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Vladimir Nesterov
Concept of “information” is widely used in modern
science; Latin “informatio” literally means “data” or
No scientist who dealt with basic studies of information
could discover physical essence of this concept.
Appearance of information theory was induced
by development of technical communication systems
which had to ensure information exchange. I’d like to
emphasize – technical systems, operation principles of
which are determined by physics laws, i.e. laws of material
world. Optimization of such systems operation
required first of all dealing with amount of information
which can be transmitted via communication channels.
That is why it is natural that first steps in this field
were fulfilled by employees of Bell Telephone Companie
– Н. Nyquist, R. Hartley and C. Shannon. Later
on results of these works formed a basis for Shannon’s
calculation of communication channels data throughput,
improving of messages coding and decoding methods
and solving of other questions related to optimization
of technical communication systems operation.
Collection of these notions, called by Shannon “mathematical
theory of communication”, became a basis
of classic Information theory. However in Shannon’s
works explanation of information physics was missing;
substitution of “information” and “amount of information”
concepts happened. Shannon’s Information
theory did not answer to “What is information?” question;
it only answered to “What amount of information
may be transmitted in time unit using a set certain
signals?” question. It should be understood clearly that
without revealing of “information” concept’s physical
essence and at the same time naming frequency characteristic
of code letters by “amount of information”
term, Shannon created a possibility for identification
of two absolutely different in their nature phenomena:
information as a physical category and information as
frequency of a certain message happening.
Norbert Wiener – father of cybernetics or “science
of control and communication in the animal and the maIn
the beginning was the Word.
Gospel of John
V.I. NesterovPhysical basics of informational interaction
chine” – also had no clear idea about physical essence of
information. “Information is information, not matter or
energy, it is something else”, – he wrote.
French physicist L. Brillouin noticed that Shannon’s
formula for information amount calculation
is similar in its structure to formula offered by Boltzmann,
which is used for entropy amount calculation.
Concept of messages entropy allowed Brillouin to postulate
“omnipresence” of information and assume that
measure of information amount, related to a certain
object, may be a complexity of its internal structure.
Abovementioned postulates and their consequences are
given by L. Brillouin in his studies in details. Brillouin
took the following value as the universal measure of information
I = k ∙ ln p, where
p – a “complexity” of a certain object’s structure; k – a
constant depending on chosen system of measure units;
ln – a natural logarithm.
This formula resembles Boltzmann’s formula for
entropy amount calculation:
S = k ∙ ln W, where
S – entropy, k – Boltzmann constant, W – thermodynamic
Hence appears one important circumstance: when
we lose information we increase entropy of a system, in
other words – we decrease level of its internal structural
I + S = const
as a consequence of the second law of thermodynamics
– entropy of a closed system is a constant value and
it cannot decrease with time.
In the 60’s of the last century thanks to L.
Brillouin “negentropy principle of information” appeared
and became widely known. Differing from
entropy, regarded as irregularity measure of a certain
system, negentropy usually means measure of order
or structural “complexity” of surrounding system related
to various entropic processes in physical world.
Brillouin offered to express information I and entropy
S in the same units – informational (bits) or entropic
B. Kadomtsev notes that values I and S are formally
equal because I corresponds to information of one single
state of many possible states, S is defined by multitude
of all states.
In modified in accordance with modern ideas
Information theory information is regarded from the
point of view of physical statistics as a certain mathematical
abstraction, a measure of algorithmic state of
chaos. Information theory describes principal laws of
information exchange, but it does not reveal its physics.
Quantum-entropic logic theory became a theory
regarding information as a material category revealing
physical essence of entropic-information interactions
and describing interaction of mass, energy and information
within a system.
Quantum-entropic logic theory postulates:
1. Information is a material category, just like energy
and mass of a system.
2. Due to the fact that information is material it follows
the conservation law. Information cannot disappear
without a trace or appear from nowhere. Total amount
of information in a closed system (a system which does
not exchange mass, energy and information with environment)
– is a constant value.
It should be noted that Quantum-entropic logic
theory deals with negentropic properties of information
only. Object of this branch of learning is something
poorly resembling what we call information in everyday
life. Indeed, in everyday life semantic, intensional aspect
of information prevails, but Quantum-entropic logic
theory does not consider semantics of information at all.
