 "Hypercomplex Numbers in geometry and Physics" 1 (21), Vol 11, 2014
j021
Content of Issue
 Hyperbolic «statics» in space-time
2014jax | PavlovD.G., Kokarev S.S. // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia; RSEC Logos, Yaroslavl, Russia, geom2004@mail.ru, logos-center@mail.ru
With using the concept of matter event as a matter source, concentrated on metric sphere of null radius — light cone of Minkowski space-time, — we derive the analog of
Coulomb’s law for hyperbolic space-time field, universally acting between events of space-time. The collective field, providing interaction of the world lines of a
pair of particles, consists of 3D Coulomb’s part and logarithmic term. We reveal, that the Coulomb’s part is caused by tune balance between causal and geometric
properties of space-time (concordance of a two regularization procedures). Equation of motion (in fact — equation of 4D static) for self-consistent configuration of
two world lines are integro-differential ones. It is shown, that these equations may be rewritten in the form of relativistic second Newton’s law, where the force and
the mass are special parts of universal hyperbolic interaction. We discuss principles and perspectives of using of the device called hyperbolic lense, which is 4D
analog of dielectric lense of standard electrostatic.
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About the modern point of view on the A.Einstain, sprinciple of general relativity
2014jbx | Zhotikov V.G. // Moscow Institute for Physics and Technology (State University), Moscow, Russian Federation, zhotikov@yandex.ru
Paradoxical situation has long been formed in the physical sciences. From the middle of the last century, in estimating the value of the general principle of
relativity (GPR), the opinion of the physics community was divided into two oppositely point of view. We will not enumerate all the supporters and opponents of any of
them, and for the sake of brevity, we combine them with the names of their representatives – the greatest physicists of the 20th century. Let’s call the first one –
the point of view of V. Gisnzburg (see, eg, [1]), and the second – the point of view of V. Fock (see, eg, [2, 3]). The first interprets the general theory of
relativity (GTR) of A. Einstein as the most important achievement of physical thought of the 20th century. The second denies the role of GPR as a fundamental physical
principle. Purpose of this work – give an idea of the current state of the question. The true meaning of the principle of relativity is revealed in the introduction of
new geometries to the physical science, that are more general than the geometry of Riemann spaces, serving as the mathematical foundation of general relativity. These
include the geometry of Finsler spaces and its generalizations — the geometry of spaces with an areal metric (see, eg. [11,14]).
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Maxwell electromagnetic equations in the uniform medium. An alternative to the Minkowski theory of special relativity
2014jcx | Balan V., Ovsiyuk E.M., Red’kov V.M., Veko O.V. // Mozyr State Pedagogical University, Mozyr, Belarus; University Politehnica of Bucharest, Bucharest, Romania; B.I. Stepanov Institute of Physics, NAS of Belarus,
vladimir.balan@upb.ro; e.ovsiyuk@mail.ru; redkov@dragon.bas-net.by; vekoolga@mail.ru
Two known, alternative to each other, forms of presenting the Maxwell electromagnetic equations in a moving uniform medium are discussed. The commonly used Minkowski
approach is based on two tensors; the relationships between them change their form under Lorentz transformations and take the shape of Minkowski equations, depending
upon the 4-velocity of the moving particle in an inertial reference frame. In this approach, the wave equation for the electromagnetic 4-potential has a form which
explicitly involves this 4-velocity vector of the reference frame. Hence, the Minkowski electrodynamics implies the absolute nature of mechanical motion. An
alternative formalism (proposed by Rosen & al.) may be constructed in new variables, when the Maxwell equations are written in terms of a single tensor. This form of
Maxwell equations exhibits symmetry under modified Lorentz transformations in which, everywhere, instead of the vacuum speed of light cone uses the medium speed of
light c*c. Due to this symmetry, the formulation of Maxwell theory in this medium can be considered as invariant under the mechanical motion of the reference frame,
while the transition must follow modified Lorentz formulas. The transition of the Maxwell equations to 4-potential leads to a simple wave equation which does not
contain any additional 4-velocity parameter, so this form of the electrodynamics presumes a relative nature of the mechanical motion; also, this equation describes
waves which propagate in space with light velocity kc, which is invariant under the modified Lorentz formulas. In connection with these two theoretical alternative
schemes, an essential issue must be stressed: it seems reasonable to perform the Poincar´e-Einstein clock synchronization in uniform media with the help of real light
signals influenced by the medium, which leads us to modified Lorentz symmetry. A similar approach is developed for a spin 1/2 particle obeying the Dirac equation in a
uniform medium.
