Presented at the 6th Congress of the
European Union of Systemics, Paris, 19-22 September 2005.
On Fractaquantum Hypothesis
In this contribution, we present the following: restore some of the fractal
geometry key elements, introduce an extension of the atom notion,
restore the importance of the quantum
mechanics which is needed to describe the microscopic world. We
introduce the fractaquantum hypothesis, which was
for the first time at the 5th
Congress of the European Union of Systemics at Heraklion in 2002. We discuss
also about the acceptance of this hypothesis. Then we develop it in three different
directions. The integration of the simple element leads us to a quantum theory of the
angel. More complex assembling can be described with the help of graph theory
and the emphasising is placed on the importance of the loops in such models.
Finally, we shall observe if the fractaquantum hypothesis joined with recent
atomic physics experiments help imagine intricate macroscopic states.
A propos de l'hypothèse fractaquantique
Dans cette contribution, nous présentons quelques éléments fondamentaux de
géométrie fractale, introduisons une extension de la notion d'atome, puis rappelons
l'importance de la mécanique quantique pour décrire le monde microscopique.
Nous énonçons l'hypothèse fractaquantique,
introduite lors du
cinquième congrès de l'Union Européenne de Systémique
à Héraklion en 2002.
Nous discutons de la recevabilité de cette hypothèse, puis nous la développons dans
trois directions. L'intégration de l'élémentaire conduit d'abord
à une théorie
quantique de l'ange. Les assemblages plus complexes peuvent être décrits par la
théorie des graphes et nous insistons sur l'importance des boucles dans de tels
modèles. Enfin, nous posons la question de savoir si l'hypothèse fractaquantique,
jointe aux récentes expériences de physique atomique, permet d'imaginer des
états macroscopiques intriqués.
In this contribution, a certain number of well-known notions of physics and mathematics
are freely used through a specialized vocabulary. When this kind of notion
appears in the text we use the expression "so-called" without any complete
explication about the associated meaning. Introducing a new notion, we describe it in
general. However, we will continue to use quotation marks all along the text, especially
for the words "atom" and "q-angel".
Intelligence is in the loops!
Intricate macroscopic states?
First statement relates to the shapes that Nature shows to our eyes. The first one is a
straight line, even if this fact has been difficult to evidence. Nevertheless, the
foundation of classical mechanics
(G. Bruno, 1584,
G. Galilei, 1632)
assumes that without
any interaction, a classical object follows a so-called uniform motion with a constant
velocity. The difficulty to evidence such a principle is the practical impossibility to
observe an object without interaction with the external world. Effectively, the
breakthrough done by
(Principia, 1687) when he realizes that "the apple and the
Moon fall down to the Earth in the same manner" is a fantastic example of mental
unification of multiple observations. We will not comment here the high value of the
so-called Cartesian doubt (see the
"Les sens me
trompent. Donc, je doute. Donc je pense..." ["Senses are deceiving me. Thus, I
doubt. Thus, I think..."].
The straight line is generalized with the geometrical notion of geodesic, i.e. the curve
of minimal length between two points. This notion is fundamental for the development of
modern theory of gravitation
1915), which is, following
E. Mach (1921),
a natural generalisation of
Newton theory. We refer the reader e.g. to the books of H. Weyl (1921) or S. Weinberg
(1972). This theory claims that the matter creates a curved space. A consequence of this
fact is the existence of so-called gravitational lens. A dark object separates a light
source from the observer on Earth. The light is curved by dark material and separates it
into several rays. An observer can display several light spots in the sky and could a priori
think of the
presence of multiple sources.
The precise observations and analysis
done by K. Chang and S. Refsdal (1979), and J. Hewitt, G. Langston and co-authors (1986)
can be considered as an example of
Descartes' preliminary remark:
"the appearances are misleading".
The trouble is more important after the discovery of
B. Mandelbrot (1975)
of the so-called
fractal geometry. The fundamental remark is as follows: if we suppose that "the big is
analogous to the little", we obtain of course the straight lines but also geometrical
shapes that are absolutely not straight lines, called fractal curves. A fractal curve has
an infinite length and remains unchanged under very simple geometric
transformations. These self-similar geometrical shapes are present in our natural
environment with trees, clouds, ferns or
among others. They are present also in our own
body with the detailed structure occupied by the lungs. A partial piece of a tree is
analogous to the entire tree and this fractal property is characteristic of the fact that
"the big is analogous to the little". Moreover, the mathematical nature of corresponding
objects is complex and non-integer dimensions have to be considered (see e.g.
