Alexandre V. Boukalov
On the quantum-mechanical description of the life phenomenon
It is proposed the description of alive organism as a macroscopic analogy of a coherent quantum system, evolving a structure, consisting from the discrete space-time levels. It is introduced the operator for the space-time structure, it is an analogy to the Hamilton operator. It is formulated a wave quantum equation, describing the evolution of the wave function of biological system in energy-momentum, or in the space of frequencies.
It is known that the life processes are characterized by the significant degree of the biochemical events ordering in the space-time. Really the biological objects are the unite coherent unbalanced system with the ordered space-time structure, which is created and supported by the continuous energy supply. It follows the possibility of the organism consideration as a coherent, functioning system of molecules, ordered in the space-time. Such a system can be considered as a macroscopic analogy of the quantum-mechanical object. It follows from the uncertainty principle that the measure of the time or space coordinate of the quantum-mechanical object causes the energy (momentum) uncertainty. The coordinate measure destroys the space-time interference and causes the energy-momentum one of the quantum-mechanical object. The exact space-time correlation among the biological events, realized by the cell macromolecules, inevitable causes the system uncertainty of these molecules energy-momentum. The biochemical transformations observations causes the destruction of the process course as well as the normal function of alive cell and its death. Thus the mentioned action can be connected with the process of reduction of the biological system wave function. The cell (and its subsystems) due to its ordering is coherent object, reacting as a one unity. Meanwhile this coherence is connected with the energy-momentum interference but not with the space-time one.
The cell as a unite coherent object with the ordered and observed metric space-time structure due to the energy supply can be considered as the unbalanced object and process, partly localized in the energy-momentum space. It follows from the character of the coordinate observation process in quantum mechanics: under the quantum object interference on diffraction slit the coordinate cannot be detected and only the momentum is measured . The object coordinate measure is produced for example by the illumination using the photons or some particles flow. In dependence of the illuminating quanta energy it is determined the object localization. But such a coordinate measurement causes the uncontrolled energy-momentum transfer to the object. This approach is valid to any coherent unbalanced object with energy supply because the quantum mechanics principles can be used for the world as a whole. The unbalanced system exists only under the current energy flow presence. One should note that energy supply by the quanta flow to the considered system is analogous to the coordinate measurement process, namely: the supplied energy-momentum flow provides the Δx and Δt-components “compress” and the ΔEi and Δp-components expansion, i.e. it causes the space-time localization of the molecules system. Simultaneously due to the uncertainty principle this process causes the uncertainty of the energy-momentum values of the molecules system. Thus the unbalanced system becomes more ordered functionally and more delocalized in the energy-momentum space.
Thus, any selforganization process in the unbalanced systems can be considered as the process of the measurement of the space-time coordinates by the energy-momentum supply (which interact with the system and are receipted by it). Thus measurement is equivalent to the formation of the observed space-time structure if the object. Due to the coherence of the macroscopic dissipative structures it rises actually, the macroscopic analogy of the uncertainty principle:
The energy supply, as it is known , amplificates the microfluctuation till the macroscopic scales  and causes the observed structures origin.
The ferments function can be considered as an illustration. They have rather presice ordered space structure. The ferment possibility to produce the correlated biochemical reactions, what is connected with the precise time correlation of the events consequence and refers to the ordering of the ferments functioning in time. Thus the ferment acting process is the presice correlated system if the degrees of freedom of the macromolecular atoms thermal vibrations as well as the surroundings solvent atoms and summarized and canalized in the ferment active centre due to the space-time ordering of the macromolecule structure. It causes the energy-momentum interference or the system increasing of the energy (momentum) uncertainty, which is used by catalyst for the energetical barrier reducing. The rised energy-momentum uncertainty is a character feature of the biochemical processes. Namely due to this energy-momentum uncertainty and the consequent space-time ordering a cell functions as a one unite. The system energy uncertainty, rising in the single ferment level, is amplificated and correlated with the energetical uncertainties of others ferments, united by the biochemical cycles in the unite space-time structures.
The molecule structures interact between them not only by the biochemical transformations products. It was marked by A.G.Gurvich  that between the molecules in cell there is the energetical exchange by the electromagnetic radiation, in particular, the ultraviolet one, which causes the energetical processes correlation within the whole cell. It was nothing but the description of the space-time energetical ordering. Gurvich determined that the coherent change of the organism condition, for example, cooling, can cause the radiation release.
