natural phenomena, which were described with the help of the Planck’s constant
[101], [117].

But Max Planck was afraid that he
could be accused of mechanism during the microworld element behaviour
description. That’s why he gave a name to his constant, which did not reflect
its physical dimensionality. He called it the quantum of minimum action [31],
[102].

Daniel and Deutsch, the American
scientists, analyzed dimensionality of the Planck’s constant. In 1990, they
wrote in the article published in the sixth volume of the journal Galilean
electrodynamics that if Planck gave his constant the name, which corresponded
to its dimensionality, quantum physics would differ greatly from the one we are
having lately [11].

Louis de Broglie, the progenitor of
the wave-particle duality concept, said: “… quantum mechanics urgently needed
new images and ideas, which could appear only with a deep revision of its basic
principles.” [8]

In the seventies, the American
physicist E. Wichmann offered the conclusion: “There is no fundamental theory
of fundamental particles yet, and we do not know what form the future theory
will take”. [122].

The situation connected with quantum
physics is described by l. Ponomarev, the Russian scientists. In the popular
book *Under the sign of the quantum* he writes: “Disputes concerning
quantum physics take place every day. These disputes can be compared with feud
of the religious sects inside one and the same religion due to their
obduracy and unappeasability. As usual
in religious disputes, the logic arguments are of no use, because the opposite
party cannot understand them: there is a primary, emotional barrier, the act of
faith; all compelling arguments of the opponents dash against it having failed
to penetrate into the sphere of consciousness” [150].

The most complete reflection of the
essence of these difficulties was offered by one of the greatest physicists of
the 20th century P. Dirac. “It seems to me very probable that some day in the
future an improved quantum mechanics containing return to causality will
appear. But such a return can take place at the expense of rejection of some
other basic idea which we now accept unconditionally. If we are going to
restore causality, we shall have to pay for it and now we can only guess what
idea must be sacrificed” [134].

Causelessness is based on the
principle of uncertainty. The importance of this principle was briefly and
fully determined by American physicist J.B. Marion: “If sometimes it is proved
that the principle of uncertainty is not valid, then we shall have to expect a
complete reconstruction of physical theory” [148].

“Beyond any doubt”, says Italian
physicist Toulio Redge, “quantum mechanics will finally be overcome, and, most
probably, Einstein’s doubts will turn out to have been reasonable. Perhaps at
present there are neither physicists, who can see an inch before their noses,
nor concrete suggestions how to overcome boundaries of quantum mechanics, nor
experimental data showing such possibility.” [151].

Meanwhile the experimenters have
“proved” the existence of quarks, the most elementary “bricks” of the matter.
In terms of generally accepted models of the fundamental particles (including
quarks) there has been little real progress since Rutherford and Bohr proposed
their models of the atom [136].

There are no commonly recognized
models of the photon (electromagnetic quantum), the electron, the proton, the
neutron or other particles. That is why physicists accept the theoretical
foundation of science which seemed to have been reliably cemented by Neuman in *Mathematical
Principles of Quantum Mechanics* [159]. Neuman demonstrated the
impossibility of the latent parameters for which many physicists cherish great
hopes believing that they can overcome the probabilistic description of
behaviour of elementary particles. But those hopes were crushed by Bell’s
theorem which seems to validate the probabilistic view of quantum mechanics
[149].

Lack of clear theoretical
relationships between the postulates of the microworld created the situation,
which was successfully summarized by Academician D. Blokhintsev: “The way to
understand the regularities dominating the world of elementary particles has
not yet been found. A modern physicist has to be satisfied with compromise
conceptions, which promise, at best, only partial success at the expense of
community and unity” [132].

Einstein examined critically the results of his investigations.
Answering the venerators of his talent, he wrote in the declension of years: “It seems to them that I look at the results of my life with a halcyon
satisfaction. But everything is to the contrary if examined closely. There
exists no concept, in relation to which I am sure that it will remain
inviolable, and I am not convinced that I am on the right track.” (F. Hernek. *Life
in the name of the truth, humanism and piece*. M.: Progress, 1966, page 16).

This is the state of theory. What do
physicists themselves say about experimental achievements in the field of
microworld research? V. Rydnik notes in his book *To See the Invisible*
that ideas about elementary particles are derived by synthesis of information
about elastic and non-elastic scatterings. In his opinion, the complexity of
this problem is comparable with the situation described in the story of the
blind men and the elephant: “One of them touched the elephant’s trunk and said
that elephant was something soft and flexible, another reached the leg and
declared that elephant looked like a column, the third felt the tail and
decided that elephant was something small.” [154].

