Q and 2m0 + v = 0 , we obtain a system of equations for waves of arbitrary polarization in a dimensionless form:

p-l = B-0Pty2Coscp

dr

= -1-

1(2

dr 2a0 , P\ yœ

P* 2y2

pwpi

PI'P±-L-L

u*

£1 = £xCoS& = £ySin&

® = tyres ~tyV\\ =

-t = œt a = —

m0vc œ

(11) (12) ) Cos(p (13)

dJyT = Ê°p±.Cos(p(PPyi+(V, + V\\)tg(p) (14)

Ve1£±

This resonance is a consequence of relativism and is possible only in the presence of a strong electrostatic field.

REFERENCES:

1. V.P. Milantiev TECHNICAL PHYSICS LETTERS - 1994 64 p. 166

2. S.P. Karnilovich, V.P. Milantiev Journal of Experimental and Theoretical Physics - 1989; P. 95

THE PHYSICS OF IMAGINARY NUMBERS IS THE NEW PHYSICS, IT IS PHYSICS OF AN INVISIBLE, BUT REALLY EXISTING WORLD

Antonov A.

Ph.D, HonDSc, HonDL, H.ProfSci, ResProf, Independent Researcher, Kiev, Ukraine

Abstract

It is quite clear that the discovery of invisible universes is an outstanding and far more significant event than even the discovery of America by Columbus. However, their discovery is hampered not only by the objective difficulties of knowledge nature, but also by the principle of non-exceeding the speed of light of the special theory of relativity (STR), from which the existence of only our visible universe follows. But in the XXI century, experimental knowledge was obtained, from which it followed that the relativistic formulas of the existing version of STR are incorrect and incorrectly explained. In other words, the version of STR created in the 20th century turned out to be not entirely correct. Therefore, an alternative version of S STR RT was created, which made it possible to prove the existence, in addition to our visible universe, of other mutually invisible universes. It is explained how these invisible universes can be seen. But invisible universes are not the only invisible objects that actually exist in nature, which are described by imaginary numbers. Other real-life invisible physical objects correspond to other imaginary numbers. Therefore, the physics of imaginary numbers is the physics of the still largely unknown invisible world. STR

Keywords: imaginary numbers; special theory of relativity; dark matter; dark energy; dark space; Multiverse; Hyperverse, invisible universes.

1. Introduction

What could be the physical sense of imaginary numbers? It has remained completely incomprehensible until very recently, unlike the sense of other numbers, such as integer and fractional, positive and negative, rational and irrational, etc, which became clear immediately after their discovery. Even today no one can

explain what is, for example, 51 kilograms, 71 seconds

or 21 meters, where i = is the imaginary unit, although imaginary numbers were discovered by Scipione del Ferro, Niccoló Fontana Tartaglia, Gerolamo Car-dano, Lodovico Ferrari and Rafael Bombelli [1] about five hundred years ago. And perhaps even earlier this scientific discovery was made by Paolo Valmes [2], who was sentenced to death at the stake by Spanish inquisitor Tomás de Torquemada for this discovery. Therefore, even Sir Isaac Newton had to regard the opinion of the Inquisition about imaginary numbers and preferred not to use1 them in his writings.

Moreover, physical sense of imaginary numbers has remained so incomprehensible until very recently as to prevent creation of the special theory of relativity (STR) in the 20th century, although it is generally believed to have been already created. And it is even presented in all university and school physics textbooks. But this generally acknowledged version of STR is not entirely correct2, since the relativistic formulas obtained in it are incorrect, they are incorrectly explained using the incorrect principle of light speed non-exceed-ance, and also from them incorrect conclusions are made about the physical unreality of imaginary numbers and the existence in nature only of our visible Universe.

Imaginary numbers are actually shown below to be physically real. And while the physics of real numbers corresponds to the world we see, the physics of imaginary numbers corresponds to the invisible (moreover, also not otherwise tangible) and therefore largely unexplored world.