Thus the external organizing energy supply is equivalent to the rise of the space-time information, which is reflected in the forming protein structures and simultaneously forms the energetical uncertainty till the cell scale.
Let us note that the terms “energy-momentum uncertainty” or “energy-momentum interference” are used in order to point out the principal, from the quantum mechanics point of view, symmetry between the wave and corpuscle descriptions of matter.
The “life whirlwind” can be considered as the coherent state of molecules, atoms and the electronic shell of the cell and organism atoms. This interference in the frequencies space, rising due to the splitting of the energetical levels of the DNA, RNA and protein molecules, forms the practically continuous spectrum. For such wave function with the continuous energetical spectrum it is valid the principle of the energetical states superposition. It also means that the biochemical reactions, being ordered in the space-time field, interference in the energetic ε-space (frequency space), in the energetical spectra space. It follows that the interference (wave) in ε-space causes some energetical structures, i.e. the real change in energetical space is nothing but the chemical compounds transformation. The frequency space (or energetical one) is practically continuous in the wide energy range, or, by other words, the dynamic structure is delocalized in energetical space and united. It means that any energetical disturbance makes its action in the summarized wave function over the whole frequency space, i.e. the system reacts as a one unite. I.e. an atom or photon makes its generalized action over the whole spectrum. Let us suppose that we consider the photons flows, which interfere after the single frequency transformation , and likewise between the biochemical structures the interference “beats” rise after the transformation to the single frequency, i.e. the biochemical reaction. The mentioned process is realized in an organism, for example by the help of ATP as the universal energy source. Another example is connected with the nervous system, when the all biochemical organism reactions are reduced to the unite processes, connected with neutron pulses. Besides, if in the one photon spectrum it is reflected the emitioning object state, thus the brain, as a coherent structure, reproduces this state, i.e. modulates, decodes it, concentrates and amplificates, producing the information reflection.
For electromagnetic radiation the interference topics in energetical of frequency space were considered in a set of works. In  it was noted that the photon, under the interference in the energy-momentum space, makes its action over the whole laser spectrum. There is a principal circumstances that the photon is emitted by a laser, which is an unbalanced system, ordered in the space-time. It was pointed that the photon interference in the frequency space means the complex structure presence. We note, that from the quantum mechanics point if view the photon has the space-time structure, reflecting the structural ordering of laser radiation. The analogous conclusion can be made in respect to the molecules of the substances, supplied to the cell: they have the inside ordering structure (characterized by negentropy) and make a contribution into the whole energetical cell spectrum. Thus the supplied molecules interfere with the whole cell and make their contribution into the total cell wave function ψ(E1…EN), which unites the ferments, DNA, RNA etc. It is obvious that the wave function reduction or the energy-momentum measurement means the organism decay due to the elimination of the space-time correlation.
The interference in the energy-momentum and E-space means, as it is follows from quantum mechanics, the interference between the energetical structures. It transforms an organism into a single unite structure, partly localized in the space-time and partly delocalized in the energy-momentum.
The observed space-time structure components can be compared with the operator, presented by the expression
Then we are able to write the quantum equation for alive organism in the supplied energy flow:
In the time field under
In this case the operator describes the discrete time levels of biochemical events, which are quanted like the energy quanting in the elementary particles physics.
The equation (3) is analogous to the Schrödinger one and thus from it follows the analogy of the integral over the Feynman trajectories. The observed reveal of this process is the competition of the energetical modes, macromolecules, biochemical cycles within cell, namely the cell and organisms, i.e. nothing but the natural selection according to Darwin. Molecules, cells, organisms, kinds complete among them on the every hierarchy level of the alive matter organization in the energy-momentum space. The mentioned properties follow from the statements of the orthodoxal quantum mechanics.
Let us also note that the description of the set of biological reactions as the energy-momentum interference simply leads us to the synergetic ideas.
For the motion in the energy-momentum space over the minimal trajectory the organism needs the space-time information, which will be exact under the energetical interference. This one also is produces under the psychical processes. The interference causes to the indiscernition of the organism parts in the life processes proceeding. It means that the information, containing in the organism, its quantity and contents have to differ essentially from the information, containing in an unalive matter, for example, in crystal.
