Submicroscopic Deterministic Quantum Mechanics

Dr. Volodymyr Krasnoholovets' Research

arXiv.org e-print archive: http://arXiv.org/abs/quant-ph/0109012

Invited talk delivered at the Fifth International Conference on Computing Anticipatory Systems (CASYS'01), Liège, Belgium, 13-18 August 2001. To appear in the American Institute of Physics Conference Proceedings.

Institute of Physics, National Academy of Sciences
Prospect Nauky 46, UA-03028 Kyïv, Ukraine
Fax: +(380-44) 265 15 89
Email: krasnoh@iop.kiev.ua
Web Page: http://inerton.cjb.net

Abstract

So-called hidden variables introduced in quantum mechanics by Louis de Broglie and David Bohm have been revived in the recent works by the author. However, the variables, as such, have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The success in the deepest description of quantum systems becomes possible due to the detailed consideration of a background that directly or indirectly influences the behavior of the quantum system studied. Namely, the start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10⁻²⁸ cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. Hence, it turns out that our space looks like the topological tessellation of a mathematical space with elementary balls (or cells, or superparticles). The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations (called "inertons") in a cellular substrate. The further study has disclosed that inertons are a substructure of the matter waves which are described by the wave ψ-function formalism. It has been found that the range covered by the inerton cloud surrounding a moving particle is defined by the relationship Λ=λc/v where λ is the de Broglie wavelength, c is the speed of light and v is the velocity of the particle (so just Λ limits the range of action of the ψ-function formalism). The kinetics of a particle constructed in the cellular space easily results in the Schrödinger and Dirac formalisms. Besides, the concept of the cellular elastic space has allowed resolving the spin problem, which has been reduced to a special intrinsic particle oscillation. The theory, or more exactly, the existence of inertons, has been verified experimentally: in rarefied gases they are inerton clouds of atoms' electrons which interact with a strong laser pulse and in a solid, atom's inertons induce an additional harmonic potential that contributes to the interatomic interaction (metal specimens and the KIO₃.HIO₃ crystal).

Key words: space structure, particle, inertons (elementary excitations), quantum mechanics

1. Conceptual Difficulties of Quantum Theory

The main original physical parameters of quantum theory are Planck's constant h and de Broglie's wavelength λ. These two enter into the two major quantum mechanical relationships for a particle proposed by Louis de Broglie:

E = h ν; λ = h / p. (1)

Here p was the momentum of the particle, ν was the peculiar particle's frequency that coincided with the frequency of a wave that specified by the wavelength λ and traveled together with the particle. Later when Schrödinger's equation appeared and Heisenberg proposed the uncertainty relations, the interpretation of the said characteristics changed. Namely, the notion of the particle was transformed to a "particle-wave" and hence λ and ν became characteristics of the particle-wave. Born interpreted the square of the absolute magnitude of the wave ψ-function of the Schrödinger equation as the probability of particle location in a place described by the radius vector r. Thus Born finally rejected any physical interpretation from a set of parameters that described a quantum system. Since the end of the 1920s, only one parameter has been perceived as pure physical – the particle-wave wavelength λ called the de Broglie wavelength. In experimental physics, those waves received also another name – the matter waves. Such a name directly says that corpuscles (but not dim "particle-waves") are able to manifest a wave behavior.

Since 1952 de Broglie followed two papers by Bohm (1952) turned back to his initial ideas on the foundations of the wave mechanics of particles. De Broglie believed that a submicroscopic medium interfered in the motion of a particle and the appropriated wave guided the particle. He believed firmly the causal interpretation of quantum mechanics and warned that the resolution of the issue should not be based on the wave ψ-function formalism, as the ψ-function was determined only in the phase space but not in a real one. His own attempts were aimed at seeking for the form of the so-called double solution.

In the case of the Dirac formalism things get worse. The formalism introduced new additional notions such as spinors and Dirac's four-row matrices, which allowed the calculation of the energy states of the quantum system studied and changes in the states due to the influence of outside factors. However, the formalism did not propose any idea on the reasons of the wave behavior of matter and a nature of the particle spin.

So far, modern studies devoted to the foundations of quantum mechanics have tried to reach the deepest understanding of quantum theory reasoned that just the ψ-function formalism is original and it is often exploit even on the scale of Planck length – (Gℏ/c³) ~ 10⁻³³ cm. This is especially true for quantum field theory including quantum gravity. Besides, there are views that a gravitationally induced modification to the de Broglie's wave-particle duality is needed when gravitational effects are incorporated into the quantum measurement process. Other approaches try to introduce a phenomenological description based on the metric tensor gᵢⱼ in typical quantum problems. Classical Einstein gravity is also exploited in condensed matter: some parameters such as mass, spin, velocity, etc. are combined to provide an effective "metric" that then is entered into the quantum mechanical equations.