In 1923 duke Louis de Broglie, a young French
nobleman, assumed that wave properties are typical not
only for light but for matter also. His arguments were
that Einstein’s equation
E = mc2
(с – speed of light in vacuum) links mass with energy,
but on the other hand Einstein and Planck linked energy
and wave frequency. Combining these two principles
one may conclude that mass should have wave
incarnation also.
Quantum-entropic logic theory expands de Broglie
conclusions to all material mediums, including information.
It shows that all matter display wave properties.
Quantum-entropic logic theory offered a formula
for information wave radiation quantum which links in
with energy of a system through Planck constant.
I =
(h – Planck constant) links energy of any material
system with level of its complexity, in other words,
with level of its structural organization. Level of complexity
(structural organization) is the same essential
quality of any material system as mass and energy
of this system. Information has even more universal
character than mass, because a number of fundamen–6-
tal particles, such as photon, have no mass at all. But
all material objects, with no exceptions, have more or
less complex structure, that is why we probably should
speak not about quantum-wave dualism (where
“wave” term means force fields only), but about triunity
in description of material world, when information
is included into equation together with mass and
energy as a full member.
Electron interference phenomenon discovered
by Davisson and Germer demonstrated in reality that
electrons are similar to waves. Austrian physicist Erwin
Schrödinger assumed that these waves are electrons
“spread” along space. But this concept was too
inaccurate. How can “spread” electron be in several
places at the same time? It complicated interpretation
of what “spread” electron really is.
In 1926 German physicist Max Born suggested his
own interpretation of electronic wave. Born’s theory
relates to one of the most strange and incomprehensible,
from the point of view of human logic, property
of quantum theory. Nevertheless it is proven by great
amount of experimental data. According to this theory
electronic wave must be interpreted from the point
of view of statistical probability. But rightful question
arises: “How can probability function, a certain
mathematical abstraction govern electron behavior,
as if it is real physical field?” Here lies obvious logic
disagreement. Statistical probability, from the classic
physics standpoint, is non-material category and it
cannot be related to implementation of fundamental
laws of physics. As Einstein said about it: “He (God)
does not play dice”. Any physical theory, even if it is
mathematically flawless, must have internal noncontradictory
logical structure. Supporters of quantum
mechanics, in their try to fix logical disagreement,
say that probability in quantum-mechanical calculation
have higher fundamentality than roulette has.
But it is still unclear what this higher fundamentality
consist of? Probably wave function would get even
higher fundamentality in one case only: if it could be
regarded as a physical field. What is probability according
to Information theory – it corresponds to information
(I) of one state out of many possible states.
Hereby terms “probalbility” and “information” may
be unified in this context. From the point of view of
Quantum-entropic logic theory information is a material
substance, a physical field directly linked to energy
and mass of an object.
Thus application of Quantum-entropic logic theory
postulates may eliminate severe logical contradictions
existing in quantum mechanics.
One of properties of information fields, which
follows from quantum mechanics postulates, is that
information fields must be transferred by some class of
microparticles, just like electromagnetic forces, at the
level of fundamental particles, are transferred by photons.
In physics there is a tradition to call interaction
fields particles with names with “-on” endings, such
as “photon”, “gluon”, etc. that is why fundamental
particle of information-entropy exchange was also
called “informon”. So infomons are the most fundamental
quantum beam of information. Although infomons
are still to be experimentally proven (if it is even
possible someday), one can say with certainty that infomons
must have the following properties: they must
have no mass; they must have negligibly and vanishingly
small, but not zero, interaction energy and have
spin 2.
What is spin of a particle? Spin is a quantum-mechanical
term corresponding to moment of momentum
in classic mechanics. Fundamental particles have
“inherent” number of spin, equal to integral or halfintegral
number (in Planck constant units), which
never changes.
All known particles in the Universe may be divided
into several groups: particles with spin 1/2, which
form matter of the Universe; particles with spin 1,
which create forces acting between particles of matter
– photons, weak gauge bosons and gluons. Infomon
must have double spin of photons, gauge bosons
or gluons, i.e. spin 2, in order to transfer informationentropic
Superstring theory starts with suggestion about
what is the lesser indivisible component of matter.