As we have demonstrated, the
symptoms of theoretical delusions in physics began to manifest at the turn of
the last century, and at present the global size of these delusions wins
international recognition.

Since the
year of 1990 the publication of the scientific journals has begun in order to
analyze such results. The journal *Galilean Electrodynamics* is published
in USA [12], [14], [19], [100], [107], and the journal *Apeiron* is
published in Canada [96], [97]. Since the
year of 1999, the Internet journal __http://www.journaloftheoretics.com__
has been published [175], [179], [180], [181], [183], [184], [191], [192]. At the same time, the international
conferences began to be held in Russia. It is impossible to count the books on
this theme, which have already been published in Russia, USA and Western
Europe. Modern theoretical physics has already been criticized well enough
[22], [64], [88], [143], [128].

In general ,the representatives of
orthodox science ignore this criticism, but it does not reduce the number of
the critics. This process goes on quite rapidly. The situation is such that the
critics cannot convince the representatives of official science, and the
representatives of official science do not want to make out with the essence of
criticism. It is known that criticism should be either recognized or
demolished. But neither action takes place. It proves the fact that its is not
simple to digest the essence of the scientific problem, which has taken place
[157], [146].

For example, criticism of the
theories of relativity of A. Einstein has begun since the day of their elaboration
and takes place hitherto [7], [162], [169]. A question arises: if the theories
are erroneous, why is this erroneousness proved for a long time? The answer is
simple. The critics analyse the consequences of these theories, not the
foundation, on which they are based. Chiefly, the Lorentz
transformations suffer. The critics do not pay attention to the fact that they
are the results of the statement concerning intersection of parallel straight
lines, which has received the status of an axiom.

Thus, in order to prove reliability
or erroneousness of the theories of relativity of A. Einstein it is necessary
to analyze the connection with reality of not the Lorentz transformations, but the axiom on intersection of parallel
straight lines.

In reality, fundamental sciences
are based on a small quantity of the framework obvious affirmations, or axioms.
But the developers of exact sciences did not pay attention to it, they gave the
status of axioms to unlimited number of statements, far from being palpable,
even absurd sometimes [31]. The unity of the foundation of exact sciences has
been destroyed, and it has turned out that some foundations have been built on
sand [30].

We have understood the existing
situation of exact sciences nearly ten years ago. We have cherished vague hopes
that it will be understood by many people, and a joint scientific thought will
be formed in order to solve it. But this hope did not come true. An unknown
force deters consciousness of the world scientific community from understanding
significance of this problem. One thing remains: it is necessary to agree with
Max Plank’s opinion concerning scientific truth acknowledgement: “Usually
scientific truths gain victory not in the way that their opponents become convinced
and say they are not right, but mainly due to the fact that the opponents die,
and the next generation takes the truth for granted” [8] and to submit for
approval of the scientific community its concept of the decision of this
complicated problem.

**2.1. General**

** **

It is considered that the birthday
of quantum physics is December 14, 1900, when Max Planck has made a report “On
the Theory of the Energy Distribution Law of the Normal Spectrum” at the
sitting of the German society on physics [31], [102]. In order to get a
mathematical model of the black body radiation law, he introduced “a universal
constant” *h*, which pointed out to the fact that radiation is distributed
not continuously as the wave concepts on electromagnetic radiation nature
demanded, but as portions (quanta) in such a way that energy of each portion
(quantum) is determined by elementary dependence *hv*.

Incompatibility of the concepts
concerning the continuous wave process of electromagnetic radiation with the
concepts of portion radiation is a strong reason to acknowledge the crisis of
classical physics. Since this period it has been supposed that the terms of
reference of the classical physics laws is limited by the macro world. In the
micro world, other finer laws operate: quantum laws, which conflict with
classical laws of physics of the macro world. The new direction was called
quantum physics [31], [102].

Later on, Ervin Schroedinger got an equation, which predicted only density of electron stay probability in the given area of the atom, but did not give the opportunity to disclose the structure of the electron and the mechanism of its interaction with the atomic nucleus. It permitted to calculate the spectra of hydrogen-like atoms, but was useless during the calculation of the spectra of the atoms with many electrons. Nevertheless, it has been acknowledged that in the description of the micro world this equation plays the same role as the equation of the second law of Newton in the description of the macro world [133].

The famous equations of
electromagnetic field suggested by James Clerk Maxwell in 1865 did not give the
opportunity to disclose the structure of electromagnetic radiation, in particular,
the structure of the photon [16], [123].

Further development of this
direction has led to elaboration of various useless field theories, which have
led to string theories [47], [80], [88].