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Displacement of light during satellite laser ranging
2014jdx | Ignatenko Yu.V., Ignatenko I.Yu., Tryapitsyn V.N. // Crimean Laser Observatory of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Yalta, Republic of Crimea; Federal State Unitary
Enterprise “Russian Metrological Institute of Technical Physics and Radio Engeneering” (VNIIFTRI), Mendeleevo, Russia, igig@vniiftri.ru
This article describes the results of a study of the anomalous deviation of light detected during laser ranging of the Earth artificial satellites. A special technique
developed for construction of a three-dimensional vector of the laser beam deviation based on processing of its projections onto a focal plane of a telescope is
stated. Appropriate equations are derived. A method and results of test measurements of the displacement of light near the surface of the Earth, confirming the
universal nature of this phenomenon, are described. From these results, the conclusion of the motion of light medium, traditionally called the luminiferous ether, at a
rate in magnitude and direction close to but not equal to the velocity of the Earth is derived. Measured the deflection of light from a given direction is the result
of adding the relative velocity of the satellite, velocity of the Earth, and finally light medium speed. This last fact explains the seasonal dependence of the
measurements.
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Comments to the paper by Ignatenko Yu.V., Ignatenko I.Yu. and Triapitsyn V.N. «Light deviation detected in the laser ranging».
2014jex | Siparov S.V. // Civil Aviation State University, Saint-Petersburg, Russia, sergey.siparov@gmail.com
The comments clarify the essentials and results of the mentioned paper for the theoreticians who are not well aquainted with the experimental technic. It is also
suggested to feel more free while using the notion of «ether», if this helps to demonstrate the heart of the matter. It is also shown that alongside with the
interpretation given by the authors which is based on this notion, it is possible to use the geometrical approach.
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Inadequacy of the linear vector space formalism at metric approach to geometry
2014jfx | Rylov Yuri A. // Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia, rylov@ipmnet.ru
It is shown that formalism of linear vector space is inadequate at the metric approach to geometry, when geometry is described completely in terms of the distance functiond, or in terms of the world function σ=d^2/2. Operations of the linear vector space appear to be ambiguous, if they are introduced at the metric approach to geometry.
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Investigation of possible space-time effects of hyperbolic field: frequency shift of ultrastable quartz generator in neighborhood of powerful electric discharge
2014jix | Pavlov D.G., Chalkin S.Ph., Panchelyuga M.S., Panchelyuga V.A. // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics of the Russian Academy of
Sciences, Pushchino, Russia, panvic333@yahoo.com
Present paper continues investigation of possible manifestations of hyperbolic field. The paper contains preliminary results of experimental studies of ultrastable quartz generator frequency change in neighborhood of powerful electric discharge. Obtained results show that in moment of discharge appears frequency shift in output signal of quartz generator. Under the same condition but without the discharge the frequency shift is absent. Obtained results may be considered as possible evidence
of hyperbolic field existence.
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Local fractal analysis of noise-like time series by all permutations method
2014jgx | Panchelyuga V.A., Panchelyuga M.S. // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics of the Russian Academy of
Sciences, Pushchino, Russia, panvic333@yahoo.com
In the present work local fractal analysis of non-stationary time series by all permutations method (APM) is developed. APM-method [1] incorporates ideas of method of minimal cover [2] and histograms method [1]. Analysis of histograms method achieves that some periods in noise-like time series can be revealed only by means of the
method and cannot be find out by traditional methods of time series analysis like correlation analysis, spectral analysis, dispersion analysis and so on. Connection between shapes of smoothed histograms constructed on the base of short segments of time series of fluctuations and fractal dimension of the segments is studied. Is shown that fractal dimension posses all main properties of histogram method. On this base a further development of fractal dimension determination algorithm is proposed. This algorithm allows precision determination of fractal dimension by using short (30-60 points) time series segments. This property of APM-method leads to possibility of analysis of non-stationary time series.
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SOME PRELIMINARY RESULTS OF LOCAL FRACTAL ANALYSIS OF NOISE-LIKE TIME SERIES BY ALL PERMUTATIONS METHOD FOR PERIODS 1-120 MIN
2014jpx | Panchelyuga V.A., Panchelyuga M.S. // Research Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia; Institute of Theoretical and Experimental Biophysics of the Russian Academy of
Sciences, Pushchino, Russia, panvic333@yahoo.com
Results of local fractal analysis of 329 1-day time series of Pu-239 alpha-decay rate fluctuations by means of all permutations method (APM) [1] are presented. The APManalysis reveals in the time series some steady frequency set. Coincidence of the frequency set with the Earth natural oscillations was demonstrated. Short revue of periods in fluctuations of various processes (physical, chemical, biological) in range 1-120 min described in works of different authors are given. We shown that periods observed in cited papers corresponds to periods, which revealed in present report. Such correspondence leads to conclusion about some common mechanism, which may cause observed periodicity in processes of different nature.
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Ternary product over three-dimensional matrices
2014jrx | Lapshin A.V. // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, lavexander@mail.ru
The paper presents the ternary generalization of the standard algebra of matrices to the case of spatial (cubic) matrices. In addition to the definition of the ternary
operation itself and to its basic properties, the multy-dimensional versions of the other conventional concepts, operations and mapping such as transposition, unit element, commutativity, associativity and others that are used in the standard algebra of matrices are constructed. The relationship between the constructed ternary operation and the algebra of polynumbersP3is discussed.
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PROFESSOR DR. GHEORGHE ATANASIU 1939-2014
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PROFESSOR DR. HOWARD EDWARD BRANDT 1939-2014
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