Casimir Vacuum State of the Relativistic Quantum Scalar Field System in Living Cells
Fundamental Relativistic Quantum Field’s Interactions by Additional Causal and Boundary Conditions And Cryo Biologically Scientifics’ Treating of the Living Cells

1 Institute for Cryobiology and Food Technologies, BG – 1674 Sofia, Bulgaria
2 Institute for Nuclear Researches and Nuclear Energy, BG – 1113 Sofia, Bulgaria


Tsvetkov, Ts. D. and G. Petrov, 2013. Casimir vacuum state of the relativistic quantum scalar field system in living cells. Bulg. J. Agric. Sci., 19: 387-396


The physical fundamental equations describing the absorption and emission of light waves by atoms are symmetric with respect to the sign of the time parameter also the principle of the detail equilibrium is in force – that is, there is no directionality of “time’s arrow” at the microscopic level of this physical phenomena; it is only at the macroscopic level when following Einstein from the macro causality properties of view the irreversible character of time begins to assert itself in the classical sense of the Minkowski space-time, and then for no other reason than probability in the thermodynamically sense by the understanding of his nature. Following this thought it is to remark that the physical phenomena by the light absorption and emission has a relativistic character also the time parameter is not so gut understanding by definition in Minkowski space without Lorenz transformations between the Lorenz manifold’s points of the Lorenz globally geometry whiles the gut understand thermodynamically “time’s arrow” as a physical phenomena is non relativistic and the time is absolutely also the Galileo transformation between the Riemann manifold’s points is in force. All that is connected with the more fine understanding of the symmetry by transformations of the vector valued functional state as the so called super symmetry as by the time inverse connected with the mutuality principles and the principle of detail equilibrium and so as the charge conjugation. For the light propagation in the vacuum at the microscopically level the geometrical understanding of this manifolds is practical from one and the same nature described by local quantum wave fields which was understanding physically very gut as phenomena but not so gut from the so called pure mathematic point of view. Furthermore following the quantum character of the causality properties of the observed physical quantum entities it is clear that the application of the usual mathematic analysis is not more sufficiently to describe this by the help of the fundamental equations. The generalized functions and more special the tempered distributions make possibly the understanding of the nature by those physical phenomena from the mathematical point of view too, e.g.without to consider the set of the zero measures i.e. by Lebesgue’s integrations. The entity of the distributions consist in them that by dropping the knowledge of the function which define the Lebesgue’s zero measure it is possibly to define wide class of generalized functions, included different Dirac δ-functions and his derivations.
The real massless photon as a fundamental light quantum particles of the fundamental quantum electromagnetic field is the quantum field vector valued entity of non restrained electric charge of the fundamental relativistic quantum leptons charge field’s systems localized in the so called “strings” in the time like light cone of the Minkowski space coming out from the double cone of definition for the quantum electromagnetic vacuum state. The virtual leptons are the carrier of the electromagnetic field’s energy at the quantum level given by the quantum electromagnetic current and intensity operators. The notion of temporal symmetry in the equations of the quantum interaction between the fundamental particles electrons and photons of the fundamental electron and quantum electromagnetic fields at this level was simply assumed, including the famous Feynman’s diagrams, where the photon is virtual carriers of the interaction’s force between the local quantum currents of those see particles. Then the acausal, atemporal, justification, ignoring: 1) the principle of causality; 2) the time dimension; 3) the gravitational field of matter; 4) the principle of entropy has disregarded the causal, temporal, and local properties of leptons and by implication, all massive particles also all that must be proven anew by the help of the mathematic-physical methods of the theoretical physics. Moreover prove of the causal properties of the Casimir world with given additional boundary conditions are necessary. Than the vacuum is called a physical vacuum and the observed physical entity must fulfilled cinematically conditions (G. Petrov, 1978).
For the gravitational field of matter to day is knowing that the aggregate energy represented by the virtual scalar particles, like other forms of energy spectra of the zero fluctuation, could exert a gravitational force, which could be either attractive or repulsive depending on physical principles that are not yet understood, e.g. there are physical phenomena not understanding from the phenomenological point of view. In this case the axiomatic-mathematical physics has his advantages so that we can make predictions for physical phenomena from the point of view of the causality properties of the fine structure of the matter with additional boundary conditions in the global Lorenz geometry induced by the geometry of the Minkowski space-time which describe the special relativistic theory too.
By the living cells as an object of the fundamental cryobiological researches i.e. the metabolisms is minimal and also it is possibly by the help of the axiomatically physic-mathematical methods of the relativistic quantum field’s theory to take in the account the problem of a “time’s arrow” at the microscopic level by the contemporary considerations of the quantum vacuum in the Casimir world as a ground state of anyone relativistic quantum system become a fixture by the lyophilized elementary living cells and represented by the symmetrical selfaddjoint Hamiltonian operator taken for simplicity by definition of the quantum scalar fields operator Φ given in the Minkowski space-time. The probability interpretation of his spectral family give as the physical interpretation of the observed entity even for the thermodynamically structure of his ground state, i.e. by the vacuum interactions in the Casimir world, e.g. the Casimir force to day is measured with 5 % exactness. Moreover the Casimir vacuum state may be not belonging in the operator definition domain of the field’s operators, but fulfill the additional causal and boundary conditions for the carrier of the interaction force, the virtual fundamental scalars particles. So also the Casimir vacuum in the asymptotic past at the left of the non moved plate for this case contains from the micro causal point of view the virtual particles for an so one initial observer and in the asymptotic future at the right of this plate and the left of the moved plate the see particles for the late-time observer, e.g. the Maxwell demon, and moreover at the right of the moved plate anew the virtual particles system.
