Aleksandr Efremov
Doctor of Physics and Mathematics
Professor, Full member of the Russian Academy of Natural Sciences,
When we know how the physical world works, we will find out what we are needed for in this world.
1961 - 1965
Studied at Moscow Aviation Instrument Making College named after S. Ordzhonikidze, qualification - “Technician-mechanic, aviation devices”.
1966 - 1969
Served in the Soviet army, qualification - “Technician-heating”.
1969 - 1974
Studied at Peoples’ Friendship University named after P. Lumumba (now RUDN University), qualification - “Physicist”.
1974 - 1977
Postgraduate course of Peoples’ Friendship University named after P. Lumumba (now RUDN University) (Theoretical Physics), thesis on “Research of gravitational fields and cosmological models in torsion spaces” for the degree of Candidate of Physical and Mathematical Sciences was defended.
1977 - 1986
Senior lecturer at the Faculty of Physics, Mathematics and Natural Sciences of Peoples’ Friendship University named after P. Lumumba (now RUDN University), worked in the Department for work with students.
1982 - 1983
Research internship at the University of Houston, Houston, USA.
1986 - 1992
Senior lecturer, associate professor of the Department of Natural Sciences of the Preparatory Faculty of Peoples’ Friendship University named after P. Lumumba (now RUDN University).
1992 - present
Head of the Department of Physics: 1992-2000 - of the Preparatory Faculty, 2000-2020 – of the faculty of Russian Language and General Educational Disciplines, since 2020 - of Educational and Scientific Institute of Gravitation and Cosmology RUDN University.
1994 - 1998
Vice-Rector for Academic Affairs of RUDN University.
1998 - 2020
First Vice-Rector - Vice-Rector for Academic Affairs of RUDN University.
1999 - present
Director of Educational and Scientific Institute of Gravitation and Cosmology RUDN University.
2005
Order of Friendship of Peoples for fruitful activities in the development of science, education, health and culture was awarded.
2005 - 2007
Member of the Commission of the Ministry of Education and Science on the implementation of the Bologna Agreement in the Russian Federation.
2006
Thesis on “Research of quaternion spaces and their relationship with reference systems and physical fields” for the degree of Doctor of Physical and Mathematical Sciences was defended.
2006 - 2010
Member of the Council for Quality of Education of the Federal Service for Supervision of Education and Science.
2011
Title of honorary worker of higher education of the Russian Federation for services to scientific and pedagogical work and training of highly qualified specialists was awarded.
2018
Gratitude of the President of the Russian Federation for fruitful long-term work in the higher education system.
Teaching
- The developer of the course: Quaternion algebra, fractal space, and General theory of mechanics iversity.org of Springer Nature.
https://iversity.org/en/courses/quaternion-algebra-fractal-space-and-general-theory-of-mechanics - The main idea of the course is to learn that a number of physical laws, initially discovered in an experiment and described by mathematical formulas, exist in the mathematical environment of hypercomplex numbers.
The author of monographs:
- Yefremov A.P. The fractal structure of space entails origin of Pauli equation / Gravitation Cosmology, 2019, 25(4), pp. 305-309.
This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world entities, this condition acquires the precise form of the Pauli equation describing mechanics of the quantum electron with spin.
https://www.researchgate.net/publication/337838143_The_Fractal_Structure_of_Space_Entails_Origin_of_Pauli's_Equation - Yefremov A.P. General theory of particle mechanics arising from fractal space / Gravitation and Cosmology, 2015, 21(1), pp. 19-27.
We trace the logical line of formulating a theory of mechanics founded on the basic relations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical and relativistic mechanics can be regarded as mathematical consequences of a single condition of stability of exceptional algebras of real, complex and quaternion numbers under transformations of primitive constituents of their units and elements. In the course of the study, the notion of a basic fractal surface underlying the physical three-dimensional space is introduced, and an original geometric treatment (admitting visualization) of some formerly considered abstract functions (mechanical action, space-time interval) are suggested.
https://www.researchgate.net/publication/276695536_General_Theory_of_Particle_Mechanics_arising_from_a_fractal_surface - Yefremov A. P. General theory of mechanics of particles, arising from the fractal space
It is shown that the physical equations of quantum, classical, and relativistic mechanics can be considered as mathematical consequences of a single condition for the stability of exceptional algebras of real, complex, and quaternion numbers under transformations of their primitive constituent units and elements. The research introduces the concept of a basic fractal surface that underlies the physical three-dimensional space, and offers an original geometric interpretation (allowing visualization) of some previously considered abstract functions (mechanical action, space-time interval).