One hundred years passed, and it became
necessary to estimate fruitfulness of such direction in the development of
quantum physics. As it originated from the electromagnetic radiation process
analysis, one should expect the discovery of the structure of this radiation
and the electromagnetic structure of elementary quantum of energy. But it did
not happen [139], [142]. Other numerous problems of the micro world have
remained unsolved.

The nature of electromagnetic
radiation was not revealed as well as the electromagnetic structures of the
photon and the electron, the structures of the nuclear, the atoms, the ions and
the molecules [137], [140]. But the main thing is that the mechanism of
combination of the atoms into molecules has remained unclear. The electrons
orbiting round the atomic nuclei cannot perform the functions of connection of
the atoms into molecules. The processes of radiation and absorption of the
photons by the electrons during their orbital transitions remain completely
unclear. The theorists failed to suggest an acceptable method of theoretical
calculation of the spectra of the atoms with many electrons. The chemists
cannot calculate binding energies of valence electrons with the atomic nuclei
corresponding to their various energy levels [2].

The culdesac state of modern
theoretical physics was manifested when it became necessary to explain the
reasons of apparition of excessive energy during various methods of water
treatment. The experimenters have shown that in some modes of conventional
electrolysis of heavy water and plasma electrolysis of light water as well as
in the phenomena of its cavitations more energy is released than spent for this
process. It put a question concerning correctness of one of most fundamental
laws of physics – the energy conservation law [51], [59], [67].

A situation was created when it was
necessary to find an explanation of the new experimental data, but both
theoretical physics and the theoretical chemistry failed to perform this
function.

**2.2. The Main Causes of Crisis and the First
Steps of Way out**

** **

We have already quoted some
scientists in connection with safety of the foundation, on which theoretical
physics is based. But these are only statements. It is not an easy thing to
find the causes of this instability; it seems that in order to solve this
problem it is necessary to have deep knowledge not only of physics, but
mathematics as well. We’ll show that it is not so. First of all, one should
know the method of the system analysis of complicated problems and have good
knowledge of physics, mathematics and other sciences.

The system analysis of the complicated
problems is based on several fundamental principles. The first, and the
foremost, one does not recommend to begin the analysis of the problem if its
beginning is not found. It means that it is impossible to begin the check of
correctness of the chosen way from its middle or from its end. It is necessary
to find the beginning of this way, to follow it and to study attentively
everything, which serves as a foundation during the selection of this way. If
there is no doubt in safety of the foundations, one can proceed taking into
consideration everything, which is met on this way, checking the correctness of
structures, trying to find possible mistakes and estimating the results, which
they have given.

The second principle says that
thousands of factors govern behaviour of any complicated system. Only some of
them influence this behaviour significantly. If this factors are not determined,
it is impossible to find the causes of the existing situation in the state and
behaviour of the system and the way of its further development.

Fundamental sciences serve as a
classical example of the complicated system. Thousands of factors determine the
development of this system, but not all of them are the main ones.

In order to find the main factors,
let us pay attention to the fact how we get the information from the
environment. You read this book, and you see the letters clearly. What brings
the images of the letters and their finest details to your eyes? The photons
bring this information to your eyes. They bring it from the aerials of radio
and TV transmitters to our receivers and TV sets.

Being in constant motion with velocity
of 300,000 km/s, the photons work without rest, they give you not only
information, but heat as well; they regulate all life processes and form the
necessary equilibrium in dead nature.

Science knows that the photons are
electromagnetic radiation. What is the structure of this radiation? The reply
to this question has been got recently, and we’ll follow the way where it has
been found. But now we are interested not in the structure of the photon, but
in its properties as a medium carrier. Photon motion straightness in space is
the main property. With the help of the photons, the astrophysicists get
information from the stars, which are situated at a distance of nearly1.0×10^{10} light years. It is due to the simple and important
property of the photons to move rectilinearly in space.

It is not difficult to imagine what
would happen if light moved curvilinearly in space as the adherents of the
theory of relativity of Einstein said. First of all, a question arises
concerning radius of curvature of any of these curves. It turns out that it is
possible to draw many curves between a remote star and our Mother Earth, and we
shall not know, along what curve the light goes to us if we accept this assumption
originating from a supposition that parallel straight lines cross in infinity.

Only rectilinear movement of light
gives complete definiteness in this case. One should bear in mind that if the
photon moves near a massive body (for
example, a star), attractive force of this body distorts its track.[1]
Thus, when we speak about rectilinear movement of the photon, we suppose that
no external force influences it.

The next step is the formulation of
the axioms for the description of the space where the photons move. It is clear
that straightness of the photon motion should be included at least in one axiom
of geometry, with what help we are going to describe space and movement of bodies
in it. Then this feature will be automatically included into all formulas of
this geometry, and there will be an opportunity to check accuracy of these
formulas with the help of the photons themselves.

