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Journal of High Energy Physics, Gravitation and Cosmology 2021年第2期7卷 416-444页

作者： jaykov foukzon Center for Mathematical Sciences Israel Institute of Technology Haifa Israel

The notion of classical well localized trajectories of a single photon in Minkowski spacetime does not make any rigorous sense by the well-known existence of a proof that single photons cannot be well localized. This leads to principal difficultness when photodetection probability on relativistic non inertial frame of reference is considered. In order to resolve this tension, we extend canonical Minkowski geometry up to relevant point-free Minkowski geometry [Ann. Physics 423 (2020) 168329]. The photodetection probability density on uniformly rotating frame endrowed with point-free Lorentzian geometry is obtained. The result of S. A. Podosenov et al. [Ann. Physics 413 (2020) 168047] is obtained without any reference to unphysical notion of the classical trajectories of photon. The paper again shows the correctness of the remarkable result of Prof. C. Corda concerning the Mössbauer rotor experiment as new proof of general relativity, which has been awarded by the Gravity Research Foundation. In addition, the paper also shows various very elementary mistakes, misunderstandings and flaws by the self-called “YARK group”, which is a group of fringe researchers who attempts to promote wrong science, in particular, against the relativity theory.

关键词： Mössbauer Rotor Experiment Uniformly Rotating Frame Photodetection Probability Density Minkowski Point-Free Geometry

New Scenario for Transition to Slow 3-D Turbulence

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Journal of Applied Mathematics and Physics 2015年第3期3卷 371-389页

作者： jaykov foukzon Department of Mathematic Israel Institute of Technology Haifa Israel

Analytical non-perturbative study of the three-dimensional nonlinear stochastic partial differential equation with additive thermal noise, analogous to that proposed by V. N. Nikolaevskii [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310035003200310033003400300034000000 -[5] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003400310035003200310033003400300035000000 to describe longitudinal seismic waves, is presented. The equation has a threshold of short-wave instability and symmetry, providing long wave dynamics. New mechanism of quantum chaos generating in nonlinear dynamical systems with infinite number of degrees of freedom is proposed. The hypothesis is said, that physical turbulence could be identified with quantum chaos of considered type. It is shown that the additive thermal noise destabilizes dramatically the ground state of the Nikolaevskii system thus causing it to make a direct transition from a spatially uniform to a turbulent state.

关键词： 3D Turbulence Chaos Quantum Chaos Additive Thermal Noise Nikolaevskii System

Non-Archimedean Analysis on the Extended Hyperreal Line *R<sub>d</sub>and the Solution of Some Very Old Transcendence Conjectures over the Field Q

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Advances in Pure Mathematics 2015年第10期5卷 587-628页

作者： jaykov foukzon Center for Mathematical Sciences Israel Institute of Technology Haifa Israel

In 1980 F. Wattenberg constructed the Dedekind completion *Rd of the Robinson non-archimedean field *R and established basic algebraic properties of *Rd. In 1985 H. Gonshor established further fundamental properties of *Rd. In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion *Rd in transcendental number theory were considered. Given any analytic function of one complex variable , we investigate the arithmetic nature of the values of at transcendental points . Main results are: 1) the both numbers and are irrational;2) number ee is transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.

关键词： Non-Archimedean Analysis Robinson Non-Archimedian Field Dedekind Completion Dedekind Hyperreals Wattenberg Embeding Gonshor Idempotent Theory Gonshor Transfer

There Is No Standard Model of ZFC and ZFC_(2) with Henkin Semantics

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Advances in Pure Mathematics 2019年第9期9卷 685-744页

作者： jaykov foukzon Elena Men’kova Department of Mathematics Israel Institute of TechnologyHaifaIsrael Lomonosov Moscow State University MoscowRussia

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models or nonstandard model with standard part. A possible generalization of Löb’s theorem is consi... 详细信息

关键词： Godel Encoding Completion of ZFC Russell’s Paradox ω-Model Henkin Semantics Full Second-Order Semantic Strongly Inaccessible Cardinal

Exact Quasi-Classical Asymptotic beyond Maslov Canonical Operator and Quantum Jumps Nature

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Journal of Applied Mathematics and Physics 2015年第5期3卷 584-607页

作者： jaykov foukzon Alex Potapov Stanislav Podosenov Israel Institute of Technology Haifa Israel The Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences Moscow Russian All-Russian Scientific-Research Institute Moscow Russian

Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.

关键词： Quantum Jumps Quantum Measurements Theory Quantum Averages Limiting Quantum Trajectory Schrodinger Equation Stochastic Quantum Jump Equation Colombeau Solution Feynman Path Integral Maslov Canonical Operator Feynman-Colombeau Propagator

The Solution Cosmological Constant Problem

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Journal of Modern Physics 2019年第7期10卷 729-794页

作者： jaykov foukzon Elena Men’kova Alexander Potapov Department of Mathematics Israel Institute of Technology Haifa Israel All-Russian Research Institute for Optical and Physical Measurement Moscow Russia Kotel’nikov Institute of Radioengineering and Electronics Russian Academy of Sciences Moscow Russia

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by the Quantum Field Theory is about 120 orders of magnitude larger then the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff-Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that the Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way. We argue that there exists hidden physical mechanism which cancels divergences in canonical QED4, QCD4, Higher-Derivative-Quantum gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost fields really exist. It means that there exists the ghost-driven acceleration of the universe hidden in cosmological constant. In order to obtain the desired physical result we apply the canonical Pauli-Villars regularization up to Λ*. This would fit in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below the scale Λ*, i.e., The small value of the cosmological constant is explained by tiny violation of the symmetry between standard matter and ghost matter. Dark matter nature is also explained using a common origin of the dark energy and dark matter phenomena.

