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European Journal of Applied Sciences – Vol. 11, No. 5
Publication Date: October 25, 2023
DOI:10.14738/aivp.115.15474
Antonov, A. A. (2023). The Corrected Version of the Special Theory of Relativity. European Journal of Applied Sciences, Vol - 11(5).
68-83.
Services for Science and Education – United Kingdom
The Corrected Version of the Special Theory of Relativity
Antonov, Alexander Alexandrovich
Independent researcher, Kiev, Ukraine
ABSTRACT
This article shows that the version of the special theory of relativity (STR)
presented in all physics textbooks is incorrect, since relativistic formulas obtained
therein are incorrect. They are incorrectly explained using the wrong principle of
non-exceeding the speed of light and have led to incorrect conclusions about the
physical unreality of imaginary numbers and the existence in nature of only our
visible universe. This version of the STR proved to be in demand only because its
authors were not able to explain physical sense of imaginary numbers. The article
provides three proofs of physical reality of imaginary numbers and explains their
physical sense in the theory of linear electric circuits, relativistic physics and
astrophysics. This made it possible to obtain corrected relativistic formulas, from
which appropriate conclusions were drawn.
Keywords: imaginary numbers, special theory of relativity, Multiverse, dark matter, dark
energy.
INTRODUCTION
The special theory of relativity (STR) [1]-[3] created in the 20th century has been deservedly
considered one of the most significant achievements of modern physics, since it introduced the
principle of relativism into science. This is why STR is now taught in all university physics
textbooks. However, the relativistic formulas obtained in this theory turned out to be incorrect
due to the lack of experimental knowledge in physics of the 20th century necessary to complete
their derivation. What is the physical meaning of named imaginary numbers and now is not
explained in any textbook? Therefore, a postulate was introduced in STR, called the principle
of not exceeding the speed of light, which allowed the physical meaning of imaginary numbers
not to be explained, since nothing supposedly corresponds to them in nature.
This is how the STR has still been studied in physics textbooks.
THE CURRENT VERSION OF THE STR IS INCORRECT
For a newly created scientific theory, this is pardonable, since such a theory must be developed.
Therefore, over time, something in it must be refuted and corrected. The author of the concept
of an open society, Sir Karl Raimund Popper, argued [4] that "... the struggle of opinions in
scientific theories is inevitable and is a prerequisite for the development of science."
And in STR there are already a lot of such denials [5]-[54]. This is the existence of shock
oscillations - tsunamis, music of pianos and other musical instruments, bell ringing in Christian
churches and even swinging swings in playgrounds. This is the modern theory of resonance
under the influence of not only sinusoidal oscillations of constant amplitude, but also damped
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Antonov, A. A. (2023). The Corrected Version of the Special Theory of Relativity. European Journal of Applied Sciences, Vol - 11(5). 68-83.
URL: http://dx.doi.org/10.14738/aivp.115.15474
sinusoidal oscillations, and even under the influence of exponential pulses. And this is even
radio engineering created earlier by STR, since STR and radio engineering mutually refute each
other.
But the authors of physics textbooks, not being able to challenge these refutations, never- theless, still do not take them into account [55]-[63].
THE CORRECTED VERSION OF THE STR
Therefore, the corrected version of the STR [64] is in demand. In its incorrect principle of light
speed non-exceedance STR denying physical reality of imaginary numbers is replaced by the
principle of physical reality of imaginary numbers proven experimentally.
Let us show how, for example, this can be done by correcting the Lorentz-Einstein’s formula
2
0
1 ( )
c
v
m
m
−
= (1)
where
m0
is the rest mass of a moving body (for example, an elementary particle);
m
is the relativistic mass of a moving body;
v
is the velocity of a body;
c
is the speed of light.
It can be seen from the graph (see Fig. 1a) that the function
m( v )
has a discontinuity at
v = с .
It corresponds to real numbers for argument values
v с
, while for argument values
v с
it
corresponds to imaginary numbers that were discovered in the 16th century and whose
physical sense remained unexplained until the 20th century. And since we have proved the
physical reality of imaginary numbers, in this situation it is necessary to explain their physical
meaning. But on the graph of the function
m( v )
, its branch at the values of the argument
v c
corresponds to a physically unstable process that cannot exist in nature. Therefore, the
Lorentz-Einstein formula cannot be explained. Hence, it is incorrect.
Fig. 1: Graphs of the function
m( v )
corresponding to the generally recognized but incorrect
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European Journal of Applied Sciences (EJAS) Vol. 11, Issue 5, October-2023
and corrected versions of STR in the subluminal
v с
and hyperluminal
v c
ranges
And the graph of the Lorentz-Einstein formula, which can be explained (see Fig. 1b), on the
range
v c
should be similar to the graph of this function (see Fig. 1a) on the range
v с .