When Euclid summed up the results of
his experiments with light and formulated the axioms concerning parallel
straight lines that it is possible to draw only one line between two points, he
did not think that he included the main feature of the photons into these
axioms: to move rectilinearly in space. He could not suppose that trigonometric
functions would take place as well as many theorems of his, Euclidean geometry,
which automatically introduced the main feature of the photon – to move
rectilinearly in space – into all formulas of his geometry due to these axioms.
He could not anticipate that the connection between his axiom on parallel
straight lines would give an opportunity to check the relationship of
mathematical formulas of his geometry with reality.

Thus, the axioms of Euclidean
geometry have proved to be the foundation for all exact sciences. That’s why we
have every reason to believe that they have become the first framework
generalization in exact sciences.

It took the mankind almost two
thousand years to accumulate the results of experiments and observations for
the second fundamental generalization. It was done by Isaac Newton in the 17th
century. He formulated the laws of mechanical movement and interactions of the
bodies. Everything, which is created by the mankind in order to travel
overland, by water, under water, by air and in space, is the result of the
implementation of Newton’s law.

The scientists of that times
invigorated with Newton’s success tried to find mathematical methods of
application of his laws. Exuberant development of mathematics at that time gave
to mankind the exact methods of mathematical analysis: differential and
integral calculations.

The successes of mathematicians were
so authoritative that they tried to check strength of the Euclidean axioms. The
axiom on parallel straight lines suffered most of all. The scientists tried to
dispute this axiom.

The Russian mathematician
Lobachevsky was the first to do it. He made an assumption that the parallel
straight lines cross at infinity. He took this assumption as an axiom and
enunciated a cycle of non-contradicting theorems, which served as a foundation
for his geometry. It is known that almost at that time the same ideas were
expressed in the manuscripts of the great mathematician Gauss, but he hesitated
to publish them. Then geometries of Riemann, Minkovsky and other non-Euclidean
geometries appeared. Now their number exceeds ten.

From the point of view of pure
mathematics it is possible to suppose that parallel straight lines cross at
infinity and to enunciate a cycle of non-contradicting theorems due to this
assumption and to set up a new geometry on their basis. It is a right of
mathematicians, and we cannot deprive them of this right, because abstract assertions
is the basis of their creative thinking, and not all of them think it over how
this abstraction will be used for cognition of the world round us.

The activity of physicists is
something different. Their main task is to explain reality. When they used any
geometry for this explanation by means of substitution of such fundamental
physical parameters as time and velocity of the photons into
its mathematical models, they should think about the consequences, maybe about
a physical right for this or that analytical procedure.

In fact, now we know that the main
property of the photons – to move rectilinearly in space – is established only
in the axioms of Euclidean geometry. We know that due to trigonometric
functions and theorems of Euclidean geometry this property is present in all
mathematical formulas (models) of this geometry. If we check the connection of
these formulas with reality by means of an experiment, the rectilinearly moving
photons will bring the information from the real object to our eye or to the
devices. Now we know that geometry of the spatial tracks, along which the
photons move, is present in mathematical models of Euclidean geometry only. We
check their connection with the reality. That’s why we have the right to put
mathematical sign only in the
mathematical models of Euclidean geometry.

As the photons are the only carriers
of information concerning the environment, the geometry, which can be served by
them, is the only one. This is Euclidean geometry. In order to serve other
geometries, with other axioms, it is necessary to have other information
carriers. The peculiarities of their motion in space, for example,
curvilinearity, should be present in the axioms of these geometries. But such information carriers have not been
found. That’s why we have only one opportunity: to use the geometry, which
axioms contain straightness of photon motion in space.

In vain, M. Kline rebuked the Good
that he did not wish to reveal the geometry, which he used during the creation
of the universe, to mathematicians [6]. Now we know that for cognition of the
universe the God created only one geometry and gave it to us via Euclid. In his
honour, we call this geometry Euclidean geometry now.

**3.
AXIOMATICS OF EXACT SCIENCES**

** **

The Euclidean axioms are known to be
the fundamental axioms of exact sciences [113]. First of all, Euclid gives the
definition to those notions, which he uses during formulations of postulates
and axioms. We’ll not adduce all these definitions, we’ll list a number of
notions, which have been determined by Euclid [113].

The famous definition of “a point”
notion occupies the first place. “A point is that which has no part”. Then the
following definitions of the notions are given: a line, a straight line, a
surface, an angle and the notions of various geometrical figures. After that
Euclid gives postulates, but he has failed to define the notion “postulate”
itself [113].