For many decades generally accepted answer was that
matter consists of particles – electrons and quarks –
which are positioned as point which cannot be divided
and have no size and internal structure. Conventional
theory stated and experiments proved that
these particles are connected by various means, forming
protons, neutrons and vast variety of atoms and
molecules, forming everything around us.
Superstring theory offers another picture. It does
not deny principal role of electrons, quarks and other
particles, but it states that these particles are not
For the first time Superstring theory was formulated
in 1968 by Gabriele Veneziano, young Italian
physicist who worked in CERN and studied strong
nuclear interactions. Leonard Susskind of Stanford
University, Holger Nielsen of Niels Bohr Institute and
Yoichiro Nambu of Chicago University have offered
physical justification of Veneziano’s discovery. These
scientists have shown that interaction between particles
happens due to smallest, extremely thin, almost
rubber-like fibers of energy, few hundreds billions
times thinner than separate atoms of nucleus. These
small elastic fibers were called strings. And just like
guitar strings vibrate in various ways, each of which
creates different chords, superstrings may also oscillate
in various ways. But these oscillations do not
produce various music notes; Superstring theory says Physical basics of informational interaction
that they produce various properties of particles. Tiny
string vibrating in a certain way will have mass and
electron charge. In accordance with the theory such
vibrating string is something we use to call electron.
String vibrating in other way will have all required
properties to identify it as quark, neutrino or any other
kind of particles.
All families of particles are unified in Superstring
theory, because each of them appear from various vibrating
states (mods) done by one and the same basic
object – superstring.
Information fields’ properties analysis allowed
making a conclusion that in spite of the fact that Superstring
theory was discovered in attempt to understand
strong interactions, it is actually may be resolution
of another problem also. It may be quantummechanical
theory of information-entropy interaction.
Such conclusion is possible because in strings
oscillation spectrum John Schwarz and Joel Scherk
have found a mod corresponding to zero-mass particle
with interaction energy value about a zero and
spin 2. Presumably these characteristics are distinctive
features of informon. Thus string theory equation
contains quantum-mechanical description of information
The only parameter necessary for strings calibration
is their tension. How to define this tension? If we
could touch a superstring we would know its hardness
and would define tension just like we do it with guitar
or another string instrument. But because fundamental
strings are so small we cannot use this method and
we face a necessity to develop an indirect method.
Schwarz and Scherk have developed an indirect
method of strings tension defining used in Superstring
theory in 1974. Their calculation showed that intensity
of interaction transferred by string oscillation in
accordance to fundamental particle is inversely proportional
to a string tension. And as soon as informon
transfers vanishingly small interaction, obtained value
of tension must be enormous, about 1039 tons – value
of so-called Planck tension.
When guitar strings are fastened, which guarantees
constancy of their length, superstrings have
no such fastening limiting their length. Instead of it,
enormous tension of informon string will force loops,
which are examined by strings theory, squeeze to submicroscopic
size. Under Planck tension, with participating
sub-Planck fluctuations, informon string may
be squeezed to a size lesser than Planck length, i.e.
lesser than 10-33 cm. Thanks to such great tension
energy of informon string oscillating loop becomes
truly gigantic in comparison with usual scale of fundamental
particles physics, millions and millions times
higher than electron string energy.
According to modern conception of quantum
mechanics, there is no such thing as distance shorter
than Planck length and time span lesser than Planck
time (10-43 seconds). If concept of informon fields is
correct it means that existing concepts of space and
time – system in which quantum mechanics operates,
turns out to be incomplete and applicable in particular
cases only. Involvement of informons fields theory
consists in the following: space and time do not lose
their meaning in extremely small scales, lesser than
Procrustean bed of Planck length, instead of that they
modify into another, more fundamental concepts.
Decreasing below Planck scale becomes possible because
concepts of space and time continue in form of
other and more universal notions.
If we look at distances scale within Planck length
we will see that quantum-mechanical fluctuations of
transforming informon field are so substantial and
may cause so strong and uneven inflation of space
that it can turn into foamed, turbulent and swollen
form. John Wheeler offered term “quantum foam” to
designate a state discovered during studies of ultramicroscopic
space and time in scales lesser than Planck
length. In this “quantum foam” terms of classic physics
such as “farther” and “closer”, “in front” and
“behind” (even “before” and “after”) become fuzzy
and vague.