Thus, the corrected Lorentz-Einstein’s formula can be written as follows
2
0
2
0
1 1 ( )
( )
( )
( )
( )
c
w
m i
q
c
v
m i
m v
q q
−
=
− −
= (2)
where
q = v c
is the ‘floor’ discrete function of the argument
v c
(see Fig. 2a);
w = v − qc
is the local velocity that in each universe takes values in the range
0 w c (see
Fig. 2b).
Fig. 2: Graphs of functions
q( v )
and
w( v )
illustrating the meaning of the ‘floor’ function
of discrete mathematics
Therefore, at
q = 0
the formula (2) should be written as (1), and at
v c
it should be
written as follows
2
0
2
0
1 ( 1) 1 ( )
( )
c
w
im
c
v
im
m v
−
=
− −
= (3)
The graph of the function
m( v )
in Fig. 1b shows that the value
q = 1
corresponds to a fragment
of this function on the interval
c v 2c
. Those on this interval
c v 2c
it corresponds to
universe adjacent to our universe. And this other universe is already invisible to us, as it is
located beyond the event horizon. Therefore, for definiteness, we call it tachyon universe. Our
visible universe will then be called tardion universe. The value
q = 2
corresponds to an
invisible tardyon antiverse, for which
2c v 3c
. The value
q = 3
corresponds to an invisible
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Antonov, A. A. (2023). The Corrected Version of the Special Theory of Relativity. European Journal of Applied Sciences, Vol - 11(5). 68-83.
URL: http://dx.doi.org/10.14738/aivp.115.15474
tachyon antiverse, for which
3c v 4c
. Etc.
Therefore, it follows from the corrected Lorentz-Einstein formula that the statement con-tained
in physics textbooks about the existence in nature of our only visible universe is incorrect. In
fact, we are in the Multiverse, which, due to the mutual invisibility of the universes in it, we will
call the hidden Multiverse.
But to make sure that the invisible universes really exist, we need an appropriate experiment
that made it possible to see them.
COROLLARIES OF THE CORRECTED VERSION OF THE STR
How to See Invisible Universes
And in order to understand what this experiment can be, first of all, it is necessary to un- derstand that in Formula (2) the parameter
q
is an additional spatial dimension in which
mutually invisible parallel universes1 somehow drift relative to each other. They touch each
other and even slightly penetrate into each other generating respective passages through which
their matter content is exchanged. These passages are commonly referred to as portals [65],
[66] or stargates [67]. And the entrances to them are presumably at least some of the
anomalous zones, of which there are a lot on Earth [68]-[71]. And since in other universes the
constellations in the sky inevitably differ from the constellations in our earthly sky, then when
moving through the portals from the Earth to any neighboring universe, the map of our starry
sky will gradually be transformed into a map of the starry sky of the neighboring universe.
Fig. 3: Scheme of an astronomical complex for the detection of invisible universes
And if a telescope is placed in such a portal, then by comparing the position of the stars in the
sky in the portal and outside the portal (see Fig. 3), changes in the position of the stars can be
detected. These other constellations in the starry sky in the portals will be the desired
1
Since, despite their infinity, they do not intersect
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European Journal of Applied Sciences (EJAS) Vol. 11, Issue 5, October-2023
experimental evidence [72]-[77]. The corresponding experiments2 is very low-cost and easily
implemented. Moreover, some observatories are already in anomalous zones. As, for example,
the Main Astronomical Observatory of the National Academy of Sciences of Ukraine, which is
located 12 km from the center of its capital, Kiev, in the Goloseevsky forest.
The Need Geophysical Research of Portals
Naturally, the farther the telescope is placed in the portal, the more the constellations in its
starry sky will differ from the constellations observed outside the portals. And the more
convincing will be such astronomical observations. In addition, as a result of such astronomical
observations, it will be possible to determine how many different neighboring invisible
universes are located next to our visible universe [78]-[88]. But the great value of such
observations lies not only in this. And also, in the fact that the study of the geophysical
characteristics of portals will make it possible to create artificial portals, with the help of which
it will be possible to move from our universe to other currently invisible to us, and therefore
unknown universes. That will accelerate the transformation of human civilization into a super- civilization. However, people now avoid any visit to the portals, as the portals are invisible
labyrinths in which it is impossible not to get lost. Therefore, in order to make visiting portals
safe, it is necessary to create means of portal orientation that will allow invisible portals to be
seen in the same way that a compass allows navigators to see the invisible magnetic field of the
Earth. And this is quite possible to do if we use the fact that the intensity of the electromagnetic
radiation of terrestrial radio stations decreases as we dive into the portals. And when it reaches
the neighboring universe, this radiation will disappear completely. After all, on Earth there is
no such electromagnetic radiation from neighboring universes.
