CC BY
12PHYSICAL SCIENCES
ANTIPODES IN SPACE 1
Antonov A.A.
HonDSc, HonDL, H.ProfSci, ResProf Independent Researcher, Kiev, Ukraine
Abstract
The article shows that the special theory of relativity (STR) created in the last century was based on postulates due to the lack of the required experimental information and turned out to be incorrect, as its principle of light speed non-exceedance was refuted by studies of special processes in linear electric circuits in the 21st century. Therefore, an alternative version of the STR has been proposed. Its relativistic formulas imply the existence of numerous mutually invisible parallel universes and antiverses. It is explained how they can be seen. And in these antiverses are antimatter, as well as anti-space and anti-time.
Keywords: Imaginary numbers, Special theory of relativity, Invisible universes, Multiverse, Hyperverse, Antimatter, Anti-space, Anti-time
1. Introduction
In 1826, when Georg Simon Ohm discovered the law named after him, the science of physics did not yet exist. There was a natural philosophy. Alexander Grigorievich Stoletov wrote in this regard: "...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...". And in 1828, Ohm was fired by personal order of Minister of Education for publishing his physics discoveries. The senior official believed that the use of mathematics in physics was unacceptable.
In 1897, Charles Proteus Steinmetz proposed his interpretation of Ohm's law in respect to linear AC circuits [1]. Now it is daily used by millions of engineers in their practice. Moreover, in addition to its direct purpose of calculating electrical circuits it also proved physical reality of imaginary numbers in the simplest and most convincing way, and thereby refuted generally accepted version of the special theory of relativity (STR).
However, the STR had to be first created and then refuted. And such a version of the STR was created by efforts of Joseph Larmor [2], Nobel laureate Hendrik Antoon Lorentz [3], Jules Henri Poincare [4] and Nobel laureate Albert Einstein [5] in the 20th century. Due to the lack of experimental data required for its creation, that were obtained only in the 21st century, it was created using the postulates, i.e. assumptions from which the principle of light speed non-exceedance turned out to be incorrect.
But that's not a big deal. Ultimately, all scientific theories are created as a result of identifying and correcting the errors of previously created theories. And
then, sooner or later, they are inevitably refuted by subsequent newer theories. Otherwise, science would not have developed. Therefore, this article further proposes a corrected version of the STR.
2. Refutation of the principle of light speed non-exceedance
Since the principle of light speed non-exceedance in the generally accepted version of the STR, set forth in all university and school textbooks of physics, has still been believed to be true, it will be necessary to explain why this is not so and why this principle, which is just a postulate, since it has never been proven by anyone, turned out to be in demand.
That is because the relativistic formulas obtained in the generally accepted version of the STR couldn't be explained by its creators. For example, the relativ-istic mass m, apparently, takes imaginary values at hyper-light speeds, when V > C, in the Lorentz-Ein-stein formula
where m0 is the rest mass of a moving physical
body (e.g. elementary particle);
m is the relativistic mass of a moving physical body;
V is the velocity of a physical body;
C is the speed of light. However, the authors of the STR did not know how to explain such a result. As well as no one could explain physical meaning of imaginary numbers 400 years before them. Admittedly, today no one can do it so far. Indeed, everyone knows what 2 kg is, but, no one knows what 2 i kg is, where i = V— 1 .
1 This is an extended version of the article "Antonov A.A. 2021 Antimatter, anti-space, anti-time. Journal of Modern Physics. 12(5). 646-660".
Figure 1. Graphs of functions (1) and (2)
Even if the relativistic mass m at hyper-light speeds, when v > c , in function (1) corresponded to real numbers, then its graph would still be inexplicable in this velocity range (see Figúrela), since it corresponds to a physically unstable process that cannot exist in nature. Consequently, formula (1) is incorrect and that is why it could not be explained.
After all, physical reality of imaginary numbers has been proven and explained in publications [6] -[21]. In order not to repeat these proofs, we only note that it follows from them that if the principle of light speed non-exceedance were true:
• no shock oscillations such as tsunami, Indian summer, noise of bells, piano music could exist in nature, and even a kid's swing couldn't swing after being pushed by parents;
• there could be no resonance in electric circuits, as well as no electric filters could exist; and thus, there would be neither television, nor telecommunication, nor radiolocation, nor many other things without which modern life would be unthinkable;
• even Ohm's law in Steinmetz's interpretation would not exist.