Thus, the trend has been forward the entire intricacy: the formalism of ψ-function penetrates to the Planck length interior and the Einstein metric formalism advances to the same scale as well. Nobody wishes accept the fact that on the size comparable the de Broglie wavelength λ of an object methods of general relativity fail. No one wants to go deeply into de Broglie's remark that the ψ-function is only a reflection of some hidden variables of a particle moving in the real physical space. The ψ-function is not the mother of particle nature and therefore it cannot serve as a variable of the expansion of a particle's characteristic in terms of ψ at the size less than the particle's de Broglie wavelength λ.

2. New Understanding

Among new approaches describing gravity in the microworld, we can notice the mathematical knot theory, which has been developed attempting to find rules to establish when one knot can be transformed into another without untying it. In the theory, the question is reduced to a certain knot invariant problem, which does not change with knot deformations; knot invariants being deformed constantly by gauge transformations should stay unchangeable. The approach is similar in many aspects to concepts elaborated in elementary particle physics.

Of special note is the approach proposed by Bounias (1990, 2000) and Bounias and Bonaly (1994, 1996, 1997). Basing on the topology and the set theory, they have demonstrated that the necessity of the existence of the empty set leads to the topological spaces resulting in a "physical universe". Namely, they have investigated links between physical existence, observability, and information. The introduction of the empty hyperset has allowed a preliminary construction of a formal structure that correlates with the degenerate cell of space supporting conditions for the existence of a universe. Besides, among other results we can point to their very promising hypothesis on a non-metric topological distance as the symmetric difference between sets: this could be a good alternative to the conventional metric distance which so far is still treated as the major characteristic in all concepts employed in gravitational physics, cosmology, and partly in quantum physics.

In my own line of research I started from the fact that on the scale ~10⁻²⁸ cm constants of electromagnetic, weak and strong interactions as functions of distance between interacting particles intersect. On the other hand, in the high energy physics theorists deal with an abstract "superparticle" which different states are electron, muon, quark, etc. A simple logical deduction suggests itself: the physical space at the said range has a peculiarity that could be associated with presence of structural blocks which one can call just superparticles (or elementary cells, or balls). Then one may expect that a theory of the physical space densely packed with those superparticles will be able to overcome many difficulties which are insuperable in formal theories of both quantum gravity and high energy physics. Thus a submicroscopic theory being based on the structure of fine-grained space will be able to widely expand our knowledge about the origin of matter, the foundations of quantum mechanics and the foundations of quantum gravity.

The first step of the theory focused on the appearance of a particle from a superparticle, which initially was found in the degenerate state. The particle has been defined as a local curvature, or a local deformation of a superparticle and hence the appearance of the deformation in a superparticle means the induction of mass in it, m = CVsup/Vpart (C is the dimensional constant, Vsup is the initial volume of a degenerate superparticle and Vpart is the volume of the deformed superparticle, i.e. the volume of the created particle). So the real space was regarded rather as a substrate, or quantum aether, and the notion of a particle in it was adequately determined.

In condensed matter, we meet the effect of the deformation of the crystal lattice in the surrounding of a foreign particle and the solvation effect in liquids. Therefore, the second step of the theory was the proposition that around a particle a deformation coat was induced. This coat should play the role of a screen shielding the particle from the degenerate space substrate. Within the coat, the space substrate should be considered as a crystal and superparticles here feature mass. Thus the coat may be treated as a peculiar crystallite. The size of the crystallite was associated with the Compton wavelength of the particle, λCom = h/mc.

The next step needed a correct physical model of the motion of the particle. From the solid state physics we know that the motion of particles is accompanied with the motion of elementary excitations of some sort, namely, the particle when is moving in a solid emits and absorbs quasi-particles such as excitons, phonons, etc. By analogy, the motion of the physical "point" (particle cell) in the entirely packed space must be accompanied by the interaction with coming "points" of the space, i.e. superparticle cells. Hence the particle is scattered by structural blocks of the space that in turn should lead to the induction of elementary excitations in superparticles, which contact the moving particle. The corresponding excitations were called "inertons" as the notion "inertia" means the resistance to the motion (thus particle's inertons reflect resistance on the side of the space in respect to the moving particle). Each inerton carries a bit of the particle deformation, that is, an inerton is characterized by the mass as well. An inerton migrates from superparticle to superparticle by relay mechanism. The deformation coat, or crystallite, is pulled by the particle: superparticles, which form the crystallite, do not move from their positions in the space substrate, however, the massive state of crystallite's superparticles is passed on from superparticles to superparticles along the whole particle path.