Dark Matter, Dark Energy
Having proved the existence of mutually invisible parallel universes, we need to find out their
location in the hidden Multiverse, or, in other words, the structure of the hidden Multiverse.
Fig. 4: The six-dimensional space of the hidden Multiverse, in which
q,r,s
are the coordinates
of invisible parallel universes, and
x, y,z
are the coordinates of the material content in each
such parallel universe
2 They are analogous to the experiment of Sir Arthur Stanley Eddington in 1919.
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Antonov, A. A. (2023). The Corrected Version of the Special Theory of Relativity. European Journal of Applied Sciences, Vol - 11(5). 68-83.
URL: http://dx.doi.org/10.14738/aivp.115.15474
We also need to understand the meaning of dark matter and dark energy called as such because
of their incomprehensibility and because no chemical elements have been found therein, as well
as because they neither absorb nor emit nor reflect nor refract electromagnetic radiation.
However, they account for more than 95% of the whole mass-energy in space. More precisely,
according to the data obtained by the WMAP spacecraft [89], the mass-energy of our visible
universe (actually, the hidden Multiverse) consists of 4.6% of baryonic matter, 22.4% of dark
matter and 73.0% of dark energy. And according to more recent data obtained by the Planck
spacecraft [90], the entire
Fig. 5: Possible structure of the hidden Multiverse universe (actually, again, the entire hidden
Multiverse) consists of 4.9% of baryonic matter, 26.8% of dark matter and 68.3% of dark
energy.
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Therefore, the truth and completeness of knowledge in modern physics, which cannot explain
the phenomena of dark matter and dark energy, raises serious doubts. And since it was proved
above in the most indisputable way that in nature there is not the Monoverse, but the
Multiverse, then in addition to searching for the clues to the nature of the phenomena of dark
matter and dark energy at the Large Hadron Collider in the microcosm, it is also necessary to
search for their clues in the macrocosm of our hidden Multiverse. After all, Albert Einstein
himself said: “Insanity: doing the same thing over and over again and expecting different results”.
The search for a solution to this problem in the hidden Multiverse allows us to assume that [91],
[92]:
• dark matter and dark energy are evoked by invisible parallel universes of the hidden
Multiverse, creating a kind of its own gravitational shadow in our visible universe;
• dark matter is evoked by invisible universes of the hidden Multiverse adjacent to our
visible universe;
• dark energy is evoked by the rest of the universes of the hidden Multiverse, except
for our visible and adjacent invisible universes;
• chemical composition of dark matter and dark energy cannot be determined because
they are just images.
Such an explanation of the phenomena of dark matter and dark energy provides important
information about the structure of the hidden Multiverse. Indeed, given that mutually invisible
universes of the hidden Multiverse are interconnected by numerous portals through which they
exchange their matter content it can be argued that their mass-energy has significantly
averaged over billions of years of their existence.
Thus:
• the whole hidden Multiverse should consist of 100% / 4.6% = 21.8 parallel universes
according to the experimental data obtained by the WMAP spacecraft, and of 100% /
4.9% = 20.4 parallel universes according to the data obtained by the Planck spacecraft;
• the whole hidden Multiverse should consist of 100% / 4.6% = 21.8 parallel universes
according to the experimental data obtained by the WMAP spacecraft, and of 100% /
4.9% = 20.4 parallel universes according to the data obtained by the Planck spacecraft;
• dark matter should consist of 22.4% / 4.6% = 4.9 parallel universes according to the
experimental data obtained by the WMAP spacecraft, and of 26.8% / 4.9% = 5,5 parallel
universes according to the data obtained by the Planck spacecraft;
• dark energy should consist of 73.0% / 4.6% = 15.9 parallel universes according to the
experimental data obtained by the WMAP spacecraft, and of 8.3% / 4.9% = 13.9 parallel
universes according to the data obtained by the Planck spacecraft.
However, these results are inconsistent with the formula (2), since according to the WMAP and
Planck spacecraft data, five-six rather than two invisible universes should be adjacent to our
visible universe. Therefore, the relativistic formula (2) must be corrected again as follows:
2
0 1 2 3
1 [ ( )]
( ) ( ) ( )
( , , )
q r s
c
v
m i i i
m q r s
q r s
− − + +
= (4)
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Antonov, A. A. (2023). The Corrected Version of the Special Theory of Relativity. European Journal of Applied Sciences, Vol - 11(5). 68-83.