B. Sapoval, 1997).
This discovery has an important development in a lot of fields of knowledge, from
mathematics with A. Douady and his team in Orsay (see e.g. the film about the so-called
rabbit dynamics realized with F. Tisseyre and C. Weingarten, 1996), astrophysics and the
so-called scale relativity
(L. Nottale, 1998),
(G. Cohen-Tannoudji and
M. Spiro, 1986), finance markets (J.P. Bouchaud, M. Potters, 2000), up to urbanism
(N. Salingaros, 2001).
Let's bare in mind that there is no constraint, Nature offers a spatial
self-similarity: the "big" is analogous to the "little", even if the corresponding shapes take
a complex appearance. A final remark relates to the straight line: if we imagine that the
natural evolution is always a straight line, in what kind of mathematical space a fractal
geometry can be considered as a straight line? In which "space" the development of a
cauliflower follows a straight line?
Following a vision that comes from the antic Greek culture (we refer to
J. Salem, 1997),
we call "atom" (or elementary particle) any natural object whose qualitative properties
are modified at least in one subset if we divide it into two parts. Of course, the modern
J. Perrin (1913)
that are studied with the so-called atomic physics are "atoms" in
our understanding. Note here also that it is also the case for all classical elementary
particles of microphysics: proton, neutron, and electron. A stable structure like a
molecule is also an "atom" in our understanding. Moreover, the notion of "atom" is not
reduced to the micro-scale and we consider here a living cell as an "atom", due to all the
properties that are strongly modified or destroyed if it is cut into two parts. We extend
the family of "atoms" to highly organised living organisms, including mammals and human
beings. At a superior scale, it is not clear for us that the entire social organisation of
life and exchanges on Earth constitutes or not an "atom", as suggested by
J. Lovelock (1979) or
P. Teilhard de Chardin (1955).
The quantum theory considers that Nature is composed with elementary grains, insecable
components (see e.g. the book of
B. Diu, and
F. Laloë, 1977). It has
been founded during the period 1920-1930 by a collaborative approach of well-known
L. de Broglie,
M. Planck and
among others. It gives on a
microscopic scale a mathematical description of "what can be measured and predicted with
the human experiments". This theory consists in a semi-empirical approach and also demands
a high level of mathematical developments. In this contribution, we will reduce the latter
to the strict minimum.
The main issue due to quantum theory according to us is the separation between "matter" and
"relations". On the one hand, matter is composed with so-called fermions (protons,
electrons, etc.) that are indistinguishable and follow the
statistics of Fermi-Dirac.
On the other hand, the relations, i.e. the interactions between elements of matter, are
composed by so-called bosons, like photons, that are the elementary components of
light. The bosons are also indistinguishable and follow the
statistics of Bose-Einstein.
The indiscernability of identical quantum "atoms" is a fundamental postulate
of the theory that is in clear accordance with the experiments. In particular, it is not
possible to distinguish between two electrons or between two photons. According to
(1951), [page 494 of the Dover edition of his book]: "... different electrons do not have an
identity, since they do not even act like separate and distinct objects, which are
capable, in principle, of being identified". Moreover, the Fermi-Dirac statistics implies
also the so-called
Pauli exclusion principle
that claims that two analogous fermions
cannot occupy the same position in space. Our comment about the
Pauli exclusion principle
is that "matter creates space, bosons give it a structure".
The fractaquantum hypothesis is motivated by the two preceding remarks; Nature is both
fractal and quantum. Consequently, the fractaquantum hypothesis
(2002) express that the
quantum approach is relevant for all the "atoms" in Nature, whatever their size.