3. Submicroscopic Mechanics

The Lagrangian that is able to satisfy the described motion of a particle and the ensemble of its inertons can be written as:

L= (1/2) gᵢⱼ dXⁱ/dt dXʲ/dt + (1/2) Σₛ g⁽ˢ⁾ᵢⱼ dx₍ₛ₎ⁱ/dt₍ₛ₎ dx₍ₛ₎ʲ/dt₍ₛ₎

– Σₛ δt-Δt(s), t(s) (π/T₍ₛ₎) [Xⁱ · (gᵢqθε₍ₛ₎qj) dx₍ₛ₎ʲ/dt₍ₛ₎ + (v₀)ⁱ · (gᵢqθ ε₍ₛ₎qj) x₍ₛ₎ʲ] (2)

where the first term characterizes the kinetics energy of the particle, the second term characterizes the kinetics energy of the ensemble of N inertons, emitted from the particle and the third term specifies the contact interaction between the particle and its inertons. Xⁱ is the ith component of the position of the particle; gᵢⱼ is metric tensor components generated by the particle; (v₀)ⁱ is the ith component of the initial particle's velocity vector v₀. Index s corresponds to the number of respective inertons; x₍ₛ₎ʲ is the component of the position of the sth inerton; ε₍ₛ₎ᵢⱼ is the metric tensor components of the position of the sth inerton. 1/T₍ₛ₎ is the frequency of collisions of the particle with the sth inerton. Kronecker's symbol δt-Δt(s), t(s) provides the agreement of proper times of the particle t and the sth inerton t₍ₛ₎ at the instant of their collision (Δt₍ₛ₎ is the time interval after expire of which, measuring from the initial moment t = 0, the moving particle emits the sth inerton). The interaction operator · (gᵢqθε₍ₛ₎qj) possesses special properties: θ = 0 during a short time interval δt when the particle and the sth inerton is in direct contact and θ = 1 when the particle and the sth inerton fly apart along their own paths. Note that in the model presented the metric tensor characterizes changing in sizes of the particle and superparticles.

[The article continues with detailed mathematical derivations of equations of motion, solutions for particle and inerton cloud behavior, and the derivation of quantum mechanical relationships from the submicroscopic theory...]

4. Spin and Relativistic Approximation

The notion of spin of a particle is associated with an intrinsic particle motion. Several tens of works have been devoted to the spin problem. Main ideas are reduced to a moving particle that is surrounded by a wave, or a small massless particle, or an ensemble of small massless particles, which engage in a circular motion.

Having tried the introduction of the notion of spin in the concept presented, let us look at the situations in which the particle spin manifest itself explicitly. First, it appears as an additional member ± ℏ/2 to the projection onto the z-axis of the moment of momentum r × Mv₀ of a particle. Second, it introduces the correction ± eBzℏ/(2M) to the energy of a charged particle in the magnetic field with the projection of the induction onto the z-axis equals to Bz. Third, it provides for the Pauli exclusion principle.

Of course, it seems quite reasonable to assume that the spin in fact reflects some kind of proper rotation of the particle. However, we should keep in mind that the operation 'rotor' is typical for the electromagnetic field that the particle generates in the environment when starts to move. In other words, the appearance of the electromagnetic field in the particle surrounding one may associate just with its proper rotation of some sort. In our concept, superparticles that form the space net are not rigid; they fluctuate and allow local stable and unstable deformations. Thus the particle may be considered as not rigid as well. In this case along with an oscillating rectilinear motion, the particle is able to undergo some kind of an inner pulsation, like a drop. Besides the pulsation can be oriented either along the particle velocity vector or diametrically opposite to it.

[The section continues with detailed mathematical treatment of spin, intrinsic motion, and derivation of the Dirac formalism...]