Since, in accordance with Ohm's law in Steinmetz's interpretation, inductive and capacitive reactances the values of which are imaginary numbers, are measured by the devices available in each radio engineering laboratory, this unambiguously proves their physical reality. After all, it is exactly the ability to register with devices X-ray, radioactive, ultraviolet and infrared radiation, infra and ultrasound, magnetic field, atoms and subatomic particles, as well as many other physical entities that are not registered by the human senses, proves their physical reality. Why, then, a simple and cheap experiment using an ordinary tester (see Figure 2), in physics is less convincing in solving the problem of proving physical reality of imaginary numbers than the unique expensive OPERA and ICARUS experiments at the Large Hadron Collider?
In fact, since mathematics is the unique universal language of all exact sciences, the correct mathematical interpretation of, let's say, radio engineering and any other experiment is indisputably convincing for all other exact sciences. After all, the Nature is unique, and only people, solely because of their barrenness of intellect, invented many sciences to describe it.
Figure 2. And this is all that is needed instead of the Large Hadron Collider for the experimental proof of the
physical reality of imaginary numbers.
Due to experimental proof of the principle of physical reality of imaginary numbers in the STR, the principle of light speed non-exceedance is no longer required and there is a need for corrected relativistic formulas that allow explaining STR at speeds V > C .
3. Relativistic formulas of the corrected version of the STR
How can corrected relativistic formulas be obtained? Different approaches can, actually, be proposed to solve this issue. And one can reason as follows [22]. The graph of the corrected Lorentz-Einstein function in the range of velocities , must in some respect be similar to the graph of this function in the range of velocities . For example, as in Figure 1b. A simple and understandable analytical description can be offered for such a graph
mo (i)q mo(i )q
m =
(2)
^ - ( % - q)2 f-^)
is the 'floor' function of argu-
where q = ' v
ment yc in discreet mathematics (see Figure 3a);
w = v—qc is the local velocity (see Figure 3b), the meaning of which will be explained below.
Other relativistic formulas can be corrected in a similar manner.
4. Explanation of relativistic formulas of the corrected version of the STR
A simple explanation can be proposed for the simple formula (2). The quantity q = 0 obviously corresponds to our visible universe, which is assumed to be the one and the only in the existing version of the STR. However, this version turned out to be incorrect, as its
principle of light speed non-exceedance had been refuted.
Therefore, the quantity q = 1 corresponds to another really existing universe, for which v = w + 1c follows from w = v — 1c, i.e. we get c < v < 2c for 0 < w < c. In other words, another adjacent universe is beyond the event horizon and therefore is invisible to us. Therefore, let it for definiteness be called a tachyon universe, like subatomic particles possessing superlu-
minal speed. Herewith, we get m = m0i for a tachyon
universe from the formula (2).
By a similar argument let our visible universe be called a tardyon universe. For our tardyon universe
m = m0.
Subsequently, the quantity q = 2 corresponds to one more really existing universe, for which v = w + 2c follows from w = v — 2c, i.e. we get 2c < v < 3c for 0 < w < c. Consequently, this one more universe is also beyond the event horizon and therefore is also invisible to us. It is also invisible to the adjacent universe that is closer to us. Herewith, we get
m = —mo for this universe from the formula (2). That
is, this universe can be called an antiverse in relation to our universe.
The quantity q = 3 corresponds to one more really existing universe, for which v = w + 3c follows from w = v — 3c, i.e. we get 3c < v < 4c for o < w < c . Consequently, this universe is also beyond the event horizon and therefore is also invisible to
us and to other universes. We get m = —im^o for this
universe from the formula (2). And therefore let it be called a tachyon antiverse. Etc.