**Postulates**

Let the following be postulated:

1.
To draw a straight line from any point to any point.

2.
To produce a finite straight line continuously in a straight line.

3.
To describe a circle with any centre and radius.

4.
(Axiom 10) That all right angles equal one another.

5.
(Axiom 11) That, if a straight line falling on two straight lines makes the
interior angles on the same side less than two right angles, the two straight
lines, if produced indefinitely, meet on that side on which are the angles less
that two right angles.”

Then
there is the headline

**(Axioms)**

** **

1.
Things which equal the same thing also equal one another.

2.
If equals are added to equals, then the wholes are equal.

3.
If equals are subtracted from equals, then the remainders are equal.

4.
If equals are added to the unequals, then the wholes are unequal.

5.
The duplicates of one and the same thing equal one another.

6.
The halves of one and the same thing equal one another.

7.
Things which coincide with one another equal one another.

8.
The whole is greater than the part.

9.
Two straight lines do not contain space.

It is unbelievable, but it is so.
This information serves as a foundation for all exact sciences. Let us pay
attention to the fourth postulate. In the parenthesis, it is given as the tenth
axiom, and the fifth postulate – as the eleventh axiom. We do not know why the
fourth and the fifth postulated statements are considered to be axioms. Or one
should suppose that they can be simultaneously considered as the postulates and
the axioms. If Euclid managed to define the notions “a postulate” and “an axiom”, the fourth and the fifth postulates could
be in the list of axioms.

The disputes of the scientists in
relation to correctness of wording of the fifth postulate of Euclid are known
[6]. They have taken place due to the lack of definitions of the notions “a
postulate” and “an axiom”. Further definitions of these notions have not
acquired significance in consciousness of the scientists, which could be given
to them if they were in “Euclid’s Elements”. Nevertheless, we should treat this
drawback as a natural one without infringement of genius of Euclid [18], [70].

Nearly two thousand years after
Euclid, “Mathematical Principles of Natural Philosophy” by Isaac Newton
appeared. As Euclid, he paid great attention to the definition of the new
notions, on which his laws are based. His mathematical principles begin from
the headline [114].

**DEFINITIONS**

** **

The quantity of matter (mass) is its
measure of the same, arising from its density and bulk conjunctly”.

Then
Newton determines the notions “the quantity of motion”, “an innate force”, “an
impressed force”, “a centripetal force”, etc.

After it Newton describes his notion
of absolute space and absolute time without application of axiomatic meaning to
these notions. His main ideas are given under the headline [114]

**Axioms, or laws of motion**

**Law
1**

Every body continues in its state of
rest, or of uniform motion in a straight line, unless it is compelled to change
this state by forces impressed upon it.

**Law
2**

The change of motion is proportional
to the motive force impressed; and is made in the direction of the straight
line in which that force is impressed.

To every action there is always
opposed and equal action; or, the mutual actions of two bodies upon each other
are always equal, and directed to contrary parts”.

Then Isaac Newton formulates the
effects originating from these laws.

The above-mentioned laws deal with mechanical motion of the
bodies. Their trustworthiness has been confirmed by experiments completely.
After these laws, many other laws have been discovered, which describe electrical,
magnetic, electromagnetic and other properties of bodies, gases, liquids and
various physical phenomena. We’ll not enumerate and analyse them. The main
thing for us is that their trustworthiness has been confirmed by experiments.

When we analyse the postulates of
Euclid and the axioms or laws of Newton, we see that they were the first to
attach importance to the necessity to determine the notions, which they used.
It was done for the purpose to get uniformity in understanding the essence of
these notions, because no mutual understanding was possible without it.

Then one should pay attention to the
fact that the fundamental notions, which serve as the basis for the rest
proofs. Euclid divided into two classes: the postulates and the axioms. Form
his “Elements” it is difficult to see, what principles he was guided by when he
attributes some statements to the class of postulated and other statements to
the class of axioms. Newton did not give any definition in this respect as
well. He called his laws axioms.

The followers of Euclid and Newton
attached no importance to this issue as well, that’s why the process of
attributing the fundamental scientific statements to the class of axioms or to
the class of postulates has become a chaotic one. Each scientist had no exact
criterion concerning evaluation of the essence of his fundamental scientific
statements and attributed them either to the class of postulates or the class
of axioms. There was no exact notion of the fact that in order to strengthen
significance of various axioms in scientific research it is necessary to
arrange them according to the level of community and importance. There is an
impression that we have understood this necessity only when the features of
crisis of theoretical physics have been exposed. We cannot overcome it if we
fail to put in order the fundamental scientific notions, which we use.