5. Inertons in Action: Experimental Verification

§1. The photoelectric effect occurring under strong irradiation in the case that the energy of the incident light is essentially smaller than the ionization potential of gas atoms and the work function of the metal has been reconsidered from the submicroscopic viewpoint. It has been shown that the (nonlinear) multiphoton theory, which has widely been used so far, and the effective photon concept should be changed to a new methodology. The author's approach was based on the hypothesis that inerton clouds are expanded around atoms' electrons. That means that the effective cross-section σ of an atom's electron together with the electron's inerton cloud falls within the range between λ² and Λ² (i.e. 10⁻¹⁶ cm² < σ < 10⁻¹² cm²) that much exceeds the cross-section area of the actual atom size, 10⁻¹⁶ cm². The intensity of light in focused laser pulses used for the study of gas ionization and photoemission from metals was of the order of 10¹² to 10¹⁵ W/cm². Thus several tens of photons simultaneously should pierce the electron's inerton cloud and at least several of them could be engaged with the cloud's inertons and scattered by them. Consequently, the electron receives the energy needed to release from an atom or metal. The theory indeed has been successfully applied to the numerous experiments.

§2. In condensed media, inerton clouds of separate particles (electrons, atoms, and molecules) should overlap forming the entire elastic inerton field, which densely floods in the media. It has been theoretically shown that in this case the force matrix W that determines branches of acoustic vibrations in solids comprises of two members: W = Vac + Viner. Here the first member is responsible for the usual elastic electromagnetic interaction of atoms and is responsible just for the availability of acoustic properties of solids, but the second one is originated from the overlapping of atoms' inerton clouds. It is remarkable that each of the members has the same right. Therefore, an inerton wave striking an object will influence the object much as an applied ultrasound. Among the features of ultrasound, one can call destroying, polishing, and crushing. It was anticipated that inerton waves would act on specimens in a similar manner. A power source of inerton waves is the Earth: any mechanical fluctuations in the Earth should generate corresponding inerton waves. Two types of inerton flows one can set off in the terrestrial globe. The first flow is caused by the proper rotation of the Earth. Let A be a point on the Earth surface from which an inerton wave is radiated. If the inerton wave travels around the globe along the West-East line, its front will pass a distance L₁ = 2πREarth per circle. The second flow spreads along the terrestrial diameter; such inerton waves radiated from A will come back passing distance L₂ = 4REarth. The ratio is:

L₁/L₂ = π /2. (37)

If in point A we locate a material object which linear sizes (along the West-East line and perpendicular to the Earth surface) satisfy relation (37), we will receive a resonator of the Earth inerton waves.

We have studied specimens (razor blades) put into the resonator for several weeks. By using the scanning electron microscope, in fact, we have established difference in the fine morphological structure of cutting edge of the razor blades while the morphologically more course structure remains well preserved.

Note that the Earth inerton field is also the principal mover that launched rather fantastic quantum chemical physical processes in Egypt pyramids, power plants of the ancients that has recently been proved by Dunn (1998).

§3. Just recently, the inerton concept has been justified in the experiment on the searching for hydrogen atoms clustering in the δ-KIO₃·HIO₃ crystal. It has been assumed that vibrating atoms should induce the inerton field within the crystal. This in turn should change the paired potential of interatomic interaction. Taking into account such a possible alteration in the potential, we have calculated the number of hydrogen atoms in a cluster and predicted its properties. Then the crystal has been investigated by using the Bruker FT IR spectrometer in the 400 to 4000 cm⁻¹ spectral range. Features observed in the spectra unambiguously have been interpreted just as clustering of hydrogen atoms.

6. Concluding Remarks

Thus, we have uncovered that the interpretation of quantum mechanics in the framework of the double solution theory indeed is possible. However, the theory presented is distinguished from de Broglie's (1987), which he actively developed seeking for the solution of deterministic interpretation of the problem. The major point of the given concept is an original cellular construction of a real space, the introduction of notions of the particle, mass, and elementary excitations of the space. The mechanics constructed is based on the Lagrangians (16) and (23), equations of motion, and solutions to them, (17)-(22). The Lagrangians explicitly include elementary excitations of the space, which accompany a moving particle and directly interact with the particle. The main peculiarities of the mechanics called submicroscopic quantum (or wave) mechanics are the free path lengths for the particle λ and its inerton cloud Λ and, because of that, the mechanics is similar to the kinetics theory. The particle velocity v₀ is connected with λ by relation v₀ = λ/T where 1/T is the frequency of the particle collisions with the inerton cloud (and 1/2T = ν is the frequency of the particle oscillation along its path). Since the motion of the particle is of oscillating nature, it permits the construction of the Hamiltonian-Jacobi equation (25) and the obtaining the minimum increment of the particle action within the period ν⁻¹ that is identified with Planck's constant h. This allows one derives the principal quantum mechanical relations (1) and then constructs the Schrödinger and Dirac formalisms.

