It is shown that Ohm’s law is not only the main electrical engineering law, but also a generally scientific worldview law of the extreme significance, as in the interpretation of Steinmetz it proves physical reality of imaginary numbers theoretically and experimentally in the most indisputable way. Thus, it refutes the principle of light speed non-exceedance, which is fundamental in the special theory of relativity. Moreover, unlike the MINOS and OPERA experiments recognized by physical com-munity as not enough reliable, which were conducted for the same purpose, alternative experiments were performed during the research of oscillation processes in linear electric circuits. Therefore, they are absolutely reliable and conclusive as can be repeated and verified in any electrical engineering laboratory. The principle of phy-sical reality of imaginary numbers proven by the electrical engineering experiments is generally scientific, since mathematics is the universal language of the exact sciences. Therefore, all scientific theories and hypotheses in quantum mechanics, relativity theory, geo-physics, cosmology, optics, radio electronics and other sciences should be adjusted accordingly, given the principle of physical reality of imaginary numbers. There is an example of how this can be done in the special theory of relativity and astrophysics. This approach allowed explanation of dark matter and dark energy, which correspond to the invisible parallel universes existing in extra dimensions.
In 1826, after nine years of experimental research, the great German physicist Georg Simon Ohm (1787-1854) published his article [
However, Ohm’s contemporaries were more than cool to his discoveries, because at that time it was commonly supposed that the truth in science should be learned theoretically, whereas experience could not (and even should not!) be taken into account. And according to Ohm’s critics (including top-ranking) his works smelled rather of sweat than of “supreme harmony”. In this regard, the famous Russian physicist Alexander Grigorevich Stoletov (1839-1896) wrote: “…physics especially tempted natural philosophers. What a favorable theme were electrical phenomena for the most riotous imaginations… Attractive and vague deductions were in the foreground: hard work of experimenter and exact mathematical analysis were not honored; they seemed superfluous and harmful in the study of nature…”.
In 1828, Ohm was even fired where he worked by personal order of Minister of Education for publishing his physical discoveries. A senior official believed that the use of mathematics in physics was unacceptable. Only after French physicist Claude Servais Mathias Pouillet (1791-1868) obtained the same experimental results in 1831-1837, Ohm’s law was recognized by scientific community.
In 1897, the eminent American engineer and inventor Charles Proteus Steinmetz (1865-1923) suggested his own interpretation of Ohm’s law [
Currently, Ohm’s law is studied in the school course of physics, and therefore it is known to all educated people. However, its great significance to all exact sciences has not been still realized. Even in physics.
This feature of Ohm’s law is covered in the article.
The main advantage of Ohm’s law in the interpretation of Steinmetz turned out to be the fact that in addition to capability to calculate electric circuits, it allows convincing and indisputable proof of physical reality of imaginary numbers, which have been fiscovered over five hundred years ago by Scipione del Ferro (1465-1525), Niccolò Fontana Tartaglia (1499-1557), Gerolamo Cardano (1501-1576), Lodovico Ferrari (1522-1565) and Rafael Bombelli (1526-1572) [
Mathematics and other exact sciences have always developed simultaneously, including in the process of emergence of new types of numbers and better understanding of their sense. Thus, integers appeared first. Then, there were fractions, positive and negative numbers, etc. But when the process concerned the imaginary, complex and hypercomplex numbers, they ceased being understood. Works of AbrahamdeMoivre (1667-1754), Leonhard Euler (1707-1783), Jean Le Rond D’Alembert (1717-1783), Caspar Wessel (1745-1818), Pierre-Simonde Laplace (1749-1827), Jean-Robert Argand (1768-1822), Johann Carl Friedrich Gauss (1777-1856), Augustin Louis Cauchy (1789- 1857), William Rowan Hamilton (1805-1865), Pierre Alphonse Laurent (1813-1854), Karl Theodor Wilhelm Weierstrass (1815-1897), Georg Friedrich Bernhard Riemann (1826-1866), Oliver Heaviside (1850-1925), Jan Mikusi?ski (1913-1987) and of many other outstanding mathematicians contributed to the development of a perfect complex variable theory [
Therefore, due to inability to explain imaginary values of mass, time and other physical quantities appearing in relativistic formulas at superluminal speeds within the special theory of relativity (STR) [
The principle seemed to be substantiated quite conclusively. Since the value of relativistic mass
where
Mass
However, such substantiation is refuted even by simple household arguments. Indeed, inability to overcome a barrier dividing two adjacent rooms in our house, which is a wall in this case, does not mean that the next room does not exist or that there is no possibility to get into it through the door. The universe, which is arranged much more complicated than our house, can actually have its possibilities to overcome the light speed barrier. And it really does, as shown below.
