Global Journal of Physics
Vol. 2, No 2, October 21, 2015
www.gpcpublishing.com
ISSN: 2454-7042
Ohm’s Law explains astrophysical phenomenon of dark matter and dark
energy
Alexander Alexandrovich Antonov
Research Centre of Information Technologies “TELAN Electronics”, P.O. Box 73, Kiev, 03142, Ukraine
Abstract
It is shown that Ohm's law in the theory of linear electric alternating current circuits proves the physical reality of the
named imaginary numbers with its very existence. Thus it refutes the expansive interpretation of the current version of the
second postulate of the special theory of relativity. Version of the special theory of relativity that was corrected in
accordance with the principle of the physical reality of imaginary numbers allowed to produce a hypothesis about a hidden
Multiverse, which explains the astrophysical phenomenon of the dark matter and dark energy.
Indexing terms/Keywords
Dark matter, Dark energy, Ohm’s law, Imaginary numbers, Multiverse, Special theory of relativity.
Academic Discipline and Sub-Disciplines
Physics, Astrophysics, Theory of electrical circuits.
SUBJECT CLASSIFICATION
Physics Classification, Electrical Engineering Classification.
TYPE (METHOD/APPROACH)
Physical and Mathematical Analysis
INTRODUCTION
At the present time, Ohm's Law is known to all educated people. It is even studied at schools. But its fate, same as the
fate of many others truly great scientific discoveries, was not easy.
Ohm's Law was discovered in 1826. However, despite great scientific importance of this discovery, it was not properly
appreciated by its contemporaries; moreover, some met it even with hostility. Indeed, on the personal order from the
Minister of Education, Ohm was fired from his job at the school for publication of his research in the newspapers. Only in
1842 after Ohm’s election as a member of the Royal Society of London, and later in 1845 as a member of the Bavarian
Academy of Sciences, Ohm’s Law was recognized by the scientific community. In 1881 at the International Congress of
Electricians in Paris, unit of electrical resistance was given a name ‘Ohm’ that is so common now.
However, as shown below, the true significance of Ohm's Law is not yet comprehended.
OHM’S LAW PROVES PHYSICAL REALITY OF IMAGINARY NUMBERS
In a point of fact, there are two interpretations of the Ohm’s Law at the present time:
·
Ohm's law as applied to linear electric direct current circuits are formed by resistors or equivalent devices, which is
now understood in the same manner as it was understood by Ohm in his time;
·
Ohm's law as applied to the linear electric alternating current circuits, is understood somewhat differently, since such
circuits distinguish between the resistance of the resistors measured by real numbers, and resistance of the inductors
and capacitors, measured by imaginary numbers with different polarities.
The second interpretation of Ohm's law was made possible due to the use of the so-called symbolic method that was
proposed by Steinmetz [1] and according to which instead of universal formulas
iR ( t ) = uR ( t )
uL ( t ) = L di L ( t )
iC ( t ) = C
145 | P a g e
(1a)
R
dt
duC ( t )
dt
(1b)
(1c)
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Global Journal of Physics
Vol. 2, No 2, October 21, 2015
www.gpcpublishing.com
ISSN: 2454-7042
as applied to sinusoidal currents
i( t ) and voltages u( t ) were proposed the following formulas
uR ( t ) = Ri ( t )
(2a)
uL ( t ) = L dI exp( jwt )
dt
iC ( t ) = C dU exp( jwt )
dt
= jwLiL ( t )
= jwCuC ( t )
(2b)
(2c)
As seen, in contrast to differential and integral dependencies (1b) and (1c), dependencies (2b) and (2c) proved to be
algebraic resulting from the use of symbolic method. It allowed to introduce the concept of resistance both, for inductors
and capacitors
XL =
uL ( t )
= jwL
iL ( t )
(3a)
XC =
uC ( t )
1
=
iC ( t ) jwC
(3b)
Thus, it was found that while resistance of the resistors R is measured with real positive numbers according to the
expression (2a), resistance of the inductors L and capacitors C is measured with imaginary numbers of different
polarities according to expressions (3a) and (3b).
Therefore, the amplitude of the current
Im
flowing through any electrical LCR-circuit in full accordance with Ohm's Law
is determined by the amplitude of the voltage
Im =
Um
Z ( jw )
Um
applied to the circuit and module of its complex impedance
Z ( jw )
(4)
Over the past few years, millions of engineers around the world received practical results every day that were always in
full correspondence with the formula (4), which confirms the validity of Ohm's Law as interpreted by Steinmetz.