Submicroscopic quantum mechanics has solved the spin problem reducing it to special intrinsic pulsations of a moving particle. As a result, an additional correction (positive or negative) is introduced to the particle's Hamiltonian transforming it to a matrix form that in its turn has provided the reliable background to the Dirac's linearization of the classical relativistic Hamiltonian.

Inertons are treated as a substructure of the matter waves and yet inertons surrounding moving particles are identified with carriers of inert properties of the particles. The inerton concept also determines the boundaries of employment of the wave ψ-function and spinor formalisms reducing the boundaries to the range covered by inerton cloud amplitude Λ of the particle studied.

At last, inertons, which widely manifest themselves in numerous experiments, can be treated as a basis for anticipation in physical systems because just inertons represent those inner properties to which Dubois (1999a,b) referred constructing anticipation as actually embedded in the systems.

Further studies need widening the scope of applying of quantum mechanics. In particular, one could apply inertons to the problem of quantum gravity because inertons may also be considered as real carriers of gravitational interaction. Bounias (2001) has just found other application of inertons, namely, to biological systems: the availability of the inerton wave function of an object allowed him to construct the Hamiltonian of living organism considering it as an anticipatory operator of evolution.

References

Ahluwalia D. V. (1994). Quantum Measurement, Gravitation, and Locality. Physics Letters B 339, 301-303.
Ahluwalia D. V. (2000). Quantum Violation of the Equivalence Principle and Gravitationally Modified de Broglie Relation, arXiv.org e-print archive gr-qc/0002005.
Amaldi U. (2000). The Importance of Particle Accelerators. Europhysics News 31, 5-9.
Bohm D. (1952). A Suggested Interpretation of the Quantum Theory, in Terms of "Hidden" Variables. I. Physical Review 85, 166-179; (1952). A Suggested Interpretation of the Quantum Theory, in Terms of "Hidden" Variables. II, ibid., 85, 180-193.
Bohm D. (1996). On the Role of Hidden Variables in the Fundamental Structure of Physics, Foundations of Physics 26, 719-786.
Bounias M. (1990). La creation de la vie: de la matiere a l'esprit, L'esprit et la matiere, Editions du Rocher, Jean-Paul Bertrand Editeur.
Bounias M. (2000). The Theory of Something: a Theorem Supporting the Conditions for Existence of a Physical Universe, from the Empty Set to the Biological Self, International Journal of Computing Anticipatory Systems 5-6, 1-14.
Bounias M. (2001). "The Hamiltonian of Living Organisms: an Anticipatory Operator of Evolution." Computing Anticipatory Systems: CASYS'01 – Fifth International Conference. Edited by Daniel M. Dubois, Published by The American Institute of Physics, AIP Conference Proceedings, to be published.
Bounias M., and Bonaly A. (1994). On Mathematical Links Between Physical Existence, Observebility and Information: Towards a "Theorem of Something", Ultra Scientist of Physical Sciences 6, 251-259; (1996). Timeless Space is Provided by Empty Set, ibid. 8, 66-71.
Bounias M., and Bonaly A. (1996). On Metric and Scaling: Physical Co-ordinates in Topological Spaces, Indian Journal of Theoretical Physics 44, 303-321.
Bounias M., and Bonaly A. (1997). Some Theorems on the Empty Set as Necessary and Sufficient for the Primary Topological Axioms of Physical Existence, Physics Essays 10, 633-643.
Bounias M. and Krasnoholovets V. (2002). Scanning the Structure of Ill-known Spaces. II. Principles of Construction of Physical Space, to be submitted.
Chashihin J. (2000). To the Physical Nature of Spin. A Way to Unified Theory of Matter, Spacetime & Substance 1, no. 3, 128-131.
Danilov Yu. A., Rozhkov A. V., Safonov V. L. (1996). Possibility of Geometrical Description of Quasiparticles in Solids. International Journal of Modern Physics B 10, no. 7, 777-791.
De Broglie L. (1960). Non-linear Wave Mechanics. A Causal Interpretation. Elsevier, The Netherland.
De Broglie L. (1986). Heisenberg's Uncertainty Relations and the Probabilistic Interpretation of Wave Mechanics. Mir, Moscow.