The task, which should be solved, is
not a simple one. First of all, it is necessary to find its beginning. Without
it we’ll fail to systematize our fundamental scientific statements and
establish their completeness. We see that it is necessary to begin with the
analysis of the essence of the main properties of the notions, which we use
now. This area of investigations belongs to the theory of knowledge. We should
begin from it [35].

**3.2. Definition of Notions, which Characterize
the Primary Elements of the Universe**

** **

Probably, the process of knowledge has
begun when separate sounds uttered by human beings have started to form the
words, which have led to the formation of images, which correspond to sense
content of these words. The range of the things and the phenomena formulated as
words have widened. Now a man uses so many words, which have various meanings,
that uniform understanding of the essence of this content has become one of the
most complicated problems of communication between people, including between
scientists [8], [26].

Any notion is formed by our brain, that’s why the cognition theory is
closely connected with the process of our thinking. The process of the
connection of notions into the logical structures, which form our notions on a
cognizable object, serves as a foundation of thinking. It means that exactness
of our knowledge depends on exactness of the notions being used and
completeness of reflection of cognizable essence with the help of these
notions.

Exactness of the notions used by us is determined by their notional
capacity. The less the notional capacity of a notion, the better it reflects
the essence, which this notion has, and the deader it is understood by whose,
who use this notion. For example, the notion “point” is one of the notions with
small capacity, that’s why it bring about approximately the same notions with
almost everybody who uses this notion and does not cause discords in
understanding the essence of this notion.

Let us compare the notion “point”, which has small capacity, with the
vast capacious notion “cognition”. It is clear that it inevitably forms diverse
meaningful essence with various people and various meaningful capacity of the
cognition process. For example, there exists the cognition of meaning of life,
the cognition of happiness, the micro world, the Universe, the cognition of
rules of arithmetic, the cognition of the taste of food by a human being or an
animal, etc.

It is impossible to give such definition to the notion “cognition” which
could reflect all possible or conceivable variants of this process. It means
that this notion forms personal apprehensions concerning the very core of the
cognition process with a person who uses them. Thus, every man understands the
concept capacity of each notion in his own way. Taking this capacity into
consideration he judges on authenticity of this or that assertion. Diverse
concept capacity of one and the same notions with different people is the main
obstacle on the way of exact transmission and exact reception of information.
It appears from this that complexity of cognition is increased with the increase
of the concept capacity of the notions being used, because the difficulties
with its definition are increased with the increase of the concept capacity.
For example, let us take the notion “happiness” and try to define it. We see at
once that it is impossible to do it, because it is closely connected with the
feeling perception of the outward things of a human being. A person who has
lost a precious thing feels unhappy. A person who has found this thing feels
happy.

Mathematics is the most exact science. It is no wonder, because it uses
the notions of the smallest capacities, which can be defined more or less
exactly. For example, the notions unit, zero, two, three, point, line, plane,
angle, triangle, etc. cant be defined easily, and it is easy to connect them
with the numbers, which are automatically included in mathematical dependencies
describing various characteristics of the essence of these notions.

We’ll
not go into details in this analysis, but we should note an importance of sense
capacity for their uniform understanding, without which science cannot exist.
Now we understand why Euclid and Newton, geniuses of the mankind, have begun
from the definition of the notions being the basis for their proofs.

It is natural that not all
scientific notions have similar generalized sense and, as a result, similar
significance for scientific knowledge. It means that it is important to arrange
the fundamental scientific notions according to the level of generalized sense
and scientific importance.

What notions do we use when we
cognize the world around us? The answer is simple: we use the notions, which
determine the fundamental or primary elements of the universe. Can the world
exist outside the space? Certainly, not. That’s why “space” notion is
attributed to the primary element of the universe, without which existence is
impossible. Thus, “space” notion occupies the first place due to the level of
significance for scientific cognition of the world.

If we put “space” notion on the
first place due to the level of significance for scientific cognition of the
world, we should define it. But it is simple to do it, because “space” notion
belongs to the notions with large sense capacity. Nevertheless, the majority of
people have formed the like or similar notions concerning the essence or the
sense content of this notion. We’ll take advantage of it. For us, the
definition of “space” notion is of less importance than the fact that it is the
receptacle of all main points, that’s why we put it on the first place due to
its significance for the scientific cognition.

Now it is necessary to define the
main features of space, on which precision of our knowledge depends concerning
everything that exists in this space. The first and foremost feature of space
is its **absoluteness**. What is it? How can absoluteness be determined?
Modern level of knowledge allows us to consider space as absolute one, because
there are no phenomena in Nature, which could influence space: compress, expand
or distort it [101].

The statement concerning relativity
of space, on which theoretical physics of the 20th century was based, has no
uniform experimental proof, that’s why we do not take it into consideration
[1], [162].