\q 1 w
V / / / / / / / *
a b
Figure 3. Graphs of functions q(v) and w(v)
Hence, it turns out that we live in the Multiverse containing a plenty of mutually invisible universes, rather than in a unique visible universe as asserted in the generally accepted version of the STR. Let this Multiverse be called a hidden Multiverse [23] - [27]. 5. Dark matter, dark energy, dark space Many interesting hypotheses of the Multiverse have been proposed by now [28] - [35]. However, they all are unverifiable, i.e. their truth or falsity can be proven experimentally neither now nor in the distant future. Therefore, they are of limited interest. Another drawback is the fact that they do not anyhow explain
extremely incomprehensible phenomena of dark matter and dark energy [36] - [48].
Such extreme incomprehensibility refers also to the hypothesis of the visible Monoverse in the generally accepted version of the STR, about which Albert Einstein spoke very clearly: "Insanity: doing the same thing over and over again and expecting different results"
However, the phenomena of dark matter and dark energy can be quite explicable within the framework of the hypothesis of the hidden Multiverse. Besides the
phenomenon of dark space can also be discovered and explained:
• invisibility of dark matter and dark energy is explained by the fact that they are actually neither matter, nor energy, nor any other material physical substance, but only images (though not optical and still less electromagnetic, but gravitational), a sort of a shadow;
• impossibility of detecting any of the chemical elements known to us in the composition of dark matter and dark energy is also explained by the absence of any material content in them, since they are just images;
• at the same time the phenomenon of dark matter is evoked by invisible parallel2 universes of the hidden Multiverse adjacent to our visible universe;
• the phenomenon of dark energy is evoked by other universes except for our visible universe and invisible parallel universes of the hidden Multiverse adjacent to it;
• in addition, the phenomenon of dark space is similarly evoked by invisible universes outside the hidden Multiverse;
• universes located in and beyond the hidden Multiverse together form the Hyperverse.
6. Analysis of WMAP and Planck spacecraft
data
However Albert Einstein did not exclude such correction of the STR in future. He wrote: "No single idea, which I would be sure that it will stand the test of time". And he was absolutely right. After all, if this were not so, then the development of science would be impossible.
An example of the structure of such a hypothetical hidden Multiverse is shown in Figure 4. As can be seen, the universes drifting in the extra spatial dimension are interconnected through portals
Figure 4. The screw structure of the hidden Multiverse corresponding to the formula (2), which illustrates the
existence of other Multiverse beyond its borders
2 Since, despite their infinity, these universes do not intersect anywhere
[49], [50] indicated by single two-sided arrows. The portals arise due to shallow mutual local penetration of the universes into each other. Moreover, the end universes in such a helical structure, evoking the phenomena of dark matter and dark energy, are connected with the universes of dark space.
In order not to repeat the mistake of Albert Einstein due to erroneous assumptions, it is useful to check these results for compliance with the data obtained in the 21st century by the WMAP [51] and Planck [52] spacecraft. According to the WMAP data, the entire universe (in fact, the entire hidden Multiverse, as suggested in the article) is 4.6% of baryonic matter, 22.4% of dark matter and 73.0% of dark energy. According to more recent Planck data, the entire universe (in fact, the entire hidden Multiverse) is 4.9% of baryonic matter, 26.8% of dark matter and 68.3% of dark energy.
Based on these data, it is conceivable that mass-energy of parallel universes of the hidden Multiverse has largely averaged over billions of years of existence as a result of the mutual exchange of their micro- and mini-content through the portals (even if for some reason their mass-energy in different universes turned out to be different immediately after the Big Bang) and it is equal to the mass-energy of our visible universe, with precise accuracy.
Thus:
• according to Planck data, the hidden Multiverse contains 100%/4.9%=20.4 parallel universes (according to WMAP data 100%/4.6%=21.8 parallel universes), i.e. probably 20 ... 22 parallel universes;
• according to Planck data, the hidden Multiverse contains 26.8%/4.9=5.5 parallel universes (according to WMAP data 22.4%/4.6%=4.9 parallel universes), evoking the phenomenon of dark space, i.e. probably 5 ... 6 parallel universes;
• according to Planck data, the hidden Multiverse includes 68.3%/4.9=13.9 parallel universes (ac-
cording to WMAP data 73.0%/4.6%=15.9 parallel universes), evoking the phenomenon of dark energy, i.e. probably 14 ... 16 parallel universes.