De Broglie L. (1987). Interpretation of Quantum Mechanics by the Double Solution Theory. Annales de la Fondation Louis de Broglie 12, no. 4, 399- 421.
Dubois D. M. (1999a). "Review of Incursive, Hypercursive and Anticipatory Systems – Foundation of Anticipation in Electromagnetism". Computing Anticipatory Systems: CASYS'99 – Third International Conference. Edited by Daniel M. Dubois, Published by The American Institute of Physics, AIP Conference Proceedings 517, pp. 3-30.
Dubois D. M. (1999b). "Computational Derivation of Quantum Relativist Electromagnetic Systems with Forward-Backward Space-Time Shifts". Computing Anticipatory Systems: CASYS'99 – Third International Conference. Edited by Daniel M. Dubois, Published by The American Institute of Physics, AIP Conference Proceedings 517, pp. 417-429.
Dubrovin B. A., Novikov S. P., and Fomenko A. T. (1986). Modern Geometry. Methods and Applications, Nauka, Moscow, 1986, p. 291 (in Russian).
Dunn C. (1998). The Giza Power Plant: Technologies of Ancient Egypt: Technologiests of Ancient Egypt. Bear & Company, Inc., Santa Fe.
Kempf A., Mangano G., and Mann R. B. (1995). Hilbert Space Representation of the Minimal Uncertainty Relation. Physical Review D 52, 1108-1118.
Krasnoholovets V., and Ivanovsky D. (1993). Motion of a Particle and the Vacuum. Physics Essays, 6, no. 4, 554-563 (also quant-ph/9910023).
Krasnoholovets V. (1997). Motion of a Relativistic Particle and the Vacuum. Physics Essays, 10, no. 3, 407-416 (also quant-ph/9903077).
Krasnoholovets V. (2000a). On the Nature of Spin, Inertia and Gravity of a Moving Canonical Particle. Indian Journal of Theoretical Physics, 48, no. 2, 97-132 (also quant-ph/0103110).
Krasnoholovets V. (2000b). Space Structure and Quantum Mechanics. Spacetime & Substance 1, no. 4, 172-175 (also quant-ph/0106106).
Krasnoholovets V. (2001a). On the Theory of the Anomalous Photoelectric Effect Stemming from a Substructure of Matter Waves, Indian Journal of Theoretical Physics, 49, no. 1, 1-32 (also quant-ph/9906091).
Krasnoholovets V. (2001b). On the Way to Disclosing the Mysterious Power of the Great Pyramid. http://gizapyramid.com/DrV-article.htm .
Krasnoholovets V., and Byckov V. (2000). Real Inertons against Hypothetical Gravitons. Experimental Proof of the Existence of Inertons. Indian Journal of Theoretical Physics, 48, no. 1, 1-23 (also quant-ph/0007027).
Krasnoholovets V., Lev B., Gavrilko T., Puchkovska G., and Baran J. (2001). Clustering caused by crystal lattice's inerton field. H-clusters in the δ-KIO₃·HIO₃ crystal, arXiv.org e-print archive cond-mat/0108417.
Leonhardt U., and Piwnicki P. (1999). Optics of Nonuniformly Moving Media. Physical Review A 60, 4301-4412.
Okun L. B. (1988). Physics of Elementary Particles, Nauka, Moscow (in Russian).
Plyuschay M. S. (1989). Massless Point Particle with Rigidity, Modern Physics Letters A 4, 837-847.
Plyuschay M. S. (1990). Relativistic Particle with Arbitrary Spin in non Grassmannian Approach, Physics Letters B 248, 299-304; Relativistic Model of the Anyon, Physics Letters B 248 107-112.
Plyuschay M. S. (2000). Monopole Chern-Simons Term: Charge Monopole System as a Particle with Spin, Nuclear Physics B 589, 413-439.
Pullin J. (1993). Knot Theory and Quantum Gravity in Loop Space: a Primer. In Proceeding of the V Mexicon School of Particles and Fields, ed. J. L. Lucio, World Scientific, 1992.
Rangelov J. M. (2001). Physical Model of Schrödinger's Electron. Heisenberg Convenient Way for Description of its Quantum Behaviour. arXiv.org e-print archive quant-ph/0001099; Physical Model of Dirac Electron. Calculation of its Mass at Rest and own Electric and Magnetic Intensities on its Momentum Location.arXiv.org e-print archive quant-ph/0002019.
Sahni V., and Wang L. (2000). New Cosmological Model of Quintessence and Dark Matter. Physics Review D 62, 103517.
Schiff L. I. (1959). Quantum Mechanics. Izdatelstvo Inostrannoi Literatury, Moscow (Russian translation), p. 373.
't Hooft G. (1998). Transplanckian Particles and the Quantization of Time. arXiv.org e-print archive gr-qc/9805079.
Wallace D. (2000). The Quantization of Gravity – an Introduction. arXiv.org e-printarchive gr-qc/0004005.