The main drawback of the fractaquantum hypothesis is the contradiction of quantum
indiscernability with macroscopic appearances concerning human beings for example. It is
obvious that "we are all different"! A brutal position is to stop this research and to admit
that some kind of macroscopic quantum effects do not exist. Nevertheless, in the same
spirit than from previous authors like
W. Heisenberg (1969) for pioneering
ideas concerning quantum extensions,
M. Locquin (1995) for the human language,
J.J. McFadden (2000) for biology or
H. Stapp (1993) for mind and brain, it
seems important to incorporate the quantum approach in our understanding of the world at
our macroscopic scale. We prefer hereafter to discuss the acceptance of the fractaquantum
Firstly, the classical philosophy of
Descartes insists on a preliminary fact that "our
senses are deceiving us". Even if the appearances are contradictory, the fact of thinking
creates the fact of being. Secondly, the history of science shows (see
A. Koyré (1966)
and his introduction to the famous book of
N. Copernic, 1543) an example where the initial
mathematical hypothesis was not completely correct, thus in contradiction with the precise
know-how developed at this time.
Copernic supposes that the planets follow exact circles
around the sun whereas ellipses
(J. Kepler, 1609)
are necessary to explain the complex
apparent movement of planets in the sky for one year. Thirdly, if we go back to the human
example, the common points between two human persons are much more important than the
different ones. The existence of medicine establishes empirically this fact! Moreover,
recent discoveries concerning the genomic structure of deoxyribonucleic acid
in each human cell (J. Venter et al, 2001) show that two human
deoxyribonucleic acid sequences coincide
up to 1 for 10000 parts. Even if the so-called single nucloitidic polymorphism is widely
studied in order to make in evidence local mutations (see e.g. Z. Zhao et al, 2003), the
first established accounting fact from genomic studies is that two human beings have the
same sequence of deoxyribonucleic acid up to 99.99%!
It is very interesting in our quest to review the possibilities of inter-changeability of
two cells during the embryogenesis. As we all know (see e.g. the book of U. Drews, 1993),
a complex organism such as a human being comes from a single cell that divides many times
and particularizes themselves. At a certain step of embryogenic development, all the cells
are identical, they are a priori interchangeable and after a certain time,
they are different, they
look different and most important, they have been specialized in specifc functions in
order to promote the development of the entire "atom" to the superior scale. The
understanding of the exact dynamics during the embryogenesis still is an open question
(see e.g. D. Weisblat, 1998). We consider here that ethical reasons naturally limit the
field of scientific research. We can also consider this fact as a macroscopic version of the
Heisenberg inequalities (see his
book (1969), p. 147 of the
French edition): "we
cannot make any observation without disturbing the phenomenon under observation".
We can conclude this discussion about the acceptance of the fractaquantum hypothesis by
stating that is relevant for small space scales (nuclear physics, atomic physics,
chemistry). Because macroscopic "atoms" are recognized, this hypothesis can be
considered a priori as irrelevant for macroscopic
scales that include biology or sociology. One could
conclude that the fractaquantum hypothesis is absurd and one could not consider it
anymore. Our motivation to go one-step further is firstly motivated by classical
philosophical observations introduced by
Descartes (1641): " appearances are
deceiving". We do not forget also that history of science shows examples where a
contradiction between theory and observation can be present at the "zero order"
of the theory. Thus our research is going further.
Once the fractaquantum hypothesis is taken into consideration, we can explore its
consequences for simple associations and configurations. Let us consider a system composed
by two identical particles of matter; two fermions linked together by one relation, in
fact a set of identical bosons that establishes the structure. Such a structure is present
Fermi gases (see e.g. D. Petrov, M. Baranov and
G. Shlyapnikov, 2003). For such
a quantum system, the so-called spin, i.e. the way the "atoms" are turning punctually
around themselves (!) has discrete values of the type 0, ½, 1, 3/2, ... and we refer
again to the book of D. Bohm or the one of
G. Cohen-Tannoudji and co-authors. Moreover,
the so-called spin-statistics observation assumes that fermions may only have a spin of
the semi-integer type ½, 3/2, ...)
and bosons have an integer spin equal to 0, 1, 2, ...
We insist on the fact that this notion of spin, necessary to explain some
precise structure in atomic spectra, like for example the so-called abnormal Zeeman
effect, has no classical analogous. Moreover, the notion of spin is mathematically
associated with the way the so-called
group of rotations of the usual three-dimensional Euclidian
space can be mathematically represented by matrices of various dimensions.