What
scientific notion is the second due to significance? Matter. Without it, space
would be empty. Now we understand that extremely large sense capacity of this
notion excludes the possibility of its simple definition. Essence, which is
reflected by this notion, has such large quantity of various features that we
cannot find the sign of this essence, which could give us the reason to
consider matter as an absolute one. We can be guided by more or less similar
comprehension of the essence of “matter” notion by the scientists, and it is
enough for us at the given stage of scientific knowledge development [101].

“Time” notion is the next one due to
importance for scientific cognition of the world round us. Essence, which is
present in this notion, has manifested when matter has taken place in space.
There was no time in empty space. The experience accumulated by mankind in the
process of understanding the essence of “time” notion shows importance of its
main feature: irreversibility. It goes only in one direction. Contact rate of
its course is another important feature of time. That’s why we have every
reason to believe that **time is absolute**, and we can define this feature
in the following way. Time is absolute, because there are no phenomena in
Nature, which could influence the rate of its course: increase or decrease this
rate [101].

The statement concerning relativity of
time, on which theoretical physics of the 20th century was based, has no direct
experimental proof of its trustworthiness. The change of the rate of the course
of time registered with the help of various devices reflects the features of
the devices themselves, but not the fact of the change of the rate of the
course of time. That’s why we think that this delusion will disappear from the
field of the actual activities of the scientists and become history.

Thus, we have determined three
primary elements of the universe, on which it has been based since the day of
its creation if the one existed.

Now we should pay attention to the
thing, which has remained unnoticed by Euclid, Newton and their followers and
which plays such important role in cognition of the world by us as the notions
“space”, “matter” and “time”. How are the essences, which are reflected in these
notions, connected with each other?

First of all, matter cannot exist
outside space. Time passes only in space, which contains matter. All three
primary elements of the universe are inseparable. As this important property
remained unnoticed, the theories took place, in which a spatial value of a
moving object seems to be independent of time. It has turned out that time can
be separated from space as it is done in Lorentz transformations, and
regularity of the passing of time can be analysed separately [152].

As space cannot be separated from time
and it is impossible to imagine existence of matter outside space,
inseparability of these three primary elements of the universe is an axiom.
This is the third important axiom of exact sciences.

Now, when we address to Euclid’s
postulates and axioms, we feel that it is necessary to determine these notions.

**An axiom is an obvious statement,
which requires no experimental check and has no exceptions [101].**

** A postulate is a non-obvious
statement, its reliability being proved in the way of experiment and results
from the experiments [101].**

Certainly, one can challenge the
accuracy of these statements. But these statements are enough in order to
divide all fundamental statements of exact sciences into two classes: the
axioms and the postulates.

Taking into consideration these
definitions of the notions “a postulate” and “an axiom”, Euclid’s postulates
and axioms can be considered as axioms with some correction of their content.
Newton’s axioms or laws become postulates automatically, because the essence
reflected in them is not obvious, and reliability of his statements requires
experimental check.

As we have decided to systematize
the axioms of exact sciences, and to be more precise of knowledge of nature,
and to arrange them according to the level of significance and general sense,
let us give an updated list of the axioms of Natural science.

**3.3. Axioms of Natural Science**

** **

**1-
space is absolute;**

**2 -
time is absolute;**

**3 -
space, matter and time are inseparable;**

**4 -
it is possible to draw only one straight line between two points;**

**5 -
it is possible to produce a finite straight line in both directions;**

**6 -
it is possible to describe a circle with any centre and radius;**

**7 -
all right angles equal one another;**

**8 -
if a straight line falling on two straight lines makes the sum of the interior
angles on the same side equal two straight angles, the two straight lines, if
produced indefinitely, will never meet;**

**9 -
things which equal the same thing also equal one another;**

**10 -
if equals are added to equals, then the wholes are equal;**

**11-
if equals are subtracted from equals, then the remainders are equal;**

**12 -
if equals are added to the unequals, then the wholes are unequal;**

**13 -
the duplicates of one and the same thing equal one another;**

**14
- the halves of one and the same thing
equal one another;**

**15 -
things which coincide with one another equal one another;**

**16 -
the whole is greater than the part.**

** **

As it can be seen, we have added three
new axioms to Euclid’s axioms, but as far as the level of general sense and
significance for natural science is concerned, they are on the first place. We
think that mathematicians should extend a list of axioms [128].