However, these results do not correspond to the structure of the hidden Multiverse shown in Figure 4, since our visible universe should have not two, but 5.. .6 adjacent invisible universes.
Admittedly, each tardyon universe in Figure 4 is adjacent to one tachyon universe and one tachyon antiverse. And according to the above mathematical analysis of the data obtained by the WMAP and Planck spacecraft, each tardyon universe should have three tachyon universes and antiverses. Therefore, the assumption that the structure of the hidden Multiverse is described by complex numbers and has one extra spatial dimension turned out to be incorrect. In fact, the hidden Multiverse has three extra dimensions and is described by hyper-complex numbers
fq,r,S(x,y,z) + iq + + hs [53], where the function fq,r,s (X, y, z) describes distribution of material
content of the corresponding parallel universe with coordinates in coordinates X, y, Z, and the imaginary
units ij, i2,13 are connected by the following relations •2 -2 -2 t
l1= i2 = h = 1 (3)
• • • • • • • • • . . .
11I2I3 ~ I2I311 ~ I3I1I2 ~ (4)
• •• ••• ••• ^ , —>.
I1I3I2 I2I1I3 I3I2I1 1 (5)
Lisa Randall wrote in this regard: "We can be living in a three-dimensional space sinkhole in a higher-dimensional universe". And she was right.
7. Correction of relativistic formulas of the corrected version of the STR
Repeatedly corrected relativistic Lorentz-Einstein formula will be written as follows
Figure 5. The structure of the hidden Multiverse corresponding to the formulas (6), (7) and (8)
m_ mo(i1 )q(i2)r(i3)s _mo (i, )q(i2)r(i3)s (6)
^¡1—[% - (q+r+s)]2 ^—wc )2
where w = v — (q + r + s)c is the local velocity for the corresponding universe, which can take values only in the range o < w < c.
Other relativistic formulas can be corrected in a similar manner [54] - [57]
At = Ato(i1)q(i2)r(is)s^1 — lv/c — (q+r+s)]2 = = At0(i1)q(i2)r(i3)s^1 — (w/c)2
l = l0(i1)q(i2)r(i3)sh — [V — (q + r + s)]2 =
v /c (8)
= lo(i1)q(i2)r(is)^1 — (w/c)2
The structure of the hidden Multiverse corresponding to the formulas (6), (7), and (8) can be as shown in Figure 5. As can be seen, its quaternionics [58], [59] structure differ from the one shown in Figure
4 in that it contains three tachyon universes ij,i2, i3
and three tachyon antiverses ij, Í2, Í3, which provides
three required extra dimensions. Thus, the six-dimensional space of the hidden Multiverse (see Figure 5) has three extra dimensions q,r,s , where parallel universes are located, and three dimensions x, y, z, where material content of each of these universes is located. Moreover, the structure of the hidden Multiverse corresponding to the formulas (6), (7) and (8) differs from the one shown in Figure 4 by the fact that it contains unidirectional portals corresponding to the formulas (4) and (5) in addition to bidirectional portals corresponding to the formula (3).
8. Antipodes in space
The 20th century turned out to be rich in outstanding physical discoveries, such as special and general theory of relativity, quantum mechanics, radio electronics, radioactivity, X-ray, dark matter, dark energy, etc. And if radioactivity and X-ray were almost immediately explained and used, dark matter and dark energy have remained unexplained to this day.
Antimatter [42], [60], [61] is another no less incomprehensible astrophysical object than dark matter
and dark energy. It is now generally accepted that the Big Bang produced not only matter, but also antimatter. Moreover, they were generated in equal quantities. However, no antimatter has been found in any noticeable quantities in our visible universe. It was obtained only in the form of subatomic antiparticles and some antiatoms, and also was found in some natural phenom-
ena in negligible quantity for a very short time3. Synthesis of such antimatter was extremely expensive. Thus, one gram of anti-hydrogen would cost $ 662.5 trillion.