Therefore, such a simple solution of a complex physical-mathematical problem offered by the authors of the STR did not seem convincing to everyone. At the beginning of the twenty-first century very complex MINOS [
However, as according to the author of the “open society” concept Karl Raimund Popper [
Since mathematics is the common language of all exact sciences, the principle of physical reality of imaginary numbers proved by electrical engineering experiments is valid for all other exact sciences. Consequently, all the theories and hypotheses of quantum mechanics, relativity theory, optics, radio electronics, geophysics and other sciences should be adjusted accordingly.
Whereas dozens of scientific publications were devoted to searching for ways of refutation of the OPERA experiment (between the dates of publication of OPERA and ICARUS experimental results) in a half-year period, alternative electrical engineering experiments have not been commented in at least one article over the past few years. Some of the publications criticizing the OPERA experiment even claimed that the principle of light speed non-exceedance in the STR was so important that if the OPERA experiment refuted it, its authors would have deserved the Nobel Prize for such a scientific achievement. However, the principle turned out to be refuted and the authors of the publications immediately lost interest in this issue.
Therefore, one cannot but suppose that the refuters of the MINOS and OPERA experiments needed confirmation of the alleged irrefutability of the principle of light speed non-exceedance and thus preservation of the belief in accuracy of the existing STR version rather than scientific truth. However, unlike the results of the MINOS and OPERA experiments, the results of the alternative electrical engineering experiments turned out to be quite reliable and irrefutable. Consequently, they did refute the existing version of the SRT.
The most interesting thing is that the current version of the STR has been actually refuted by Charles Proteus Steinmetz by Albert Einstein’s famous publication [
Indeed, according to the Steinmetz’s interpretation of the Ohm’s law not only resistors, but also inductors and capacitors have electric impedance. Besides, impedance of capacitors and inductors is measured by imaginary numbers, the value of which depends on the frequency of sinusoidal voltage applied to the electric LCR-, LC-, RC- and RL-circuits. However, under the dominant influence of STR, denying physical reality of imaginary numbers, imaginary impedance of capacitors and inductors is actually believed to be imaginary, i.e., physically non-existent.
The fallacy of this opinion is easily verified experimentally by changing the frequency of sinusoidal voltage applied to any electric LCR-, LC-, RC- or RL-circuit and measuring the value of electric current flowing through the circuit. All engineers have known for over a century that the electric current is changed in such experiments. This is possible only if frequency-dependent impedance of capacitors and inductors really exists. Moreover, instruments for measuring frequency characteristics of electric circuits confirming such changes have been created many decades ago and still widely used in engineering practice. Consequently, imaginary electric impedance of capacitors and inductors is physically existent [
Finally, physical reality of impedance of capacitors and inductors is also confirmed by the existence of resonance phenomenon [
All this indisputably confirms physical reality of imaginary numbers. As well as existence of the relevant instruments and measurements made using them confirms the existence of ultra- and infrasound, ultraviolet and infrared radiation, magnetic and gravitational fields, X-rays and radioactivity, and almost everything else that we know about the world around us.
In the early twentieth century, authors of the STR did not know that. However, supporters of the existing version of the STR keep not knowing that even now, as they are convinced of the validity of the principle of light speed non-exceedance.
For a complete understanding of the physical essence of imaginary numbers
However, what, for example, does 10i gr or 20i sec mean? This question is more difficult, but we try to give an answer.