The quanted macroscopic whirlwinds in the superfluidity liquids, such as He-II or He-III, have their analogy, which is the biochemical cycle in the alive cell. The biochemical cycle of the matter transformation is a temporal structure, moving in the energy-momentum of the current matter, i.e. the ordered in the energy-momentum space. The current energetical cycle also can be considered as a “whirlwinds” in time or the biochemical energetical cycle, developing in time as a temporal structure of events, expressed by the operator. The biochemical “whirlwinds” existence means the correlation of the organism molecules motion in space and time; the quanting of this correlation (cycles) points out the discrete character of the space-time events.
The Benar cells are the obvious but an elementary energetical cycle with the momentum concervation for the every structural component (due to the continuity); whereas the dynamical character of Benar cells , laser radiation etc. means the correlation in the space-time.
There are various approaches to the ferments functioning modeling [2, 3, 13] whereas from the observed system point of view the ferment functioning is realized due to the ordering of the energetical zero vibrations in the space-time ferment structure, i.e. the random vibrations channeling by some degrees of freedom. Really in the ferment functioning the all life principles are present: the space-time structure existence provides the energy-momentum states (oscillators vibration) correlation, i.e. the vacuum quantum vibration ordering. The integration of the 10N degrees, what provides an essential decrease of activation energy. Under the energy supply to the dissipation structures the virtual fluctuation amplification has place as well as their separation and domination. The permanent energy supply provides the space-time levels ordering, i.e. the energy supply dynamics provides the vacuum “superconduction” state of the alive matter and the origin of the dynamical “quantum crystal”, in which it is provided:
The main mass of organism is consisted by proteins, including ferments, which provide the ordering of the large number of the degree of freedom of the cell water molecules and, possible, the vacuum fields.
The biochemical cycles and their sets form the space-time internal structure of organism because they have the high events correlation. The space-time symmetry violation means the presence of correlation between the parts of system in energy-momentum. The renormgroup method provides the effective reducing of the number of the considered degrees of freedom, because after the phase transition the system symmetry is destroyed and the degrees of freedom number is sharply reduced:
One can see that the described phenomenon is completely revealed in alive organism under the degrees of freedom integration in unite motion and the provision of essential delocalization in the (ε, p)-space with the condition of the phase space conservation. Meanwhile the amplification coefficient K»Natoms characterizes the degree of the organism parts correlation or the degree of the symmetry destruction in the space-time (x, t).
On the base of the most general approach the Universe phase space can be divided by the two parts: the vacuum (Λ+-transformation according Prigogine ) and the matter and life (Λ–-transformation). In the expansing Universe the Λ+-transformation describes the trajectories divergence whereas the processes of the matter and life selforganization can be compared with the Λ–-transformation, describing the joined trajectories.
By other words the space-time localization is connected with the delocalization in the energetical space, what causes the coherent behaviour in the energy-momentum of the alive organism space-time structure. Such the correlation organism behavious points out the existence of the Λ–-transformations or the joining K-flows (according Prigogine), what causes the system behaviour coherence. On the macro-level of the alive organism structure it reveals by the fractal structure of lung as well as the blood, nervous and others systems. The correlation behaviour also can be considered as a phase transitions, caused by the metric operator , what stimulates the ordered molecule motion in the energy-momentum space. Under this motion is rised the hierarchy of biocycles and the chemical vibrations (probable, fractal) due to the destruction of the space-time structures.
We have noted that the ferments ordering in the space-time field causes the delocalization of the energy-momentum of the ferment active centre, what reduces the activation threshold due to the interference in the (ε, p)-space. I.e. the energy momentum uncertainty increases with the rise of the space-time precision of ferment motion. According to L.Blumenfeld [2, 3] the protein molecule change (substrate or inhibitor addition to active centre etc.) causes the appearance of the conformation unbalanced state. Thus the appearance of the new more ordered space-time ferment structure in the space-time is equivalent to the appearance of some energy ΔE, used for catalysis. It was noted in  that the presence of the degrees of freedom, separated in the space and time, provides the consideration of the space and time displacements, which have place in the different parts of macromolecule, as the changes, produced by one action. We suppose that this unite action, i.e. the energetical transformation or the energy-momentum displacement, is caused by the space-time operator , describing the matrix or the events set, connected with the space-time ordering of the ferment macromolecule.
By such a way it is realized the underbarrier catalysis or elementary biochemical action. Meanwhile all the biochemical cycles consist of the set of such elementary actions: firstly, the parallel production of such operations; and secondly, the consequent production of ones (for example, the simple molecules splitting). I.e. in the course of the cycle production it has place (in respect to the supplied product) the consequent delocalization in (ε, p) (staged). Due to the mentioned process the initial product under the interference in (ε, p)-space really interferes with the whole cell (or an organism), making its action in the total system wave function ψbio, ordered in (ε, p). This is the difference between the alive unbalanced system and the quantum liquid.