However... this result is only possible if the imaginary inductance and capacitance resistances, which correspond to the
expressions (3a) and (3b), are physically real. Meaning, that each measurement confirming the validity of Ohm's law
in electrical alternating current circuits also proves the physical reality of imaginary numbers that were introduced
500 years ago.
Otherwise, if the imaginary resistances defined with imaginary numbers (3a) and (3b) would not be actually physically
existent, value of the sinusoidal current flowing though the electric LCR-circuit would not change at the change of the
frequency of sinusoidal current applied to such circuit. Therefore, in particular, resonance should not exist in electric LCRcircuits. But, as it is known, it exists.
This is a unique feature of Ohm's Law as compared to other laws of the exact sciences. This feature of Ohm's Law is a
prerequisite for the inevitable future revolution in physics and other exact sciences, because, sooner or later, scientists
would have to acknowledge the reality of imaginary numbers which currently being denied by the special theory of
relativity. With everyday engineering practice Ohm’s Law proves what was not possible to prove even in the 21st century
with complex physical experiments MINOS at the US Tevatron collider and OPERA experiments at the European Large
Hadron Collider.
[2-8] also presents other evidences of the physical reality of imaginary numbers, using the study of oscillatory processes in
linear electric LCR-circuits, which can be replicated in any radio and electronic laboratory. These experiments, therefore,
in contrast to MINOS and OPERA experiments, are absolutely reliable and conclusive.
PHYSICAL ESSENCE OF IMAGINARY NUMBERS: STRUCTURE OF THE
MULTIVERSE.
Let us repeat it again as it is very important that Ohm's Law allowed to prove in the simplest and most accessible way the
principle of the physical reality of imaginary numbers, which could not be proved or disproved by scientists in physics and
mathematics for 500 years. Although this principle is proved in the theory of linear electric circuits, it is certainly a general
scientific principle as there is only one Nature. Therefore, all scientific theories and hypotheses in all sciences should be
mutually consistent (although, this requirement is not always observed: in physics, the theory of relativity and quantum
mechanics openly contradict each other). Consequently, in accordance with this principle, such theories should be
corrected.
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ISSN: 2454-7042
There is no need to correct anything in the theory of linear electric circuits, since application of Ohm's law has already
brought everything to an order.
But, there is a lot to correct in other sciences: theory of relativity, quantum mechanics, optics, hydraulics, acoustics, etc.
Let us show, for example, how this can be done in the special theory of relativity (STR), generally accepted version of
which currently affirms the principle of non-exceedance of the speed of light without any proofs. It is not difficult to guess
why it is being affirmed that way. The fact is that mass, time and other physical values that become imaginary at hyper
light speeds in the relativistic formulas, which are used in the STR to carry out all so-called mental experiments. But
founders of the STR failed to explained this.
Therefore, the second postulate, in addition to its original wording on the constancy of the speed of light [9], was
consequently amended with the formulation (which supposedly was equivalent to the original wording) on non-exceedance
of the speed of light. But, no one could prove this equivalence [10]. It was merely explained with inconclusive comments
on the impossibility of overcoming the light speed barrier in accordance with, for instance, the formula of Lorentz-Einstein
m=
where
m0
1 - ( v )2
c
(5)
m0 ‒ is the rest mass of the moving body (e.g., an elementary particle);
m ‒ is the relativistic mass of the moving body;
v ‒ is the speed of the body;
c
‒ is the speed of light.
As it is seen from the formula (5) that
lim v ® c m ( v ) = ¥ . Therefore, it was argued that infinitely greater energy is
required to overcome the light speed barrier and so, it is impossible to overcome it.
But the following obvious facts were ignored, at the least:
·
inability to overcome any barrier (for instance, inability to jump over the precipice) does not prove that there is nothing
behind this barrier;
·
inability to overcome any barrier (for instance, a wall dividing the room in your apartment) does not mean that it is
impossible to get behind the walls in any other way (e.g., through the doors and corridor).
Thus, to correct STR [11] in accordance with the principle of the physical reality of imaginary numbers, it is necessary to
explain what physical meaning can have imaginary mass, imaginary time, imaginary length, etc. in relativistic formulas at
v > c.
The following explanation was suggested [12-16]. Since mass, time, and other physical values become imaginary at
v > c , the corresponding physical objects (e.g., tachyons, which, by definition, cannot be registered in our universe) exist
in a different universe that was called tachyon universe for clarity purposes. But for us, this tachyon universe is invisible as
it is behind the horizon of events. At the same time, our universe is called tardyon universe (derived from the name of
elementary particles that move with sub-light speed ‒ tardyons). Invisible Multiverse that includes tachyon universe and
our tardyon universe is called hidden. The universes included into this hidden Multiverse are inertial reference systems
and, therefore, physical, chemical, biological and other laws in such universes are practically identical due to the first
postulate of STR.