Basic principles of general theory of relativity and
quantum mechanics allow defining of approximate
scale of distances, passing to which turns off laws of
existing physics and turns on other quantum-entropic
logics. Smallness of Planck constant and vanishingly
small value of information-entropy interaction force
has negligibly small size, about 10-33 cm. Here is an
example to illustrate this size: if we scale up size of
atom to a size of the Universe, Planck length in this
case will be equal to height of two-storied building.
There is a concept of phase states in physics. In
general case phase relates to possible descriptions
of physical system at changing of its parameters on
which this system depends (for example, temperature,
string tie constant, type of space, time, etc.).
In respect to a matter phase state means one of
possible states of the matter: solid, liquid and gaseous.
We take ice as an example. If you increase its temperature
above 0 degrees Celsius, solid ice will melt
down and eventually turn into water. Ice is a rock-solid
state, water is viscous liquid. Simple observations
show no evident signs that their molecular composition
is identical – H2O. If you continue to heat up
water, in some period of time, when temperature of
water reaches 100 degrees Celsius, another transformation
will happen: liquid water starts to boil and
turn into steam, which in its turn does not resemble
water and ice in appearance at all. Although of course
all three substances have the same molecular composition.
Changes from solid to liquid and from liquid to
gaseous are known as phase transitions. -8-
So many words about ice, water and steam and
their phase transitions – how can it be related to matter
and information? Quantum-entropic logic theory
states that not only a substance may be subjected to
phase transition, but all matter also may. There are
grounds to be sure that when matter goes through
specific critical states, similar to 100 degrees Celsius
for steam and 0 degrees Celsius for water, it is also
subjected to radical extensive transformation.
Substance may be conventionally represented
as “frozen part” of matter. When a particle of a substance
reaches speed close to speed of light in vacuum
(300 thousand kilometers per hour) it starts to “melt”
and turns into energy. Therefore force fields may be
rendered as “liquid” part of matter. When size and energy
of a particle decreases down to Planck values energy
starts to “boil” and transform into information.
Thus information field may be represented as “gaseous”
part of matter.
Big bang theory is the basic theory of space origin.
This theory describes evolution of space from
split second after something had happened to the existence
of the Universe, but it does not say a word
about time zero. Big bang theory does not cover the
bang itself. It says nothing about what had exploded,
why it had exploded, how exactly it had exploded
and, frankly speaking, had there been an explosion
at all? The Big bang is a totally mysterious phenomenon.
What could be that outside directed force which
started the expansion of the Universe? Certain types
of strong repulsive forces must have played a crucial
role in the bang, but what natural forces could
it be? For many decades this most important of all
cosmological questions remains unanswered. And
only in 2000s was made a suggestion that this force
could be transforming informon field. During time
span, in comparison with which nanosecond might
seem eternal, early Universe provided a scene where
information displayed its repulsive properties, dragging
one region of space from another with inexorable
force. Repulsive effect of transforming informon
field was so strong that it not only engaged the bang,
but revealed something which forces the Universe
to expand for already 14 billion years until the present
day. In theory, which operates information field,
early Universe expanded with overwhelming gigantic
coefficient, in comparison with standard Big bang
theory, thus enlarging our cosmological perspective
to the degree when we understand that our galaxy is
the one among hundreds of billions galaxies.
The “Information bang” theory offers the most
important modifications of standard Big bang theory
propositions, gives an idea about events which happened
at point zero and in the earliest moments of
the Universe existence. This theory gives answers to
key questions lying beyond standard model of the Big
bang theory, makes a number of predictions which
find experimental proofs.
These questions which could not be answered by
standard Big bang theory:
1) Where all this mass and energy filling the Universe
came from?
2) What causes inflation of space and matter?
were successfully redirected to Theory of extensive
transformation of information into substance and
But even in this situation some fundamental basics
remain unclear:
– Was there a time before the Information bang
and if yes, what was it like?
– What caused informon field to initiate the Information
These questions remain unanswered and still wait
for their discoverers. They are part of urgent scientific
matters that move forward cosmological studies and
remind us about many tangled knots, which we have
to untangle before we say that we completely understand
structure of the Universe.