关键词： Cosmological Constant Problem Quantum Field Theory Vacuum Energy Density Quantum Space-Time Hausdorff-Colombeau Dimension Quantum Fluctuations High-Energy Cutoff Canonical Pauli-Villars Regularization Universe

The Solution Classical Feedback Optimal Control Problem for m-Persons Differential Game with Imperfect Information

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Open Journal of Optimization 2013年第1期2卷 16-25页

作者： jaykov foukzon Elena Men’kova Alex Potapov All-Russian Research Institute for Opto-Physical Measurements Moscow Russia Department of Mathematics Israel Institute of Technologies Haifa Israel V.A. Kotel’nikov Institute of Radio Engineering and Electronics Russian Academy of Sciences Moscow Russia

The paper presents a new approach to construct the Bellman function and optimal control directly by way of using strong large deviations principle for the solutions Colombeau-Ito’s SDE. The generic imperfect dynamic models of air-to-surface missiles are given in addition to the related simple guidance law. A four examples have been illustrated, corresponding numerical simulations have been illustrated and analyzed.

关键词： Optimal Control Bellman Equation

Was Polchinski Wrong? Colombeau Distributional Rindler Space-Time with Distributional Levi-CivitàConnection Induced Vacuum Dominance. Unruh Effect Revisited

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Journal of High Energy Physics, Gravitation and Cosmology 2018年第2期4卷 361-440页

作者： jaykov foukzon Alexander Potapov Elena Men’kova Center for Mathematical Sciences Israel Institute of Technology Haifa Israel IRE RAS Moscow Russia All-Russian Research Institute for Optical and Physical Measurements Moscow Russia

The vacuum energy density of free scalar quantum field in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Cività connection. In particular we obtain that the vacuum fluctuations have a singular behavior at a Rindler horizon . Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski’s account doesn’t violate the Einstein equivalence principle.

关键词： Vacuum Energy Density Rindler Distributional Space-Time Levi-Cività Connection Semiclassical Gravity Effect Einstein Equivalence Principle Space-Time Einstein Equivalence Principle

Electrodynamics in Noninertial Reference Frames

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Journal of Applied Mathematics and Physics 2016年第4期4卷 806-843页

作者： Stanislav A. Podosenov jaykov foukzon Alexander Potapov Elena Men’kova All-Russian Research Institute for Optical and Physical Measurements Moscow Russia Center for Mathematical Sciences Israel Institute of Technology Haifa Israel Kotel’nikov Institute of Radioengineering and Electronics Russian Academy of Sciences Moscow Russia

The electrodynamics both in RF with prescribed law of motion and in FR with prescribed structure is considered. Parallel comparison for solutions in “uniformly accelerated” NRF M?ller system and in uniformly accelerated rigid NFR in the space of the constant curvature is carried out. The stationary criterion is formulated. On the basis of this criterion, one of the “eternal physical problems” concerning the field at uniformly accelerated charge motion is considered. The problems of electromagnetic wave spreading, Doppler’s effect and field transformations are discussed.

关键词： Noninertial Reference Frame (NFR) Möller System Space-Time Curvature Anholonomic Transformations Doppler’s Effect Electromagnetic Wave

Schrödinger’s Cat Paradox Resolution Using GRW Collapse Model: Von Neumann Measurement Postulate Revisited

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Journal of Applied Mathematics and Physics 2017年第2期5卷 494-521页

作者： jaykov foukzon Alex Potapov Elena Men’kova Stanislav Podosenov Center for Mathematical Sciences Israel Institute of Technology Haifa Israel IRE RAS Moscow Russia All-Russian Research Institute Moscow Russia

In his famous thought experiment, Schr?dinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life. Since Schr?dinger’s time, no any interpretations or modifications of quantum mechanics have been proposed which give clear unambiguous answers to the questions posed by Schr?dinger’s cat of how long superpositions last and when (or whether) they collapse? In this paper appropriate modification of quantum mechanics is proposed. We claim that canonical interpretation of the wave function is correct only when the supports of the wave functions and essentially overlap. When the wave functions and have separated supports (as in the case of the experiment that we are considering in this paper) we claim that canonical interpretation of the wave function is no longer valid for a such cat state. Possible solution of the Schr?dinger’s cat paradox is considered. We pointed out that the collapsed state of the cat always shows definite and predictable outcomes even if cat also consists of a superposition: .

关键词： Probability Representation of Quantum States Schrödinger’s Cat GRW Collapse Model Von Neumann Measurement Postulate