The result of this formalism (the so-called
matrices, see e.g. his book, 1933) gives the possibility to compose, to
add two different spins. This addition has of course some analogies with the usual
addition of planar vectors, but the result is completely different. In particular, the
addition of two simple "½ spins" leads to a structure that has a spin equal to zero or to
the unity. We have done in our Andé's (2003) communication this classical
calculus. Moreover, the association "½ + ½ = 1"
is related to symmetric states. This is in
contradiction with the
Pauli exclusion principle
that claims that two identical
particles cannot be in the same quantum state. On the other hand, the association
"½ + ½ = 0"
is giving an anti-symmetric state for the double system. This result is widely used in
atomic physics for the construction of so-called molecular orbital for complex atoms, and by
D. Bohm (1951)
as an example of so-called intricate states.
Let's bare in mind that the quantum association of two identical particles of
spin equal to ½ conducts to a boson of spin equal to zero. However, such a boson is a
relation because it is a quantum "atom" of integer spin. Therefore, the
anti-symmetric association of two "atoms" of matter naturally
defines a new relation.
A fractaquantum consequence of this microscopic property is the existence at our scale of
a lot of temporal associations that are constructed and exist in order to express some
relation, some communication, some exchange. In reference to the classical Biblical
traditions that call an angel the "messenger of the Lord", we call (since 2003) a
"quantum angel", or abbreviated a "q-angel" the association of two "atoms"
in order to express a
relation. A "q-angel" is composed by two "atoms" plus a relation between them. It is in itself
We do not insist here on the coherence of such structures and simple diatomic molecules
that found chemistry.
The first example of a macroscopic "q-angel" is the simple conversation between two
persons. The internal sense of the relations is associated with the words that are
exchanged. The energetic transfer between the two actors is very low (the energy of the
acoustic wave!) whereas the mass of this "q-angel" is quite impressive. The "q-angel" is
defined as the two actors of the exchange including their exchange, all this during the
exchange. The analogy of such "q-angel" (with a very big mass for a very weak interaction)
with the so-called intermediate boson, existing under three forms named W±
is very interesting (see C. Rubbia (1984) and the book of
M. Spiro, 1986). Bare in mind that that these intermediate boson has
a mass equal to 90 to 100 times the mass of a proton and a length of life estimated to
Other examples of "q-angels" associated with the relation between two persons can be
considered: danse, love, sexuality, etc. Moreover, different "q-angels" can be considered
in the creation of a new human being. They have in this case a complex scale dynamics. The
first "q-angel" is composed by the loving couple, then the second by the union of the two
gametes and finally the third one by the association of the mother and the foetus. Bare in
mind that during the nine months of the pregnancy, the mother associated with the foetus
can be considered as a "q-angel", i.e. a complex structure associated with
a relation defined
in this case by the development of the embryon. We could multiply the examples of "q-angels"
where two "atoms" collaborate in order to give existence for some message. What is first
important for us here is the fractal beauty of analogy between microphysics and
Intelligence is in the loops!
Having considered the relation between two "atoms", the general situation of n
"atoms" interacting together seems too much difficult. Consider
firstly that when n "atoms" interact,
the number of possible two by two interactions, the number of possible "dual bosons",
is equal to n(n-1)/2.
Remark that this number is exactly equal to n when n=0 (no interest!?) or when
n=3. The particular case of three "atoms" interacting together is characterized by the
fact that the number of dual relations is exactly that of matter elements.
A fundamental of such a triangle is present in Nature for a three atomic molecule. The
most famous example is of course
water (H20 !). Due to the differences between hydrogen and
oxygen atoms, this molecule is still very complex (see e.g. S. Zhu, M. Evans, 1996). We
prefer here to develop the internal structure of a proton or a neutron. According to
so-called quark theory developed by
M. Gell-Mann in the sixties (see his book, 1994), the
proton is composed by
(three fermions) interacting via a permanent exchange
(internal so-called coloured bosons for strong interaction). If the
observation of isolated quarks is not possible at usual low energies, the experimental
evidence of quarks is now well established (see
R. Taylor (1967) and
H. Kendall, 1972).
What matters for our communication is the kind of representation that is given by a
computer simulation of a single proton (see e.g.
J.F. Colonna, 1992).