The organism subsystems are ordered in (ε, p), but due to the existence of the unite (xμ, tμ)-level in alive organism it is risen the interference between the (ε, p) levels, i. e. these levels are indiscernible (under the correct (x, t) hierarchy) in opposite to He-II (nonlocality of x under the E0 determination). Thus there is the x-determination under the ε-undetermination, or the organism wave function ψbio is in a pure but not in mixed state, which refers to the set of separate organism or systems. Thus the energy, supplied to organism, brings the information I, which becomes significant under the interference in the space, when the ferments and organoids, being ordered in the (x, t)-space, interfere among them in the (ε, p)-space. It means the interaction of ferments, RNA, DNA, membrane etc. as well as the total interference in (ε, p)-structure, described by the unite wave function.
It is obvious that the wave function ψbio reduction means the organism decay. I. e. the (ε, p) interference means the one between the energetical levels (their indiscernition), what transforms an organism into the one unite, localized in (x, t) and delocalized in (ε, p). The (ε, p) interference is the mutual dependence of the all parts of organism. In particular, the (ε, p)-interference on the cell organization level causes the competition of the macromolecules or the whole biocycles. Thus the Darvin natural selection is nothing but the observed reflection of the (ε, p)-interference. It is valid for the macromolecules within a cell as well as for the whole organisms. The observed competition is the interferention of the space-time structures in the energetical space. The molecules, cells, organisms, kinds complete (interfere) among them in the (ε, p)-space for the way, limited by energetical structures with some geometry in the energy-momentum space, what is expressed by the distribution and the degree of the suitability of the food and others energetical resources.
The interference in the (ε, p)-spaces was not early considered in details whereas the mentioned properties are followed from the orthodox quantum mechanics statements. Really, for the motion in the (ε, p)-space an organism have to possess the (xμ, tμ)-structure in the form of the biochemical events matrix, described by the Boukalov operator . The interference causes to the indiscernition of the deposits of the organism parts in his functional structure. It means that the information, containing in organism (and reflecting its structure), has to differ from the one, containing in a nonalive crystal etc. It can be determined by the space-time characteristics, it is the dynamical information [4, 6].
Taking into account that an organism is the space-time ordered structure, it is possible to note that the space-time correlation of biochemical events and processes is unreplaceable and unchangeable. Thus every molecule has the individual space-time trajectory in organism.
By other words an organism forms the unite unchangeable space-time continuum of events, nonlocalized in (ε, p). Then for an alive organism with its 1025 molecules there are 1025 unreplaceable world (x, t) molecule lines, in opposite to the crystal, where the atoms can be replaced in space without the consideration of the time coordinate degeneration.
Thus the degree of ordering of alive organism is by 1025+N times more than the one for the mineral of the same weight, but this ordering is not a thermodynamical one [4, 6]. It includes the total energy, obtained by the organisms, obtained during the whole evolution history or the energy, treated by organisms (or the energy, which can be treated).
The generalization by the energetical coordinate explains the small thermodynamical production of entropy and information under the large stock of the I(x, t) space-time ordering. One can note that this ordering is the 1018 times more in average for biosphere or the information per the Universe barion for alive organism is in average 1018 bites/barion (or the barion entropy of Universe is 1018 ). The fractal K-flow, which is an organism, is naturally explained by the organism coherence in the energy-momentum of the energy-momentum interference of the all biochemical cycles of organism.
The space-time (x, t) ordering of organism is the destruction of the symmetry. Under the consideration of the N·h-cells phase space we can determine the symmetry destruction over the (x, t)-coordinates and the degeneration over the (ε, p)-coordinates. For the organism we have the phase space with the destructed symmetry in (x, t) and the interference in (ε, p). It is directly opposite to the vacuum field dynamics, characterized mainly by the space-time interference. Thus an organism can be described by the wave function ψbio(x, t, ε, p) and any informational (or energy-food) “communication” makes its action in the interference interaction among the different energetical organism structures. It refers to any biological macromolecules system, where the molecules energetical interference has place under the space-time localization and their structure ordering. It means that the communication (photons, chemical bonds) bring the (x, t)-ordering or provide the energy for the whole organism, possessing the I(x, t)-internal complex informational structure.I(x, t) = lnW(x, t). (5)
This structure contains the large information. According to the construction of the “receiver” (organism) the wave packet distortion has place over the energetical space of the organism subsystems or the whole organism; this process can be considered as the information communication action and its reception.