Some brand new aspects in understanding of
space expansion from the point of view of informon
field’s universal effect in any scales of matter structural
organization are worthy of mentioning separately.
Until the present days the Universe expansion
is regarded by many scientists only in mechanistic
way, as recession of galaxies, without involvement
of other astronomical and physical objects of lesser
sizes. Theory of extensive transformation of information
into substance and energy regards the Universe
expansion as global and universal process, involving
The Big Bang space with all contained in it material objects at any Physical basics of informational interaction
distances from the Universe down to separate quantum
of matter.
From this point of view, if space expands it
should mean that in addition to recession of galaxies,
inflating space within a certain galaxy will move
all its stars away from each other, in its turn inflating
space inside every star or planet or inside us or inside
anything will move all constituent atoms away from
each other, and inside atoms – electrons, protons and
neutrons and deeper and deeper down to the smallest
components of matter. So because all tissue of space
expands, all basic physical constants will expand proportionally.
Space will force every thing, including
our measuring bars, increase its size and that is why
it is impossible in the essence to recognize that some
expansion really happens.
Relying on special theory of relativity Einstein
proclaimed that gravitation and acceleration are absolutely
identical. Accelerated observer, according to
Einstein, warps space just like gravitation does. Moreover
Einstein proved that in general gravitation and
acceleration are indistinguishable.
There is scientific methodological principle,
named after philosopher-nominalist William of Ockham,
saying in simplified way: “Entities must not be
multiplied beyond necessity”.
Following this principle, if all problems related
to time-space warping may be solved from acceleration
standpoint only, it means that absolutely similar
and identical to them effects related to gravitation, in
the final analysis may be brought to accelerated movement,
not involving such category as gravitation. In
other words gravitation may be “cancelled” due to
There is no doubt that gravitation is the basic
physical category underlying modern physics including
general and special theories of relativity. Any attempt
to discard it will be interpreted as madness
rather than manifestation of scientific courage. But is
this idea crazy enough to be true?
All abovementioned requires more detailed explanation
and we will try to present it.
Theory of extensive transformation of information
into substance and energy says that space expansion
provides extension of any physical body included
in tissue of space. Thus Sun, Earth and other astronomic
objects, usually considered to be as stationary
ones, in fact extend, inflating from inside as balloons.
If we could prove that astronomical objects, including
stars and planets, not only extend, but extend with
acceleration, in this case using principle of acceleration
and gravitation equivalence, gravity effect may
be brought to accelerating extension of astronomical
body. I.e. accelerating extension may completely imitate
gravitational attraction.
Thus whole question, in general, is to define if
Universe extends with or without acceleration now?
Two groups of astronomers – one under guidance
of Saul Perlmutter in Lawrence Berkeley National
Laboratory, another under guidance of Brian
P. Schmidt in Australian National University – have
proved fact of accelerating expansion of the Universe
by measuring of remote supernovas speed in the 90’s
of the last century. Thanks to innovative technology
of simultaneous observation of thousands of galaxies
via wide-angle telescope, these teams were able to
find about four dozens of supernovas at various distances
from Earth. After careful calculation of distance
and velocity of recession both groups came to
unequivocal conclusion: speed of the Universe extension
increases, i.e. space expands with acceleration.
Researchers of supernovas concluded that observed
accelerated expanding requires directed outside repulsion
of cosmological constant, function of which
may be fulfilled by transforming informon field. Informon
field may play role of a force imitating gravitation
at phenomenon of astronomical objects accelerated
Thus when you drop a glass, it is not gravitation
field that attracts it to Earth, but expanding Earth
bumps into the glass.
Paraphrasing well known Einstein’s quote we
may say that Quantum-entropic logic theory is too elegant
to be wrong. It is characterized by inner logical
consistence; it does not contain inner logical absurdity.
It is the case when beauty and elegancy of one or
another physical theory corresponds to beauty and elegancy
of surrounding world.