1 In the atmosphere of Inquisition's omnipotence and intolerance of unorthodoxy prevailed at that time, Newton's friend William Whiston was deprived of his professorship and expelled from Cambridge University in 1710 for some of his imprudent remarks

2 Unfinished work, much less work done incorrectly is work the result of which cannot be used. After all, no one will go to work in a suit to which buttons are not sewn and does not drink coffee, in which salt was put instead of sugar.

2. The existing version of the STR is incorrect

What another conclusion could be drawn about the situation existing in physics, if the main result of the STR, its relativistic formulas, is incorrect?

Indeed, these relativistic formulas, for example:

mn

m

(1)

where mo is the rest mass of a physical body;

m is the relativistic mass of a moving physical body;

v is the velocity of a moving physical body;

c is the speed of light;

it follows that the relativistic mass m and other relativistic physical quantities are measured with real numbers when 0 < V < C, and with imaginary numbers when C < V < K. But how such a result shall be understood?

The authors of the STR did not know the answer to this question. Therefore, in order to avoid the necessity to admit this, the principle of light speed non-ex-ceedance implying the physical unreality of imaginary numbers was groundlessly introduced into the STR. In other words, this principle was postulated. And thus, it would seem that the case for might not be considered.

However, this postulate turned out to have a hard luck, since it was refuted by Nobel Prize received by Pavel Alekseyevich Cherenkov, Igor Evgenyevich Tamm and Ilya Mikhailovich Frank 1958 for discovering and explaining Cherenkov radiation [3], emitted when charged particles move through a transparent medium at a speed greater than the speed of light in that medium. Later the situation was saved by making a clarification that the principle of light speed non-ex-ceedance had implied the speed of light exclusively in a vacuum.

Therefore the principle of light speed non-exceed-ance carried little credibility after this. Attempts to detect superluminal neutrinos and thereby refute the principle of light speed non-exceedance were made in the 21st century. The OPERA experiment at the Large Hadron Collider was the latest. On September 23, 2011, the OPERA collaboration published [4] a sensational report about the allegedly successful completion of the experiment. However, on March 15, 2012, the ICARUS collaboration published [5] a no less sensational report refuting the OPERA experiment. That has even created illusion of irrefutability of the principle of light speed non-exceedance and, consequently, the existing version of the STR.

Creation of such illusion was presumably the true goal of the expensive OPERA and ICARUS experiments, which couldn't be repeated and verified due to their uniqueness, although they were intensively advertised even before their completion. At the same time, in 2008-2010, there were publications [6] - [11] about alternative proofs3 of the principle of physical reality of imaginary numbers, which could be repeated and verified in any radio engineering laboratory and therefore

made the OPERA and ICARUS experiments unnecessary. But they were ignored by the OPERA and ICARUS collaborations, even despite the fact that evidence of the principle of physical reality of imaginary numbers was published in [12] - [24] in subsequent years. This experimentally proven principle of physical reality of imaginary numbers refuted the postulated principle of light speed non-exceedance in the most indisputable way.

3. Proofs of the principle of physical reality of imaginary numbers

From the above, it thus follows that the answer to the question of whether imaginary numbers are physically real or not in the STO is extremely important. And on this answer depends on the recognition of the existing version of the workshop as correct or incorrect.

In order not to overload this article repeating the proofs of physical reality of imaginary numbers set forth in the publications mentioned above, we only note that they state the following:

• Analysis of oscillatory transient processes made it clear that if the principle of light speed non-exceedance implying the STR statement about physical unreality of imaginary numbers were true, then there would be no tsunami, church bells and musical instruments would not sound and even children's swing wouldn't sway after being pushed by parents;

• Analysis of oscillatory resonant processes made it clear that if the principle of light speed non-exceedance implying the STR statement about physical unreality of imaginary numbers were true, then we would not know such exact sciences as radio engineering and electrical engineering, television and radiolocation, telecommunication, radio navigation and many others;

• Analysis of forced oscillatory processes made it clear that if the principle of light speed non-exceedance implying the STR statement about physical unreality of imaginary numbers were true, then even Ohm's law would not exist for electric circuits.

Thus, the above proofs of physical reality of imaginary numbers are incontestable. Consequently, the principle of physical reality of imaginary numbers is true, and the principle of light speed non-exceedance is false. And Ohm's law for electric circuits in the interpretation of Steinmetz proposed in 1897 even made it possible to refute the existing version of the STR even before its creation.