URL: http://dx.doi.org/10.14738/aivp.115.15474
where
v
is the velocity measured from our tardyon universe;
c is the speed of light;
1 2 3
i .i ,i
are the related imaginary units [51], wherein
1
2
3
2
2
2
i
1 = i = i = −
(5)
1 i1
i2
i3 = i2
i3
i1 = i3
i1
i2 = −
(6)
1 i1
i3
i2 = i2
i1
i3 = i3
i2
i1 = (7)
Antimatter, Anti-Time, Anti-Space
Therefore, the hidden Multiverse has a quaternion structure in six-dimensional space (Fig. 4).
For example, shown in Fig. 5, a helical structure in which adjacent to our visible tardyon
universe is five invisible tachyon universes and anti-universes that evoking phenomenon of
dark matter, as well as sixteen other invisible universes evoking phenomenon of dark energy.
Thus, such a hidden Multiverse contains twenty-two invisible universes, which is consistent
with the mathematically analyzed data obtained by the WMAP and Planck spacecraft. In
addition, this structure is connected to two other universes that are outside the hidden
Multiverse and form, together with the hidden Multiverse, the Hyperverse. And some invisible
universes located in the Hyperverse outside the hidden Multiverse, as shown in Fig. 5 could
presumably be adjacent to our visible universe. And then they can be discovered and studied
by astronomical and geophysical research in portals.
From such a structure of the hidden Multiverse it also follows that in its cosmic antipodes of
universes/antiuniverses there are matter/anti-matter, as well as time/anti-time and
space/anti-space [93]-[101].
Deja Vu Phenomenon
The corrected version of STR allows explaining another unusual phenomenon - deja vu. It is so
unusual that until now only medical scientists have tried to explain it. Translated from the
French 'déjà vu', it means 'already seen'. And this term describes an allegedly psycho-emotional
phenomenon corresponding to the state of a person in which it seems to him that he had already
been in exactly the same situation. Moreover, psychologists say that up to 97% of all people
were in this state at least once in their lives.
And although a large number of hypotheses have been proposed to date to explain the
phenomenon of deja vu, it's all not clear here. As in the phenomena of dark matter and dark
energy. And all the deja vu hypotheses are not very convincing. They do not explain why almost
all people sooner or later find themselves in this state, regardless of place of residence, age,
gender and other factors. If it is an infection, how is it spread? Why, in spite of everything,
almost all of humanity is infected? And if it is an infection, then why without any consequences
and complications? And if not an infection, then why did the phenomenon of deja vu hit so many
people? But why not everyone?
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Therefore, we propose another hypothesis - a physical one. Very unusual, but explaining
everything. However, explaining in a different way than it is now customary in science to ex- plain, using only the knowledge gained in the past. And we will explain using knowledge that is
expected to be obtained in the future. Those suppose that in the future a highly developed
human civilization, posessing extremely perfect computers, will be able to calculate any
hypothetical situations in its development both in the past and in the future. Let's also assume
that the inhabitants of these super-civilizations will be able to travel to their past. Then, the
inhabitants of these super-civilizations, traveling into the past and making some changes to it,
will be able to correct their future as well (see Fig. 6). And people who are exposed to such an
impact, being in a time loop, from some point in time in their past further in the future will live
in a different branch of time. And they will forget their previous life in the time loop, as the
memories of everything that happened to them from their memory will somehow be erased. So
this hypothesis really explains everything.
Fig. 6: Explanation of the ‘déjà vu’ phenomenon, which is created as a result of the intersection
of the time branch ‘return to the past’ and the time branch ‘past time’ with the formation of a
‘time loop’
But a very important circumstance follows from it – the whole life of all people on Earth is
currently under the control of aliens from the future and is recorded in the memory of their
supercomputers. Therefore, they know everything about us. And they try not to interfere in our
lives because it can change their future. And then they will not be able to return to their future
to their relatives and friends. Nevertheless, sometimes they still find such situations in the past
on their supercomputers, which correct their future in a favorable way, not excluding the
possibility of returning to their relatives and friends. And these options are being implemented.
CONCLUSION
Thus, the article proves that the version of the special theory of relativity studied in the educa- tional process of all universities - even the most prestigious ones - is incorrect. And the
corrected version presented in the article has convincing experimental evidence and allows
many inexplicable things to be explained. Therefore, in the existing physics textbooks, the
presentation of the special theory of relativity must be corrected.
ACKNOWLEDGMENTS
The author gratefully acknowledges the insights, comments, and assistance of Olga Ilyinichna
Antonova.
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URL: http://dx.doi.org/10.14738/aivp.115.15474
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