What is obtained is a simple triangle:
the vertices are associated with the quarks and the edges with the permanent exchange of
coloured gluons. Our observation is simple: this kind of picture has a nontrivial
topological structure with one hole (also called loop, or cycle) inside. The correct
mathematical definition of a loop is not elementary. We just have to know here that such a
rigorous definition is possible in the framework of so-called
(see e.g. the book of
C. Berge, 1969).
Consider set of so-called vertices (or fermions for our example, "atoms" of matter) are in
relation, interact through a given set of binary links, edges between two vertices. For
example, the "q-angels" of the previous paragraph corresponds to
n=2, λ=1 whereas the
proton composed by three quarks is modelized in this approach with n=3, λ=3. More complex
picture can be considered and the use of so-called graph theory is now classical: in the
framework of chemistry
(M. Eigen, 1971),
(H. Atlan, 1979)
and even in electrical
and mechanical engineering (see e.g. our work with
F. Rapetti and
2003). Analysing a (connected) graph composed by n vertices and
λ links, the number γ of
loops or cycles is equal to γ=λ-n+1.
For a "q-angel" there is no loop (γ=1-2+1=0)
and this kind of structure can be simply topologically reduced to a
simple vertex. With the example of a triangle, we have
γ=3-3+1=1, making in
evidence one cycle. Then the interaction can circulate and be stabilized in the time the
same way than with a classical regulator in automatics (see e.g. the book of
P. Faurre and M. Robin, 1984).
The graph theory is a good mathematical framework for the description of permanent
structures. Our problematics for fractaquantum hypothesis is now the following: given a
certain number of "atoms" and relations, is it possible to consider the entire graph as a
new "atom"? Referring to
I. Prigogine (1947) and
existence of stable highly organized system demands a permanent exchange with the
environment. As a living system, our body is in continual evolution whereas we remain the
same human being! Consequently, the number n of "atoms" for the
new structure at the superior
scale has to be variable. If the number n is varying what could be permanent are the
topological invariants, the cycles, the loops for variable number of "atoms" interacting
in a permanent changing way. As we have suggested in 2004, "intelligence is in the loops"!
Loops allow the so-called feedback regulation that maintains the nontrivial topological
structure. Of course, this basic idea wants developing as per e.g. D. Harel, Y. Koren
(2001) in a "multiscale graph theory". The vertices of the structure at the upper scale
could be the permanent loops of the given graph. The interaction between these loops has
to be precisely defined. Further research has naturally to be considered...
Next step is to consider the "complex association" of "atoms" linked by "relations". Note that a
first example at the macroscopic scale is the crowd and its so-called libidinal links, as
suggested by S. Freud (1921). In this case, the structure is fragile and the rupture
of the links with the leader provokes the panic, i.e. the death. Consequent to our
hypothesis that "intelligence is in the loops", we can conjecture that the libidinal links
inside a crowd does not present any loop!
We now return to quantum theory and consider the astonishing phenomenon observed by
A. Aspect and his colleagues (1982). The story begins with the so-called
paradox (1935) and the possibility of existence of so-called
hidden variables (D. Bohm, 1951).
These authors consider a so-called Gedanken Experiment
where two systems (two spins for D. Bohm) have interacted in the past, and form a
so-called intricate structure like a "q-angel".
From a so-called classical realistic point of view, we are in presence of
two objects interacting together whereas from the quantum point of view, we are in
front of a unique "atom" that occupies two different macroscopic spatial positions during
the experiment that we will name "EPRB-atom" hereafter. It is impossible here to develop the entire
thoughts yield by this so-called EPRB paradox and we refer the reader to the books of
D. Bohm (1951),
M. Bitbol (1996).
When a measure occurs, the so-called reduction of the wave packet of the quantum approach
predicts that the "EPRB-atom" remains unique and responds in a holistic manner
even if it occupies two separate space positions! There is a natural problem with the
confrontation of such a point of view with the Einsteinian realism and in particular the
theory of relativity that claims that no interaction can proceed at a celerity superior to
the one of the light. A detailed analysis of possible cross-correlations has been proposed
by J. Bell (1964). As a result, the so-called Bell inequalities show that precise
experiment is possible in order to test whereas the two components of the "EPRB-atom"
remains correlated or not when they occupy different space positions. Finally, the
question is to know whether the quantum mechanics gives a so-called complete description
of the world, as defended by N. Bohr (1935), or not. The experiment of two intricate
photons has been proposed and realized with a great success by
A. Aspect (1982). The
result shows that quantum mechanics gives the good prediction; the Bell inequalities are
not satisfied by the experiment, even if "in many other situations, the Bell inequalities
are not violated" [A. Aspect,
public conference at Orsay University, 02 February 2005].