So, where can antimatter in the form of antiverses be found? And does it at all exist anywhere in this form? It cannot apparently be in our visible universe,
since otherwise it
Figure 6. Geometric interpretation of the concepts "anti-time" and "anti-space "
would annihilate with matter and the universe would be destroyed. By the way, this fact is another refutation of the generally accepted version of the STR. Hence, it can be found only in another universe. And the hidden Multiverse, unlike other hypothetical Multiverse, is quite suitable for this role, since it has antiverses. Moreover, tardyon and tachyon universes and antiverses alternate in the hidden Multiverse in such a way that they assuredly prevent their mutual annihilation. Thus, the hypothesis of the hidden Multiverse completely solves the problem of the existence of antimatter.
But the most interesting thing is that, just as formula (6) implies the existence of antimatter in antiverses, from formulas (7) and (8) it follows that antispace and anti-time exist in the same antiverses. In the same way as in the antipodes on Earth, the directions of gravity are opposite to each other. Moreover, people would find nothing unusual in these antiverses (as antipodes on Earth), if they got there, since there operate the same physical, chemical and other laws of nature as in our visible universe.
Figure 6 shows a fairly obvious geometric interpretation of these new concepts. As can be seen, time and anti-time differ by the sign of the value appearing in formula (7), and space and anti-space differ by the
sign of the value appearing in formula (8). Time and anti-time, in addition, can differ in their different distance on the time axis from the common origin, which depends on the time of occurrence of the corresponding universes and antiverse. Figure 6, for example, depicts a situation in which the universe and the antiverse arose simultaneously.
9. How to see invisible universes
Thus, the hidden Multiverse is quite unusual in many respects. This arouses some mistrust. Does it exist at all? Nature can give an unequivocal and convincing answer to this question only if its invisible universes are seen. And they can be seen as follows [62], [63].
Since the sky maps of invisible parallel universes are supposedly extremely different, their constellations can be confidently distinguished from those observed in the starry sky by observatories on Earth. Moving along the Earth portals between our visible universe and adjacent invisible universes, one can observe as the star map of one universe is gradually replaced by the star map of the adjacent universe. Therefore, all it takes to make sure of existence of invisible universes is to register differences between the constellations in the starry sky in the portals from the constellations
3 For example, in 1995, CERNachieved a sensational success at that time, having received nine antihydrogen atoms, which lasted 40 billionths of a second.
Figure 7.
Main astronomical observatory of the National academy of science of Ukraine located in the anomalous zone
Observatory outside anomalous zone Observatory outside anomalous zone Observatory outside anomalous zone
\ /
Observatory in anomalous zone Computer Observatory outside anomalous zone
/ j \ k
Observatory outside anomalous zone Observatory outside anomalous zone Observatory in anomalous zone
Figure 8. Scheme of an experiment to detect invisible universes by identifying differences as a result of comparing the constellations of the starry sky in anomalous zones and outside anomalous zones observed in the starry sky outside the portals.
What needs to be done to carry out such an experiment is to find a portal and perform the astronomical observation therein. And although it is clear that entrances to portals are located, at least, n some anomalous zones, which are quite numerous on Earth, no one has yet been engaged in the study of portals directly in portals, since no one has needed it. And besides, it is unsafe, since portals are a sort of invisible labyrinths. Therefore, one can get lost there without an appropriate portal orientation device (similar to marine compass). Such a danger can be minimized, if such observations are carried out at the very entrance to the portal, in the anomalous zone. It is conceivable that some astronomical observatories are already in the anomalous zones, without knowing it. As, for example, the Main Astronomical Observatory of the National Academy of Sciences of Ukraine, which is located in the Holosiivskyi forest, just 12 km from Kiev, the capital of Ukraine (see Figure 7).
Therefore, an experiment in detecting invisible universes turns out to be very simple and inexpensive in this case. It consists in comparing computer images of the same area of the starry sky provided by several observatories located close to each other, at least one of
which being located in the anomalous zone (see Figure 8); and in revealing differences in the relative position of the stars depicted in these images. If such an experiment is successful, its significance for human civilization will significantly exceed the significance of the discovery of America by Columbus.
10. Conclusions
The answer given in the article to one of the questions from the list of unsolved issues of modern physics 'where is antimatter?' turned out to be simple and quite logical: it is in the antiverses. At the same time, it has been explained that there are many pairs of universes-antiverses in nature. And therefore there are many antimatters. Moreover, it has been explained that, in addition to antimatter, there is anti-time and anti-space in the antiverses. And there are also many of them.