Of course there is no assurance that such considerations
will lead us to the truth. Nevertheless all
Receding galaxies-10-
About the author:
Nesterov Vladimir Igorevich – physician, biophysicist, full member of Academy of Medical and Technical
Sciences. Chairman of the Institute of Practical Psychophysics directorate; President of International Academy
of non-linear diagnostic systems.
the time, especially now as we enter an era when our
theories describe fields which cannot be experimentally
studied, physicists will count on such aesthetic
consideration that may help to avoid dead ends. Until
now such approach demonstrated its strength and
forecasting power many times.
Quantum-entropic logic theory is not a modest
theory. Its objectives and promises are great and it is
exciting and praiseworthy, because if a theory claims
to be a theory of the Universe, it must be equal to the
real world not only in approximate draft, but in every
small detail also.
Author would like to thank Dr. Brian Greene for his
help with this article. References
1. Claude E. Shannon, Warren Weaver. The Mathematical Theory of
Communication. UnivofIllinoisPress, 1963. ISBN 0-252-72548-4
2. C. Shannon, Papers in theory of information and cybernetics. — Moscow: Publishing house of
foreign literature, 1963. — 830 p.
3. H. Nyquist, “Regeneration theory”, Bell System Technical Journal, vol. 11, pp. 126-147, 1932
4. Hartley R.V.L. Transmission of information — Bell System Technical Journal – 7. — 1928. —
С. 535-63.
5. Norbert Wiener Cybernetics: Or Control and Communication in the Animal and the
Machine. — 1948. — Paris, (Hermann &Cie) &Camb. Mass. (MIT Press) ISBN
6. Léon Brillouin La science et la théorie de l’information (Masson, 1959)
7. Brillouin L. Scientific indeterminacy and information. – Moscow: Mir, 1966.
8. Kadomtsev, Boris Borisovich. Dynamics and information. — Moscow: Publishing house
«Advances of physics», 1999, ISBN 5-85504-010-3
9. L. de Broglie. Ondeset quanta // Comptesrendus de l’Académie des sciences. — 1923. —
Vol. 177. — P. 507—510.
10. C. Davisson, L.H. Germer (1927). “Diffraction of electrons by a crystal of nickel”. Physical
Review 30 (6): 705–740.
11. Schrödinger, Erwin (December 1926). “An Undulatory Theory of the Mechanics of Atoms and
12. M. Born. Problems of Atomic Dynamics — MIT Press, 1926.
13. Letter from A. Einstein to M. Born dated 12 December 1926 [Max Born,Physics in my
generation, Springer-Verlag, New York (1969), p. 113]. Also: “…Even the great initial success
of the quantum theory does not make me believe in the fundamental dice-game…” — Albert
Einstein, 7 September 1944 (p. 149). The Correspondence between Albert Einstein and Max
and Hedwig Born 1916-1955 with commentaries by Max Born, ISBN 0-8027-0326-7
14. Veneziano G., NuovoCim., 1968, 57A, 190 (also unpublished manuscript by Suzuki M., 1968)
15. L. Susskind, “Harmonic Oscillator Analogy for the Veneziano Amplitude,” Phys. Rev. Lett. 23,
545 (1969).
16. L. Susskind, “Dual-Symmetric Theory of Hadrons I,” IlNuovoCim. 69A, 457 (1970).
17. H. B. Nielsen, “An Almost Physical Interpretation of the N-Point VenezianoModel,”submitted
to Proc. of the XV Int. Conf. on High Energy Physics (Kiev, 1970), unpublished.
18. Y. Nambu, “Quark Model and the Factorization of the Veneziano Model,” p. 269 in Proc.
Intern. Conf. on Symmetries and Quark Models, ed. R. Chand, Wayne State Univ., 1969
(Gordon and Breach, NY 1970) .
19. Y. Nambu, “Duality and Hadrodynamics” Notes prepared for the Copenhagen High Energy
Symposium (1970).
20. Scherk und Schwarz. Dual Model for Non Hadrons. In: Nuclear Physics B. Band 81, 1974
21. Scherk und Schwarz. Dual models and the Geometry of Spacetime. In:Physics Letters B. Band
52, 1974
22. John Archibald Wheeler, Kenneth William Ford. Geons, Black Holes, and Quantum Foam: A
Life in Physics (1998). NewYork: W.W. Norton&Co, ISBN 0-393-04642-7


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