Consequently, the holistic vision of the intricate photons is now experimentally
We have to reconsider the notion of space and matter, as suggested by
(2002). In this quest, we have suggested in 2004 to consider "space"
as a mathematical non-separated continuum. With this kind of mathematical notion, the
"two" photons of the Aspect experiment occupy the same locus in space-time (!) and the
duality of photons is still an appearance! Once again, "our senses are deceiving us"!
However, what kind of mathematical model could be considered for general situations
in replacement of a
so-fundamental notion like "space"? Moreover, the quantum theory itself is founded on the
classical existence of a so-called Kantian a priori (E. Kant, 1787) called space, which is
preliminary to any experiment. Moreover, the predictions of quantum mechanics are
formulated in terms of probabilities in the usual Cartesian space! We will not discuss
here longer the aesthetic contradictions that are included inside the Copenhagen
interpretation of quantum theory... Bare in mind that quantum theory has a great value,
because... it works!
Intricate macroscopic states?
A natural question is associated with the fractaquantum hypothesis: does intricate matter,
does "EPRB-atoms" exist at a macroscopic scale? Is it possible to evidence at a
macroscopic scale phenomena that show that two apparently distinct objects belong in
fact to the same "atom"? This question is highly difficult. Firstly, the domain of scientific
knowledge is a priori limited to what is refutable by a conceivable event,
following the now classical protocols formalized by K. Popper (1935).
The next step in this direction is the industrialization of Aspect experiment. This has
been presented in cryptography for a secure exchange of keys by
A. Ekert (1991).
Nevertheless, note that if quantum cryptography has today a great interest for
applications, it is more at our knowledge with the so-called BB84 protocol (C.H. Bennett,
G. Brassard, 1984). This protocol is founded on the non-commutation of certain operators
in quantum mechanics and not on intricate states. Firstly, positive results have been
recently obtained by the group of P. Grangier (R. Alléaume et al, 2004).
Nevertheless, at our knowledge,
Ekert protocol has still to be implemented... Secondly, the possibility of development of
a so-called quantum computer has been suggested by R. Feynman (1982). It is founded on the
possibility to extract some information from the free evolution of N
intricate atomic systems of spin ½
An algorithm for "super-fast" Fourier transform has been proposed by
(1994). The first experiment [the factorization 15=3×5!] with a quantum computer has been
conducted with success by L.M.K. Vandersypen et al (2001). Note that these works are
currently in great development.
Nevertheless, the main difficulty of these micro-physics experiments is due to the
so-called decoherence, modelized by W. Zurek (1982) and experimentally established by
S. Haroche and his co-workers (M. Brune et al, 1996).
When interacting with the environment, mesoscopic quantum systems
(the so-called cat of Schrödinger?) loose quickly their coherence properties. An
intense field of development is then open in the laboratories of physics to prepare and
maintain a certain quantity of matter in an intricate state like in so-called
Bose-Einstein condensates. Concerning quantum cryptography, the different comes from the
confiict between the micro-scale of a single photon and macroscopic distances. Remember
that cryptographic applications are actually considered for distances of the order of one
kilometre, as the one proposed by N. Gisin and co-workers (A. Muller et al, 1998).
The possibility or not
for the environment to interact with an "EPRB-atom" without destroying the intrication is a
fundamental question. In some sense, if we reverse the fractaquantum hypothesis, going now
from the big scale to the little one, micro-experiments could mimic the macroscopic
structures (cells!) that remain stable due to the open exchanges.
We focus again on the fact that our goal here is not to construct new computers or new
protocols for some secure exchanges. It is simply to understand the world as it is present
in Nature all around us (and inside us also!). Generally, the reality of the fact is
hidden. We are very astonished by the importance taken by electromagnetism along the
history of science. Previous to
B. Franklin (1751), electricity is first the natural
phenomenon of thunderbolt. Because it is not well known, it provokes fear and human beings
have created gods like Zeus and Jupiter in past highly organized civilizations.