For this purpose let’s use the formula (1). It follows from the formula that relativistic mass of the moving body takes real values for
However, if the imaginary physical quantities are real, and physical bodies to which they belong exist in the universe other than ours (as in our universe the situation
Consequently, contrary to the statement of the STR about existence of monoverse, we still live in a Multiverse. It is invisible, so let it be referred to as the hidden Multiverse [
The answer to the question risen above is that the 10i gr and 20i sec in our tardyon universe are 10 gr and 20 sec in the tachyon universe. It follows that the values of physical entities in the adjacent parallel universe correspond to imaginary numbers in astrophysics.
Tardyon and tachyon universes of the hidden Multiverse should be indistinguishable in their manifestations for their inhabitants, i.e., according to the first postulate of the STR tachyon universe has the same physical, chemical, biological and other laws as in our universe, as well as it has its own life and its own intelligent inhabitants. However, relativistic formulas, including the formula (1), do not meet this condition. Therefore, the formula (1) shall be amended as follows:
where
Other relativistic formulas can be adjusted in a similar manner.
It follows from the formula (2) that tardyon universe corresponds to the value
Thus, tardyon antiverse would correspond to the value
That is, the Multiverse has a structure of either a closed (as in
screw collar. Stephen William Hawking apparently meant that when said: “Imaginary time is a new dimension, at right-angles to ordinary, real time”.
The value
Besides, parallel universes are continuously drifting in this four-dimensional space and occasionally or permanently touch each other (for example, as people in a crowd) or even slightly penetrate into each other in some spots (which are quite numerous, including those on Earth). Transition zones which in literature are also referred to as portals or star gates emerge in the places of such local interpenetrations of universes. Micro objects ranging from elementary particles to living inhabitants and their vehicles can transit from one parallel universe to another. Exception is stars and galaxies, since parallel universes could lose their stability. Portals on the Earth are so-called anomalous zones [
However, in addition to the observed and, therefore, most understandable research objects (planets, stars, galaxies, etc.) in astrophysics, there are less understandable objects (such as black holes), and even completely obscure objects of research (dark matter and dark energy). Dark matter and dark energy [
Taking into account all these features of dark matter and dark energy the problem of their explanation, to which no one could even come close in the last decade, becomes ideologically important not only for astrophysics but also for science as such. Stephen William Hawking wrote: “The missing link in cosmology is the nature of dark matter and dark energy”.
However, the problem of explaining the phenomenon of dark matter and dark energy turned out to be inexplicable, because under the dominant influence of the STR the statement of explanation task was formulated incorrectly. Its explanation has been required to be found exactly within the monoverse hypothesis corresponding to the current version of the STR, which, as shown above, is wrong. Therefore, it hasn’t been and it wouldn’t be found under such conditions. Albert Einstein stated in this regard: “Insanity: doing the same thing over and over again and expecting different results”.
If statement of the problem is changed and explanation of the phenomenon of dark matter and dark energy is found within the Multiverse hypothesis, it would become apparent [
・ Invisible dark matter and dark energy are invisible parallel universes of the hidden Multiverse other thanours;
・ Dark matter is parallel universes of the hidden Multiverse adjacent to our universe.
・ Dark energy is parallel universes of the hidden Multiverse other than our and adjacent universes;
・ Chemical composition of parallel universes of the hidden Multiverse, except ours, cannot be determined because their content is not available for analysis by our earthly tools.
Explanations provided seem quite unusual. But Sir Isaac Newton believed: “No great discovery was ever made without a bold guess”.
Data obtained from the WMAP [
According to the data, the total mass-energy of the whole hidden Multiverse consists of 4.9% baryonic matter (earlier WMAP estimate-4.6%), 26.8% dark matter (according to WMAP-22.4%) and 68.3% dark energy (according to WMAP-73%). Therefore, believing that mass-energy of all parallel universes is equal (as a result of its averaging through portals), it can be concluded that:
・ Mass-energy of our tardyon universe is 4.9% of the mass-energy of the hidden Multiverse according to Planck data;
・ The hidden Multiverse consists of
・ Dark matter consists of
・ Dark energy consists of
Thus, according to the data obtained from WMAP and Plank spacecrafts the hidden Multiverse contains twenty to twenty-two parallel universes, one of which is our universe, five or six parallel universes are its neighbors, and the other parallel universes are still further from us.