**3.4. Postulates of Natural Science**

** **

We
put Newton postulate on the first place:

**1 -
Law 1. Every body continues in its state of rest, or of uniform motion in a
straight line, unless it is compelled to change this state by forces impressed
upon it. **

**2 -
Law 2. The change of motion is proportional to the motive force impressed; and
is made in the direction of the straight line in which that force is impressed.**

**3 -
Law 3. To every action there is always opposed and equal action; or, the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.**

**4 -
When several forces act simultaneously, a material point or a body gets
acceleration equal to geometrical sum of the accelerations caused by the
influence of each of these forces separately.**

**5 -
Law of gravitation. ****Every object in the Universe attracts every other object with a force
directed along the line of centers for the two objects that is proportional to
the product of their masses and inversely proportional to the square of the
separation between the two objects. **

Let us give the formulation of the
second postulate of A. Einstein, on which theoretical physics of the 20th
century was based. “2. **Any ray of light moves in the stationary system of
co-ordinates with the determined velocity, whether the ray be emitted by a
stationary or a moving body.”**

Modern level of knowledge allows us
to give more exact formulation of this postulate.

**6 -
Velocity of electromagnetic radiation (photons) in the stationary system of
co-ordinates in relation to space is constant and does not depend on the
direction of the source, which emits the photons [8].**

We give the opportunity for
other investigators to continue the list of the postulates. It will be much
longer than the list of the axioms. One should think that mathematicians agree
with the necessity to transfer many statements, which they considered to be
axiomatic ones and which do not correspond to the notion “axiom” now, to the
class of postulates [128].

**3.5.
Discussion of Results**

** **

Thus, we have a list of axioms, which
are necessary for us in order to check the connection of the existing physical
theories with reality. If it turns out that a theory contradicts one of the
axioms of natural science, it is erroneous.

The main
role of axioms is to be a foundation of the new theories. The foundation of any
future theory, which will be built on the grounds of the above mentioned
axioms, will have everlasting strength.

In
our publications we have already shown how the axioms should be used for the
analysis of the connection of the existing theories with reality and for elaboration of the new ones [18], [68],
[69], [99], [101], [109].

Now the statement that the parallel
lines cross in infinity is not an axiom, it is a postulate and requires
experimental proof of reliability of this statement.

Thus, the first three given
fundamental axioms of natural science act as independent criteria for a check
of reliability of mathematical models of various physical theories. I’d like to
inform those, who agree with obvious trustworthiness of three given fundamental
axioms of natural science, that they are realized only in Euclidean geometry.
It results from this that there is a connection of mathematical models of this
geometry with reality.

It is necessary to emphasize a role
of the axiom of space-matter-time unity in mathematical description of the
motion process of any object in space. This axiom established strict correspondence
between motion of any object in space and the passing of time during this
motion. Mathematically, it is expressed by dependence of object position
coordinates in space on time.

It is impossible to separate matter
from space. It is impossible to imagine the passing of time outside space. Space, matter and time are primary elements
of the universe, they are inseparable
on no account. I think that trustworthiness of the statement concerning unity
of space, matter and time is obvious. It has no exceptions and contains all properties of an axiom. If
we acknowledge this fact, the axiom of space-matter-time unity become an
independent judge of reliability of mathematical models, which describe motion
of material objects in space, and the theories, to which these models belong.

Mathematical models of motion of
material objects in space built in pseudo-Euclidean geometries conflict with
the space-matter-time unity axiom. Four-dimensional Minkovky’s geometry will be
the first to be rejected as well as his idea of unity of space and time,
because the mathematical model of four-dimensional geometry postulated by him,
in which his idea is realized, contradicts the axiom of space-matter-time unity
[109], [119].

I’d like to emphasize the fact
that scientists of exact sciences are eager to call their scientific statements
axioms, especially mathematicians. An axiom is an obvious statement, which
requires no experimental check and has no exceptions. The rest are postulates.
If a theory contradicts one of the
axioms of natural science or mutually accepted scientific postulate , it is
erroneous.

It is clear that the process of
realization of the idea of observation of the given axioms of natural science
will be quicker and more fruitful if the world scientific community understands
that it is necessary to confer a status of obligation to the list of axioms.

Updated and systematized axiomatics of
natural science consists of sixteen axioms for the present. As far as the level
of general sense and significance for knowledge of nature is concerned, the
axiom **space is absolute** occupies the first place, the axiom **time is
absolute** occupies the second place, and the axiom **space, matter and time
are inseparable** occupies the third place. Value of an axiom does not depend
on its acknowledgement.

In scientific investigations, an
important role is played by the postulates - the statements, their reliability
being not obvious, but proved experimentally. The value of a postulate is
determined by the level of its reliability acknowledgement by the scientific
community.

**The
Foundations of Physchemistry of Microworld**

**Copyright ****Ó****2003 Kanarev Ph.
M.**** **

Internet Version - http://book.physchemistry.innoplaza.net

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