But in the 21st century this is still not understood in the existing physics of real numbers, since it still assumes that the principle of light speed non-exceedance is true. Norbert Wiener wrote in this regard: "Important work is sometimes delayed by the unavailability in one field of results that may have already become classical in the next field". How, it turns out, dogmatic is the modern higher physical higher education, that people with such an education were unable to understand all this. Unable to understand that their dogmas are disproved by nature and people literally every step of the way, as soon as they turn on the TV or start talking on a mobile phone, as soon as they hear music or bell ringing, as soon as they see a child on a swing, or use a GPS tracker in their car. And there is unwittingly doubt, but

3 They unequivocally proved physical reality of imaginary numbers. However, mathematics is the language of all exact sciences. So, the principle of physical reality of imaginary

numbers proved as a result of these alternative radio engineering experiments is also valid in the STR. It implies that the principle of light speed non-exceedance is incorrect

can people with such an education think so creatively as to understand the structure of distant universes and the processes taking place in them if they do not understand what is happening next to them?

4. The existing version of the STR is incorrect (continued)

And now we answer the question why the relativ-istic formulas (1) and others are incorrect and incorrectly explained. And, therefore, why the STR is incorrect?

The answer is obvious: because the principle of light speed non-exceedance is refuted by the principle of physical reality of imaginary numbers; because, in accordance with the principle of physical reality of imaginary numbers, the formula (1) and other relativistic

formulas must be explainable both at 0 < V < c and at

C < V <Ki. But in the existing version of STR at

C < V <Ki it is actually not explainable (see Fig. 1a), since it corresponds to a physically unstable process, that cannot exist in nature. Indeed, the formula (1) implies that the mass of a physical body, for example, a

rocket, decreases in the range C < V < « with the slightest increase in its velocity, as a result of which its velocity increases with the same engine thrust. And this

leads to a further increase in velocity v, and so on. Besides, the existing version of the STR cannot explain at all what the sense of imaginary physical quantities is in the physics of real numbers.

5. Alternative version of the STR

Therefore, for the corrected relativistic formulas to

be explainable, the graphs of the function w(v) should be similar at argument values V that are both lesser and greater than C , i.e. should be as shown in Fig. 1b. And such graphs in the alternative version of SRT [24] correspond to the corrected formula (1)

m ■■

m^i

¡q

mi

¡q

where q =

(w )2

(2)

is the 'floor' function of argu-

ment

y in discrete mathematics; / c

W — V — qc is the local velocity for each universe, which can take values only in the range

0 < W < C;

v is the velocity measured from our universe;

Fig. 1. Graphs of functions (1) corresponding to the existing version of the STR, and (2) corresponding to its alternative version

C is the speed of light.

Albert Einstein did not exclude such correction of the STR in future. He wrote: "There is no single idea, which I would be sure that it will stand the test of time".

6. Our invisible Multiverse

The new parameter q in the formula (2) corresponds to the fourth spatial dimension. And the quantity of this parameter, equal to q = 0, corresponds to our visible universe of real physical quantities (since i0 = 1 ), for which 0 < v < c follows from w = v - qc and 0 < w < c. The quantity q = 1 in the formula (2) corresponds to an adjacent universe of

imaginary physical quantities (since i1 = i ), for which c < v < 2c , and which therefore is already invisible to us, because it is beyond the horizon of events. Therefore, we shall call it, for definiteness, a tachyon universe by the name of hyper-light subatomic particles. For the same reasons, we shall call our visible universe tardyon. Further:

• the quantity q = 2 corresponds to a tardyon

antiverse of real physical quantities (since i2 = —1 ), which is also invisible for us, as it is beyond the horizon of events due to the condition 2c < V < 3c ;

• the quantity q = 3 corresponds to a tachyon antiverse of imaginary physical quantities (since

•3

l =—l ), which is also invisible for us, as it is beyond the horizon of events due to the condition

3c < V < 4c ;

• the quantity q = 4 corresponds to another6 tardyon universe of real physical quantities (since

•4 1

*i*Не можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

l = 1 ), which is also invisible for us, as it is beyond the horizon of events due to the condition

4c < v < 5c ;

• the quantity q = 5 corresponds to another tachyon universe of imaginary physical quantities (since i5 = i ), which is also invisible for us, as it is

beyond the horizon of events due to the condition

5c < V < 6c, etc.