However… the results are inconsistent with the structure of the hidden Multiverse shown in
Formula (3) includes similar designations as in the formula (2).
Therefore, the hidden Multiverse has the structure [
However, this structure also does not correspond to the parameters of the hidden Multiverse, calculated according to the WMAP and Planck data, as it contains twenty-four parallel universes rather than twenty or twenty-two. It actually could be turned into the structure corresponding to the WMAP and Planck data by excluding two or four universes from it. In this case it would have edges, and the most important of all it raises the question of what is hidden behind the edges of the Multiverse. There are no experimental data that would suggest the answer. Therefore, we can only assume. For example, assume that our hidden Multiverse is connected with other Multiverses which are unobservable not only by electromagnetic but also by gravitational manifestations. One of the probable structures of the hidden Multiverse is shown in
Let even more complex formations with a large number of the Multiverses including those with different structures (e.g., structure corresponding to the above-considered principle of physical reality of complex numbers) to be called a Hyperverse.
The above description of the structure of the hidden Multiverse raises a natural question whether this structure is verifiable. A large number of interesting Multiverse hypotheses, some of which are considered in [
The hypothesis of the hidden Multiverse is verifiable and therefore has every reason to be called a theory. Indeed, the theory of the hidden Multiverse:
・ is confirmed experimentally by existence of dark matter and dark energy, which are
just other names of invisible parallel universes of the hidden Multiverse, except our visible universe;
・ is confirmed by those experiments at the Large Hadron Collider and other accelerators, which have resulted, explained by the formation of tachyons and their transition into tachyon universes and antiverses;
・ can be confirmed by geophysical research of anomalous zones, proving that they are portals to adjacent parallel universes.
Thus, Ohm’s law in the interpretation of Steinmetz has allowed simple and convincing
proving of physical reality of imaginary numbers, discovered five hundred years ago, in the process of study of oscillatory processes in linear electric circuits. This result, in contrast to the failed MINOS and OPERA physical experiments, can be repeated and verified in every electrical and electronic laboratory. Therefore, it is absolutely true and conclusive.
Since mathematics is the universal language of all exact sciences, the principle of physical reality of imaginary numbers is generally scientific. And all the theories and hypotheses in quantum mechanics, relativity theory, optics, geophysics, electronics and other sciences should be adjusted in accordance with this principle.
Particularly in the STR this principle allowed identifying and correcting a number of fundamental errors that Albert Einstein had foreseen: “No single idea, which I would be sure that it will stand the test of time”.
The adjusted version of the STR has, in turn, led to creation of the verifiable hypothesis of the hidden Multiverse, which is, therefore, has every reason to be called a theory, unlike other Multiverse hypotheses. Due to the WMAP and Planck data the theory allowed identifying the quaternion structure of the hidden Multiverse containing twenty to twenty-two parallel universes in the six-dimensional space. The theory has explained the phenomenon of dark matter and dark energy, which is just another name of invisible parallel universes of the hidden Multiverse, except ours. It also has explained what and where antimatter is, why it does not annihilate with matter and where tachyons can be found.
Consequently, Ohm’s law in the interpretation of Steinmetz hasmade it possible to take the next step in the ideological revolution after the establishment of the Copernican heliocentric system, as it states that our universe is not the only one and is not the center of the hidden Multiverse. Moreover, our hidden Multiverse is as well not the only one, and it is not the center of the Hyperverse.
The author is grateful for participation in the discussion of the paper to my wife Dr. Olga Ilyinichna Antonova, whose criticism and valuable comments contributed to improvement of the article.
Antonov, A.A. (2016) Ohm’s Law Refutes Current Version of the Special Theory of Relativity. Journal of Modern Physics, 7, 2299-2313. http://dx.doi.org/10.4236/jmp.2016.716198