The Quantum World

Fundamental Principles

Quantum mechanics describes:

Subatomic particle behavior
Wave-particle duality
Energy quantization
Field interactions
Probabilistic nature

Relevance to Pyramids:

Matter is mostly empty space
Fields permeate vacuum
Geometry affects fields
Energy state changes
Quantum coherence possible

Pyramid as Quantum Device

Geometric Field Modulator

Shape-Induced Effects

The pyramid geometry:

Creates field distortions
Modifies vacuum state
Concentrates energy
Generates coherence
Induces quantum effects

Mechanism:

Boundary conditions matter
Geometry constrains fields
Standing waves form
Resonance develops
Energy focuses

Quantum Vacuum Interaction

Zero-Point Energy

The quantum vacuum:

Not truly empty
Contains fluctuations
Virtual particles
Energy present
Geometric sensitivity

Pyramid Interaction:

Shape affects vacuum
Energy extraction possible
Field reorganization
Coherent structures
Measurable effects

Wave Function Considerations

Quantum States

Matter as Waves

Quantum mechanics reveals:

Particles are wave functions
Probability distributions
Superposition states
Coherence phenomena
Measurement effects

Pyramid Influence:

Geometry affects wave functions
Boundary conditions imposed
State selection occurs
Coherence enhanced
Quantum optimization

Schrödinger Equation

Mathematical Framework

The wave equation:

Describes quantum evolution
Boundary dependent
Geometry matters
Energy eigenstates
Probability amplitudes

Application to Pyramids:

Geometric constraints
Field solutions
Energy levels
State selection
Observable effects

Field Theory Approach

Quantum Field Theory (QFT)

Modern Physics

QFT describes:

Particles as field excitations
Vacuum fluctuations
Virtual particles
Energy-time uncertainty
Field interactions

Pyramid Context:

Fields everywhere
Geometry modifies fields
Energy redistribution
Coherent structures
Measurable consequences

Casimir Effect Analogy

Geometric Effects

Casimir effect demonstrates:

Geometry affects vacuum
Measurable forces
Quantum origin
Experimental verification
Precedent for pyramid effects

Parallel:

Shape matters
Vacuum modified
Energy differences
Physical forces
Scientific validation

Coherence and Decoherence

Quantum Coherence

Organized States

Coherence means:

Phase relationships
Organized behavior
Enhanced effects
Fragile state
Environmental sensitivity

Pyramid Generation:

Geometry creates coherence
Field organization
Energy focusing
Enhanced phenomena
Observable effects

Maintaining Coherence

Decoherence Challenge

Quantum states:

Easily disturbed
Environmental interaction
Loss of coherence
Classical behavior
Measurement problem

Pyramid Protection:

Geometric shielding
Field stabilization
Coherence maintenance
Extended durations
Enhanced effects

Energy Levels and Transitions

Quantized States

Discrete Energies

Quantum systems have:

Specific energy levels
Forbidden intermediate states
Quantum jumps
Photon emission/absorption
Spectral signatures

Pyramid Effects:

Materials in pyramid
Energy state changes
Optimal configuration
Quantum transitions
Property modifications

Resonance Phenomena

Matching Frequencies

Quantum resonance:

Energy level matching
Enhanced transitions
Amplified effects
Geometric dependence
Frequency selection

Pyramid Geometry:

Specific frequencies favored
Resonance enhancement
Energy concentration
Selective effects
Optimized outcomes

Entanglement Considerations

Quantum Correlations

Non-Local Connections

Entanglement creates:

Correlated particles
Non-local effects
Instant connections
Information sharing
Quantum weirdness

Pyramid Hypothesis:

Geometry creates entanglement
Coherent field structures
Non-local effects
Information transfer
Consciousness interaction?