Thus, our Multiverse consists of many mutually invisible universes. Therefore, we shall call it a hidden, i.e. invisible Multiverse.

7. Alternative version of the STR (continued) The structure of such a hidden Multiverse can be refined in mathematical analysis of data obtained by the WMAP [25] and Planck [26] spacecraft. The following data were obtained by the WMAP spacecraft: mass/energy of the entire universe (actually the entire hidden Multiverse) consists of 4.6% of ordinary baryonic matter, 22.4% of dark matter and 73.0% of dark energy. And according to more recent data from the Planck spacecraft, mass/energy of the universe (again, actually the hidden Multiverse) consists of 4.9% of ordinary baryonic matter, 26.8% of dark matter, and 68.3% of dark energy. That is, the total mass/energy of dark matter and dark energy is more than twenty times greater than the mass/energy of baryonic matter.

However, what dark matter discovered by Jan Hendrik Oort [27] and Fritz Zwicky [28] in 1932-33 and dark energy discovered by Saul Perlmutter [29], Brian Schmidt [30] and Adam Riess [31] (who were awarded the Nobel Prize for their discoveries) in 19981999 are still remains to be found out [32] - [35]. This is the reason why the phenomenon of dark matter and dark energy is called dark. And its explanation is now sought in the microcosm, since according to the existing version of the STR there is no other place to seek in. However, it is still not found.

Albert Einstein explained the reasons for incomprehensibility of this phenomenon very clearly: "Insanity: doing the same thing over and over again and expecting different results". Sir Isaac Newton was of the same opinion: "No great discovery was ever made without a bold guess".

Therefore, taking into account the above explanation of relativistic formulas of the alternative version of the STR, according to which there is a hidden Multiverse, rather than a Monoverse as stated in the existing version of the STR, we shall look for explanation of the phenomenon of dark matter and dark energy in the macrocosm, i.e. in the hidden Multiverse, rather than in the microcosm. And then we can assume that:

• dark matter is neither micro nor macro material substance. It is merely an image (gravitational rather than optical or still less electromagnetic), probably,

a sort of a shadow, casted by invisible universes of the hidden Multiverse adjacent to our visible universe;

• dark energy is also neither micro nor macro material substance. It is merely an image (gravitational rather than optical or still less electromagnetic), probably, a sort of a shadow, casted by other invisible universes of the hidden Multiverse more distant from our visible universe;

It can also be assumed that over billions of years of existence mass/energy of universes of the hidden Multiverse has significantly averaged as a result of mutual exchange of their physical content through numerous portals [36] - [39]. Therefore, the structure of the hidden Multiverse can be specified using the above experimental data obtained by the WMAP and Planck spacecraft. Thus, assuming the mass/energy of parallel universes forming the hidden Multiverse to be approximately the same, we get the following:

• the entire Multiverse consists of 100 %/4,6 % =21,8 mutually invisible parallel universes according to the WMAP data, and 100 %/4,9 % =20,4 mutually invisible parallel universes according to the Planck data, i.e. approximately 20...22 universes;

• dark matter is generated by 22,4 %/4,6 % =4,9 mutually invisible parallel universes according to the WMAP data, and 26,8 %/4,9 % =5,5 mutually invisible parallel universes according to the Planck data, i.e. approximately 5.6 universes;

• dark energy is generated by 73,0 %/4,6 % =15,9 mutually invisible parallel universes according to the WMAP data, and 68,3 %/4,9 % =13,9 mutually invisible parallel universes according to the Planck data, i.e. approximately 14.16 universes.

And such results in the 20th century were impossible to guess by any postulates.