The concept of anti-time allowed us to answer another question from the list of unsolved problems of modern physics 'why does time have a direction?' It turned out that the 'arrow of time' concept is incorrect, i.e. contrary to popular belief, time can be not only positive, but also negative. This is how it happens in the cosmic antipodes - universes and anti-universes.
But in order to answer these questions, we first had to answer one more question from the same list 'are there invisible parallel universes?'. And the article not only makes it clear that they exist in the Multiverse, which we have called hidden, but also why they are parallel and invisible. It also clarifies how and where on Earth invisible universes can be seen.
But the answer to the third question was obtained in the process of answering two more questions from the list of unsolved issues of modern physics 'are there extra dimensions?' and 'what is dark matter and dark energy?'. Due to mathematical analysis of the data obtained by the WMAP and Planck spacecraft it has been concluded that our hidden Multiverse has a quaternion structure in six-dimensional space. And the phenomenon of dark matter and dark space is explained by the existence in our visible universe of a gravitational wave background generated by the rest of the invisible universes of the hidden Multiverse.
All these answers to the questions from the list of unsolved issues of modern physics became possible after receiving an answer to one more question, although from the list of unsolved issues of modern mathematics, 'can imaginary numbers be physically real?' An affirmative answer has been obtained as a result of theoretical and experimental studies of special processes in linear electric circuits, which made it possible to prove the general scientific principle of physical reality of imaginary numbers that, in its turn, refuted the principle of light speed non-exceedance in the STR. And this enabled us to assert that the relativistic formulas obtained in the generally accepted version of the STR are incorrect; they have been incorrectly explained and entailed wrong conclusions. Therefore, attempts to solve the above-mentioned and other physical issues within the framework of this theory were certainly destined for failure.
Thus, it is logical to conclude that the version of the STR presented in textbooks is outdated, since it does not correspond to the experimental data obtained in the 21st century, and therefore it hinders the development of modern physics.
Acknowledgements
The author is grateful for participation in the discussion of the paper to Olga Ilyinichna Antonova, whose criticism and valuable comments contributed to improvement of the paper.
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RECOMBINATION IN SILICON SOLAR CELLS
Ismoilov U.
Master student Mirzaalimov N.
PhD student Jurayeva S.
Master student Andijan State University Alijonov A. Bachelor student
Zulunova M.
Bachelor student Andijan machine building institute
Abstract
This article describes the recombination processes in silicon-based solar cells. Both the results obtained are given and theoretically analyzed.
Keywords: silicon, recombination, generation, solar cell
The demand for solar cells is growing day by day [1]. The industry mainly produces silicon-based solar cells. This is because the cost of solar cells made of silicon is cheaper than the rest [2]. Every country has a different climate. Solar elements made of silicon are also sensitive to external influences. Climate change is affecting the photoelectric properties of silicon-based solar cells (SBSC) [3]. In our research, we studied the effect of temperature on the properties of silicon and SBSC. The conductivity of silicon is directly proportional to the temperature. That is, the higher the temperature, the higher the concentration of charge carriers [4]. This results in a narrowing of the width of the silicon restricted zone. As the zone narrows, it begins to absorb more spectral light. Hence, the efficiency of SBSC should increase. But there are also negative effects of temperature [5]. That is, the concentration of phonons in silicon increases with increasing temperature. This reduces the mobility of the charge carriers in
silicon. This suggests that the efficiency of SBSC increases to a certain value, not continuously, with increasing temperature, and then decreases. The value of the temperature at which SBSC has the maximum efficiency is called the nominal operating temperature (NIT). Silicon-based solar cells typically have a NOCT value of 35 ° C.
Recombination of SRH depends on the defects, and the process of its formation is as follows. The electron in the conduction band first descends to a defective surface, then emits a phonon again, enters the valence band, and joins the cavity [6].
j^SRH _
np - n
(1)
zp (n + n ) + Tn (p + Pi) Each recombination process determines the lifetimes of electrons and cavities. That is, the less recombination, the longer the lifespan [7].
2