Tunneling and Barriers

Quantum Tunneling

Through the Impossible

Quantum mechanics allows:

Barrier penetration
Classically forbidden
Probability-based
Energy-dependent
Observable effect

Pyramid Application:

Enhanced tunneling rates
Chemical reaction facilitation
Material transformation
Biological processes
Energy transfer

Measurement and Observation

Observer Effect

Measurement Problem

Quantum mechanics:

Observation affects system
Wave function collapse
State selection
Consciousness role?
Interpretive debates

Pyramid Research:

Intention effects reported
Observer influence
Measurement challenges
Consciousness connection
Scientific controversy

Submicronic Particles

Beyond Standard Model

Krasnoholovets's Extension

Proposes particles:

Smaller than known
Information carriers
Field interactions
Mass-energy connection
New physics

Pyramid Interaction:

Geometry affects particles
Energy redistribution
Information processing
Observable effects
Testable predictions

Theoretical Predictions

Testable Hypotheses

Scientific Approach

Quantum theory predicts:

Specific frequency responses
Geometric optimization
Material dependencies
Temporal variations
Measurable quantities

Experimental Validation:

Spectroscopic signatures
Energy measurements
Field mapping
Material analysis
Statistical verification

Challenges to Theory

Scientific Objections

Mainstream Concerns:

Scale Problem:

Quantum effects microscopic
Pyramid macroscopic
Decoherence rapid
Classical regime
Size mismatch

Energy Scale:

Quantum energies tiny
Pyramid effects macroscopic
Amplification unexplained
Mechanism unclear
Theoretical gap

Lack of Evidence:

Insufficient data
Alternative explanations
Reproducibility issues
Measurement artifacts
Skepticism warranted

Theoretical Responses

Defense of Approach:

Quantum Macroscopy:

Some effects scale up
Casimir force example
Superconductivity
Bose-Einstein condensates
Precedents exist

Collective Effects:

Many particles together
Coherent amplification
Emergent phenomena
Geometric organization
Observable consequences

Experimental Evidence

Supporting Observations

Consistent with Theory:

Spectroscopic Changes:

Water structure modifications
Molecular rearrangements
Energy level shifts
Quantum signatures
Reproducible data

Field Measurements:

Electromagnetic variations
Spatial patterns
Temporal correlations
Geometric dependencies
Predicted behaviors

Material Properties:

Conductivity changes
Crystal modifications
Quantum state alterations
Energy relaxation
Observable effects

Consciousness Connection

Controversial Territory

Mind-Matter Interaction

Some propose:

Consciousness quantum
Observation affects
Intention influences
Pyramid amplifies
Mind-field coupling

Scientific Caution:

Highly speculative
Difficult to test
Alternative explanations
Remains controversial
Ongoing debate

Future Research Directions

Needed Investigations

Experimental:

Quantum spectroscopy
Coherence measurements
Entanglement tests
Field characterization
Statistical analysis

Theoretical:

Detailed calculations
Mechanism modeling
Prediction refinement
Alternative theories
Peer review

Practical Implications

Technology Applications

If Theory Correct:

Energy:

Vacuum energy extraction
Coherent field generation
Efficiency improvements
Clean energy potential
Revolutionary technology

Materials:

Quantum state control
Property optimization
Manufacturing applications
Nano-technology
Advanced materials

Information:

Quantum computing
Coherence maintenance
Information processing
Communication systems
Data storage

Integration with Other Theories

Complementary Approaches

Torsion Fields:

Another quantum approach
Spin-based effects
Geometric sensitivity
Compatible theory
Mutual support

Inerton Theory:

Krasnoholovets's development
Submicronic particles
Information carriers
Energy transmission
Pyramid interaction

Conclusion

Dr. Krasnoholovets's quantum mechanical approach to pyramid phenomena represents an attempt to ground observed effects in established physics principles while proposing extensions to current theory where needed.

Key Aspects:

Scientific Foundation:

Quantum mechanics basis
Field theory application
Mathematical framework
Testable predictions
Rigorous approach

Theoretical Development:

Mechanism proposals
Energy explanations
Coherence concepts
Geometric effects
Novel extensions

Experimental Support:

Measurable effects
Spectroscopic data
Field measurements
Material changes
Statistical significance

Challenges:

Scale considerations
Mechanism clarity
Reproducibility
Mainstream acceptance
Ongoing debate

Whether quantum mechanics fully explains pyramid phenomena or not, Krasnoholovets's work demonstrates that serious theoretical physics can be applied to these questions, moving the discussion from anecdote and speculation toward scientific investigation and theoretical rigor.

The quantum approach invites both experimental verification and theoretical critique—the proper path for advancing scientific understanding of any phenomenon, conventional or unconventional.