However, as can be seen, the results obtained do not correspond to the relativistic formula (2) and, for the same reason, to the other relativistic formulas. Thus, according to the formula (2), our tardyon universe (as well as other tardyon universes and antiverses) has actually two adjacent universes: one tach-yon universe and one tachyon antiverse. But according to the calculations given above, our tardyon universe has actually 5...6 adjacent universes: three tachyon universes and three tachyon antiverses. Hence, it follows that in fact there is three extra dimensions, rather than one.

Fig. 2. Six-dimensional space of the hidden Multiverse

Consequently, the structure of our hidden Multiverse is described not by complex numbers, as we assumed, but by quaternions [40] containing three imaginary units ij, i2,13 that are related as follows

¡2 — ¡2 — i2 — 1 (3)

/^/3/3 — /3/3/1 — ¡^¡¡2 — 1 (4)

i1i3i2 — /2/1i3 — /3/2/1 — 1 (5)

Therefore, the quaternion structure of our hidden Multiverse [41] in six-dimensional space (see Fig. 2)

will be described by the formula fgrs (X У,z) + hi+ hr + hs , where

• the term ?1q + i2r + i3s determines the coordinates of the corresponding invisible universe,

• and the term f s (x, y, z) determines distribution of physical content in this universe.

Lisa Randall assumed: "We can be living in a three-dimensional space sinkhole in a higher-dimensional universe ". Apparently, her assumption was justified. '

In this regard, the relativistic formula (2) and others have to be corrected again as follows_

Fig. 3. An example of the quaternion structure of the hidden Multiverse

m =

r-ro(i 3) '

mo(ii) "'(h)r-*&)S

y/l - [% - (q + r + s - q0 - r0 - s0)]2 ^ - )2

(6)

where qQ, r0, sQ are the coordinates of our visible universe in the hidden Multiverse;

V is the velocity measured relative to our visible tardyon universe;

c is the speed of light;

w = v - (q + r + 5 - q0 - r0 -s0)c is the local velocity of the universe corresponding to the coordinates q0, r0, s0, that can take values only in the

range 0 < w < c .

Fig. 3 shows an example of such a quaternion structure of the hidden Multiverse containing twenty-two parallel universes, of which six are adjacent to our tardyon universe. And they evoke the phenomenon of dark matter. The remaining invisible universes of the hidden Multiverse evoke the phenomenon of dark energy. As can be seen, this hidden Multiverse has a helical structure and its ends are connected to other universes beyond it. Besides, universes of the hidden Multiverse are connected to two more universes that are beyond it. Consequently, beside our hidden Multiverse there are other universes that evoke the phenomenon of dark space, which, however, has not yet been recorded with existing measuring means.

In addition to the phenomenon of dark matter and dark energy the hypothesis of the hidden Multiverse also simply explains where antimatter not annihilating

with matter and tachyons not violating the principle of causality are located. Antimatter in the hidden Multiverse is apparently

found in antiverses. That is, there are even several antimatters in our hidden Multiverse. And tachyons are apparently as well found in tachyon universes and antiverses.

8. How to see invisible universes

Thus, the hypothesis of the hidden Multiverse that simply and clearly explain the phenomenon of dark matter and dark energy, as well as where antimatter and tachyons are located in the hidden Multiverse, seems quite correct and promising for solving other problems of astrophysics. However, there is still no complete certainty about this until the hypothesis of the hidden Multiverse, like any other hypothesis, receives experimental confirmation.

It turns out that this hypothesis can receive its experimental confirmation. Moreover, the respective experiment is obvious enough. To prove this hypothesis, it is enough to prove the existence of invisible universes. For this purpose one should see invisible universes [42] and register in their starry skies constellations that have never been seen before. Indeed, since in other universes stars are located in space in extremely different ways, constellations in their starry sky might have extremely different configurations. And universes can be identified by these constellations, as people by photographs in their passports.