But as it turned out, the formula (5) of Lorentz-Einstein does not match this condition. Therefore, it had to be corrected as
follows:
m=
where
m0 ( i )q
1 - ( w )2
c
(6)
ë c û – is the discrete function “floor” of the argument v c ;
q= v
w = v - qc
v
m0 ( i )q
=
1 - ( v - q )2
c
– is the local speed for each universe, which can assume values only within the range 0
£w£c;
– is the speed measured from our tardyon universe, which we should call as tardyon speed;
c – is the speed of light.
Other relativistic formula of STR can be corrected in a similar manner.
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ISSN: 2454-7042
As it is seen from the formula (6) and other corrected relativistic formulas that such hidden Multiverse, in addition to the
corresponding q = 0 tardyon and corresponding q = 1 tachyon universes also contains at least two parallel universes:
corresponding q = 2 tardyon antiuniverse and corresponding tachyon q = 3 antiuniverse. Moreover, universes and
anituniverses, both, tardyon and tachyon, cannot be annihilated due to the indicated order of their alternation in the
Multiverse.
But in fact, as it was shown by the author's calculations using data from measurements obtained from space stations
WMAP and Planck, there are several dozens, most probably twenty-one or twenty-two, universes in such hidden
Multiverse. Moreover, all these universes are parallel universes, and despite their immensity, they do not intersect in the
corresponding multi-dimensional space. During the operation of unknown to us mechanism of automatic adjustment of
their mutual spatial position, these parallel universes always slightly move with relation to each other, sometimes even
slightly penetrate into each other. Peculiar transition zones or portals appear in numerous places of such mutual
penetration of adjacent parallel universes into each other. Relatively small physical objects ‒ from elementary particles to
living inhabitants of the universes - can travel from one universe to another through these zones or portals. And it is
possible that such movements are relatively safe (same, as, for instance, household current is safe if one do not touch it),
as according to the law of communicating vessels, parameters of the medium in pre-portal and behind-portal areas should
be almost identical.
Astrophysical phenomenon of the dark matter/dark energy can serve as experimental confirmation of the existence of
such hidden Multiverse. According to such phenomenon, the share of the visible universe (e.g. tardyon universe) accounts
for less than 5% of the total mass-energy available in the space (i.e., hidden Multiverse). This phenomenon is considered
inexplicable in modern physics, as the dark matter and dark energy are not only completely invisible for unknown reasons,
but also because no chemical elements that make up our visible universe were found in their composition. Therefore, it
would seem that the existence of the dark matter and dark energy destroys the understanding of the matter that is
common in the science.
However, listed incomprehensibilities are only conditioned by the unwillingness of supporters of the current version of the
STR to abandon incorrect interpretations of the of the second postulate [10] (and its corresponding concept of
Monouniverse) and acknowledge principle of the physical reality of imaginary numbers.
If the physical reality of imaginary numbers is acknowledged, all features of the dark matter and dark energy within the
concept of the hidden Multiverse will be completely explainable [17-23]:
·
dark matter and dark energy are invisible because they are consistent with other invisible parallel universes of the
hidden Multiverse, except for our tardyon universe;
·
dark matter corresponds to parallel universes that are adjacent to our universe, and which are six according to the
calculations of the author with the use of WMAP and Planck data;
·
dark energy corresponds to the other parallel universes that are intercepted by adjacent universes, which are fourteen
or fifteen according to the calculations of the author with the use of WMAP and Planck data;
·
inability to determine the chemical composition of the dark matter and dark energy is explained by the fact that their
content is located in other universes, inaccessible to our tools.
CONCLUSIONS
Thus, Ohm's law in the interpretation of Steinmetz most convincingly proves the physical reality of the named imaginary
numbers and is one of the greatest discoveries in the history of science.
Physical natures that correspond to the imaginary numbers are always visible. Therefore, people do not even suspect
about their existence. But they have different explanations in different sciences.
For example, in astrophysics they relate to invisible parallel universes of the hidden Multiverse. Knowledge of mechanisms
of the portals’ operation (presumably, electromagnetic), which can be used for transition from one parallel universe to
another, will allow to create artificial portals, which in turn will allow for future travels not only in space but also in time.
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