Following scientific developments during the 18th and 19th centuries, the unification of
electrostatics, electro-kinetics, magneto-dynamics and optics via the
(1873), Humanity has developed technology and has some control on the electric
energy. Moreover, electrostatics interaction with the so-called Coulombian interaction is
the fundamental phenomenon that gives the structure of the hydrogen atom (see again your
favourite book of quantum mechanics!) and by extension the structure of all "atoms" due to
Pauli exclusion principle,
as we have reminded it in this contribution. Consequently,
all molecular dynamics, all the chemistry, and all the biology could be considered as a
variation on mechanics and electromagnetism. All this electromagnetism is continuously
present in our life and a priori, we have absolute no consciousness of its presence! What
could be the situation for macroscopic intricate states?
We suggest coming back to the embryonic development. On the one hand, a single cell
develops in a short (?) long (?) time in order to create a complex highly
organized living being. The interaction with the environment is crucial and the
way some global information could be presented at the final state of embryonic
evolution is an open question that
seems to be an acceptable possibility. On the other hand, empirical
knowledge developed in China since 3000 years with the
acupuncture. A 2000 years old
classical book is named
Nei Jing Su Wen. It is presented as a conversation of the emperor
Huang Di with his advisors. Remember that acupuncture sets up some
relations between the internal organs inside the body and some precise locations
on the skin that are acupuncture points. Of course, these correlations resist to
simple explanations through classical scientific approaches, even if recent
contributions e.g. of J. Dundee, R. Ghaly (1989), H.M. Langevin, J.A. Yandow
(2002), K.P. Schlebusch, W. Maric-Oehler and
F.A. Popp (2005), A. von Bubno (2005)
among others begins to create interesting links between modern scientific protocols
and traditional acupuncture.
We suggest here that relations between acupuncture
points and internal organs could be the sign of the existence of macroscopic
intricate "atoms". The correlation with the embryologic development could be a
possibility to evidence the past interaction between the corresponding
cells. Nevertheless, direct intrusive experiments are impossible and will show
nothing else because of the reduction of the wave packet. A remaining possibility
is numerical simulation...
We could also think about true twins. They come both from a unique cell and have an
identical genetic patrimonium whereas they are two different persons with a strong
interaction between themselves (see e.g. G. Claridge,
S. Canter and W Hume. (1973) and R. Zazzo, 2001).
However, do they still compose a unique intricate
"atom"? The classical response is negative. Note also that by definition, a strange
situation like a macroscopic intricate "atom", or a macroscopic "EPRB-atom" is still to be in
the framework of artistic creation. We refer for example to the movie
Life of Veronica
K. Kieslowski, 1991). Nevertheless, the experimental result of Aspect and
fractaquantum hypothesis will have to be considered together in the future.
Our goal in this communication is to explore some aspects of
the fractaquantum hypothesis, that claims both that "the big is
analogous to the little" and "the world is quantum at the microscopic scales of Nature".
Thus it implies that "the world has quantum properties at our
macroscopic scale". This research conducts to beautiful comparisons and we
have presented the notion of"q-angel" in order to express some of them.
Consequently, it seems useful to re-define usual words as "space",
"big", "little". As an example,
our understanding of the
Pauli exclusion principle,
is "matter creates space, bosons give it a structure".
Managing scale complexity with graph theory, we suggest that
"intelligence is in the loops". Moreover, a dynamic based on
relations between loops could be a first step to link the micro-scale and
Strange situations of intricate matter are suggested by Aspect
experiment. With the fractaquantum hypothesis, we can imagine "intricate
Embryogenic development and traditional Chinese acupuncture
suggest that such "intricate macro states" could be present inside
each of us.
We will give the last word to
R. Descartes (1641):
"Senses are deceiving me. Thus, I doubt. Thus ...".
We would like to thank Florence Justes for her indispensable knowledge of
for his helpful discussions about embryology,
and all the members of
for their indispensable thoughts and critics
preliminary to this communication.
We also would like to thank Didier Seban for communicating to us the
research work of M. Locquin.
Last but not least, we wish to thank Carole Ory for her help in
English in amending the first draft of this article.
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François Dubois received a Master degree in atomic
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analysis (1988) from Paris 6 University.
He is University Professor
in applied mathematics in Paris and member of Afscet,
French Association for System Science.