Thus the introduction of such a notion as the interference of the ψbio(x, t, ε, p)-wave packet of the organism internal structure in the frequency space or in the energy-momentum one explains from the unexpected side the ferment work. As a result of the delocalization in the energy-momentum space it is risen the energy levels “washing-out” or the overcoming, the energetical barrier reduction. Thus, as we have noted, the chemical reactions description as the interference in the energetical space of some space-time structure leads us to the synergetic ideas, obtained by other ways (chemical waves, Bernar cells). The same refers to the laser photons interference .
As the psychics is the inside part of an alive structure, it is also (and by the first turns) described by the wave function ψbio(x, t, ε, p, φ, i), where x, t are the discrete, quanted space-time levels; , (ε, p) is the energy-momentum continuum, φ, i are the components of the psychic and informational (psycho-informational) space, introduced by us . It is obvious that due to the continuousness of the energetical levels the space-time coordinates (in phase space) can have discrete (or periodical) values. The same refers to the inside symmetries, which will discussed lower. Thus we consider not only the symmetry of the periodical space-time structure, but also the inside matter quanta symmetries, additional to the usual space and endowing it by the dynamical evolutional structure. We consider the layered spaces, including the movable Yung-Mills fields, or the calibrating fields (weak interaction etc.), reflecting the inside matter structure. The mentioned features prove us to consider the quantization of these spaces. It is clear that the space-time symmetries are transferred into energetical space, what causes the projection hierarchy of the Yung-Mills fields or the energetical space symmetrization under the symmetries destruction as a usual space-time (x3, t0), so the covered, inside, layered spaces (x4+N, t4) (for example, DNA as the aperiodical crystal). Meanwhile, the deduction follows rather simply from the Neter theorem or its generation over the (ε, p)-space.
In some case, the analogical to the superfluidity of the Fermi-liquid type He-III [10, 11], the biological system (alive organism) can be characterized by the fractal hierarchy of the space-time structures under the (ε, p) delocalization or from the all possible space-time discrete levels, by analogy with the energetical ones, the mentioned system is described by the zero s0= f (x0, t0) “vacuum” metrical level (form boson space-time structure) or the levels hierarchy (for Fermi space-time structure). Really, the (x, t) interference for quantum liquids means the lowest, zero energetical level. By analogy, the interference in the frequency (energy) space points to the lowest, “zero” organization levels in the (x, t) space. Thus an alive organism can be considered by analogy to the superconductor or the superfluid “Fermi-liquid” He-III, or the vacuum fields, not in the usual space, but in the energy-momentum one, for example, the sμ-quantum of event with the analogy of the minimal “energy” of the (x0, t0)-level s = ½ s0. This notion also explains the fact of the “quasiconductivity” on the unbalanced energy low (in opposite to superconductivity).
Thus the ordered flow of electrons (leptons), protons and neutrons (barions), atoms forms some space-time dynamical structure Z(xμ, tμ), produced by the energetical flow of the inside energy of supplied matter. Namely the dynamical character of the sμ-“matter”, presented in organism by the discrete space-time levels, is described by the equation (3), proposed by the author. This equation is analogous to the Schrödinger one, but it describes the evolution in the energy-momentum space (according to the quantum mechanics equation symmetries).
Thus the Boukalov operator , analogous to the Hamilton operator , can be determined as the operator of the inside quanted space-time, including the inside measures, correspondent to the covered inside symmetries or the virtual fields. The interference in energy-momentum points out that for the separate organism components of the set or organisms there is an interaction in the form of the competition of the evolution development alternatives. The similar evolution and motion are described by the Markov chains (complex or values) or the Feynman integral over the energetical trajectories. It is easy to see that the alternatives interferention is nothing but an aspect of the molecules competition in the auto-organized systems, alive organisms as well as the organisms itself within the biosphere. By other words the interference in the energy-momentum space is connected with the observed natural selection processes as well as the chemical, geochemical and biological evolution.
 The main text of the work was written in 1987. It is published firstly. Another approach, correspondent to our one and based on the consideration of the coherent electromagnetic field of organism, possessing of the self-coordinated potential, is developed by S.P.Sitko et al. .
 It was shown by us later [4, 6, 7].
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