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        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 It has required adjustment of some provisions and the change of some outdated notions.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.






         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 nearly1.0×1010 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.






3.1. Brief Analysis of the State of the Problem


        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].





        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




Common Notions



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].






Definition 1


        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.


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”.


        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.

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The Foundations of Physchemistry of Microworld

Copyright Ó2003 Kanarev Ph. M.

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[1] Later on we’ll give the calculation of this distortion