Fig. 4. Main Astronomical Observatory National Academy of Sciences of Ukraine

The last question remained is how to see them. And the answer is obvious. Just as you can see the adjacent room in your home, invisible from the room you are in now. You have to enter this room, or at least go to its door and look into the room. Similarly, in order to see the adjacent universe, you have to enter the portal connecting our visible universe with the adjacent universe, which is invisible outside the portal, and look at the starry sky of the portal. There must be other constellations. In fact, the map of the starry sky of our universe would gradually turn into the map of the starry

sky of the adjacent universe during transition from one universe to another through the portal. It would seem that stars are moving, disappearing and appearing in the sky. And since the constellations in different universes are extremely different, even with shallow penetration into portals, the entrances to which are at least some of the so-called anomalous zones [43], the maps of the starry sky in them will be different. Moreover, these differences may be even greater than the differences recorded in 1919 in a similar experiment by Sir Arthur Stanley Eddington [44].

Fig. 5. Scheme of an experiment to detect invisible universes

But until now no one even thought that such differences could be. And no one has tested this assumption. Therefore, some astronomical observatories could have been randomly located in anomalous zones. As, for example, the Main Astronomical Observatory of the National Academy of Sciences of Ukraine (Fig. 4), which is located 12 km from the center of its capital, Kiev, in the Goloseevsky forest. And then the whole experiment will consist only in comparing the positions of the stars of the same fragment of the starry sky, observed by different observatories in anomalous zones and outside anomalous zones. And identifying their differences. To do this, such information will need to be transmitted to all observatories to a single computing center (Fig. 5) and processed there. Such an experiment is extremely simple and low-cost, and it will allow in the shortest possible time to obtain confirmation (or refutation) of the existence in nature, in addition to our visible universe, invisible outside the anomalous zones of other universes.

9. The physics of imaginary numbers is the physics of an invisible world

Invisible universes are not the only really existing invisible objects in nature that are described by imaginary numbers. Imaginary inductive and capacitive reactances and conductivities are also real physical objects in the theory of electrical circuits. Moreover, they can even be touched with hands, unlike invisible universes. Of course, not reactances or conductivities themselves are meant, but capacitors and inductors with such imaginary reactances or conductivities.

Imaginary and complex numbers are widely used in exact sciences. But in order to understand their physical nature in each particular case, it is necessary to carry out an appropriate study, like that for the STR in this article.

And in this regard, the Euler's formula exp(x) = cos (x) + i sin (x) describing the oscillatory processes of any physical nature, such as mechanical, electromagnetic, acoustic, etc. is of interest. For example, in accordance with this formula mechanical oscillations of a pendulum corresponding to the term cos (x) are always accompanied by oscillatory process corresponding to the term i sin (x) of unknown physical nature and location. Anyway, the same can be said about the oscillatory process cos (x) and any other physical nature.

Therefore, explanation of physical sense of the Euler's formula requires a special study. And the only thing that can still be said about Euler's formula is that it proves the relationship between the visible and invisible worlds in which there is the same oscillatory process. Consequently, the physics of real numbers and the physics of imaginary numbers are the same science. For example, the hypothesis of the hidden Multiverse in astrophysics.

10. Conclusion

Thus, using the STR study as an example it is shown that beside the visible world studied by the physics of real numbers, there exists an invisible world that corresponds to the physics of imaginary numbers that has just begun to be developed. Moreover, the visible and invisible worlds are the same world described by complex and even hyper-complex numbers.

It is shown that the existing theory of linear electric circuits corresponds to such physics of complex numbers; whereas the alternative version of the STR described in the article and the hypothesis of the hidden Multiverse created on its basis correspond to the physics of hyper-complex numbers.

The hypothesis of the hidden Multiverse can even be experimentally confirmed by astronomical observation in the anomalous zones of constellations that are invisible outside the portals. And these observations will also confirm the existence of invisible universes.

Acknowledgements

Many famous scientists, such as Albert Einstein, Max Planck, Ernest Rutherford and others, argued that an author does not completely understand his own scientific theory if he is not able to explain it to his wife, mother-in-law and other non-specialists. Therefore, the author of this chapter, who set himself a goal of presenting the unconventional approach to solving the problems of astrophysics, astronomy, and relativistic physics proposed therein as clearly as possible, even for non-specialists, used the help of his wife for achieving it. The author expresses appreciation to Olga Ilyinichna Antonova for the help. Being an academic economist, she, nevertheless, took part in discussion of the above alternative version of the STR and its supplements. Her critical comments and valuable advice contributed to more understandable presentation of the version to a general reader.

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