Since the 1948 the mathematical description of the so called Casimir world as a part of the physical observed space-time in the relativistic sense is to be considered by the help of the Hamiltonian quantum field’s theory and furthermore it is based on the fine play between the continuity and the discrete too. The axiomatic methods of the local quantum fields theory has given the other possibility then the Lagrange quantum field’s theory and rigorously mathematical way to understand the singularities and the black holes, also the dark energy and the dark matter from one uniformly point of view to describe the fundamental interactions between the anyone concrete fundamental relativistic quantum field system with other someone or with the external and innerness material objects as an external classical fields, material boundaries and everyone internal background.
Furthermore it can be set in a Casimir world given by additionally causal and boundary conditions on the Hamiltonian scalar quantum fields system with Banach vector valued one virtual field functional vacuum state and it is element of the so called Hilbert space with infinite metric so also may be not belonging to the definitions domains of the field operators but where they are without perturbation in the set of the symmetrical virtual vacuums and a infinite set of state orbits of Banach vector valued field’s functional states with perturbation by his evolution in the time (oneness and infinity set) e.g. virtual vacuum fluctuations described by the help of the spectral family of the selfaddjoint Hamiltonian operator characterized the mass of the fundamental virtual particles and the vacuum ground state defined on the involutes field’s operators valued algebra on the Hilbert functional spaces with infinite metric in the environment and the innerness between the two parallel plates, non moved and moved with the constant velocity v at the face to the plate at the rest and with the additional causal properties and fulfilled boundary conditions on the plates. The Casimir vacuum is not connected with anyone charge moreover his structure is no more so narrow connected to the structure of the quantum system. The set of the vacuum structure will be obtained by the thermodynamic classical definitions of the Casimir world, i.e. the global structure of the Casimir vacuum state of anyone local quantum field system, e.g. the scalar wave quantum field defined in the Minkowski space-time induced Lorenz global geometry.
Also by fulfilling of the following naturally statements defined as early as from the ancient nature-philosophy by Syrian, Egyptian and Grecian in the axiomatically sense of the unity of the opposite entities:
1. boundary and infinity
2. odd and even
3. oneness and infinity set
4. right and left
5. manly and womanly
6. unmoved and moved
7. straight and curve
8. light and darkness
9. blessing and disguise
10. square and parallelogram
it is possibly to describe the interacting quantum field’s relativistic systems in the so called Casimir world (boundary and infinity) become a fixture to the environment in living cells and systems from the point of view of the usual axiomatic theory by using the idea of the vacuum as a functional ground state of the axiomatically constructed concrete fundamental relativistic quantum field’s system in the Schrödinger picture with additional adiabatically and impulse effects so that from microscopically stand point of view by the quantum causality properties and localizability of the entities seeing from the observer e.g. the Maxwell’s demon at the past t > t-2n and at the future time at t = t2n from the late-time observer for n → ∞ the “time’s arrow” can be understand micro causal without to take in to account the thermodynamically entropies character of the time as it is the case by the Einstein’s macro causality i.e. the calculated Casimir force in the vacuum act on every particle as it is the case by the electron moved in the external classical electromagnetic field with a destroyed scaling behaviour of the vacuum state of the massless Dirac fundamental electron field leaded to polarisation (electron-positron pair) of the vacuum by acting of the electric force on the localized massive electron.
From the new results by the contributions of the environmental freezing-drying and vacuum sublimation (Zwetkow, 1985; Tsvetkov and Belоus 1986; Tsvetkov et al., 1989; Tsvetkov et al., 2004 – 2012) it is hopped that by the significant form expressed e.g. by the scaling behaviours of the invariant entities in the space-time by the energy impulse tensor described the elementary living cells and systems will be possibly to describe the biological expressions at the nanophysics point of view by means the behaviour of the concrete fundamental relativistic quantum system, e.g. sea virtual quantum scalars in the physical Casimir vacuum with additional causality properties and boundary conditions on every one generic surface S too.
At the molecular level (Mitter and Robaschik, 1999) the thermodynamic behaviour is considered by quantum electromagnetic field system with additional boundary conditions as by the Casimir effect between the two parallel, perfectly conducting square plates (side L, distance d, L > d), embedded in a large cube (side L) with one of the plates at face and non moved towards the other, i.e. also the case of so called Casimir effect under consideration in the sense of the local case when the Minkowski space-time is equally of 4-dimensional Euclidian space but without the considerations of the causality properties of the relativistic quantum entities given a share in the effect, e.g. relativistic supplement to the Casimir force.
Our interests is the more realistic relativistic Casimir effect when the one of the plates is at the rest and the other moved with a constant velocity v towards the non moved plates. So the thermodynamic behavior of the elementary living cells under consideration must be globally by the relativistic quantum systems in the so called Casimir world too.

Key words: Casimir effect, time’s arrow, elementary living cells, lyophilization, nanophysics, singularities, scaling principle

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