Science
- Studied the structure of the noncommutative exceptional algebra of hypercomplex numbers with 4 units (quaternions). Proved the possibility of a vector quaternion formulation of the theory of relativity. It confirms all the predictions of Einstein's theory, but offers a symmetric (6-dimensional) structure of the model of the Universe.
- Studied the fractal structure of 3D-space - the geometric image of vector units of the quaternion algebra. Proved that the condition for the stability of algebra (and 3D-space) under the simplest deformations of a fractal subspace is precisely the Schrodinger equation – the physical equation of quantum mechanics.
- Studied methods of spacecraft control systems and calculation of space probe trajectories. Proposed a new algorithm for controlling spacecraft. Proved that the gravitational maneuver of the space probe allows to multiply the small physical effects of the deviation of bodies from the classical orbits in the Solar system.
Scientific interests
- geometrization of physical interactions
- relationship between quaternion mathematics and the laws of physics and the structure of the Universe
- study of relativistic effects of the motion of cosmic bodies
We build a Kepler model of spacecraft gravity assist maneuver near a Venus-type planet and investigate its sensitivity to changes of the impact parameter. Analytical and numerical computations give similar results indicating a great increase of the trajectory final point shift under a small variation of the assigned spacecraft-planet distance.
The general relativistic (GR) impact is assessed on the precision of the announced BepiColombo (BC) space positions at the Earth, Venus and Mercury flyby points providing planned gravity-assists. Apart of the known elliptic orbit precession, another recently specified for the Schwarzschild-Kerr metric effect of the ellipse axes contraction is considered in the thoroughly built model of BC motion from the launch point to the first assigned flyby point at Venus. The intermediate Earth gravity-assist act is shown to serve as an amplifier of the GR effects, so that the total GR-caused position shift at Venus can reach great distances, exceeding the accuracy of the assigned lengths thousands of times. Similar factors entailing possible GR deviation from BC-Mercury expected flyby points are also analysed.
This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world entities, this condition acquires the precise form of the Pauli equation describing mechanics of the quantum electron with spin.
Virtual Ring Theory implies replacement of a particle with a ghost ring endowed with certain standards that are used to measure distances and mechanical characteristics in integer numbers. This model is applied to three “classical” quantum-mechanical (QM) problems, 1D-box system, H-atom, and linear oscillator. It is shown that the relevant virtual geometric models entail the same energy levels as follow from the respective exact solutions of the Schrödinger equation.
Distortion of classical elliptical orbits of the Apollo asteroids (crossing the Earth’s orbit) in the gravitational field modeled by the Kerr metric, is calculated, and a numerical assessment is given to the general-relativistic impact on the near-Earth motion of potentially hazardous objects (PHO).
A detailed derivation is given of formulas describing the trajectory of a test body moving closely to the ecliptic plane of a rotating star whose gravitational field is modeled by the Kerr metric. It is found that the quasi-elliptic orbit parameters and the revolution period noticeably change (as compared to the classical case), and an additional orbit precession emerges, though four orders of magnitude weaker than that of the Einstein-Schwarzschild case.
Quaternion based math system of spacecraft reorientation is extended by admitting imaginary rotation parameters, thus involving hyperbolic functions. For simplicity only one simple hyperbolic rotation is added as the last one in the series of orthogonal matrices. The scheme is reduced to a single rotation about instant axis, and to transformation of primitive basis on a 2D fractal space of dimension ½. This new tool is proved to simultaneously reorient the spacecraft and to accelerate it the kinematics automatically described as relativistic. With a small speed the problem becomes a classical one.
Primitive mapping of 2D fractal spaces yields a formulation of the Schro¨ dinger equation and endows its solutions and the respective 3D objects with specific geometric images. In particular, it is shown that the simplest 1D-box solution comprising no parameters of particles motion can be interpreted as a 2D inhomogeneous string oscillating on a real-imaginary fractal surface or as a 3D static spindle with a harmonically distributed mass spectrum. The description of an inertially moving similar object is obtained using a Bargmann-type theorem applied to the Bohm equations, and, as their exact solution, a fractal function containing explicit kinematic terms.
Reorientation of an object's (spacecraft) problem is formulated in details in the and groups matrix terms using the most optional math tool of exceptional algebra of quaternion numbers. A thorough analysis of the two approaches is made resulting in original formulas linking parameters of the assigned object's consequent 3D rotations with a single rotation about a unit vector pointing the instant rotation axis, respective operational technology described with relevant examples. It is also demonstrated that an axial quaternion frame admits fractalization so that the reorientation problem is reduced to deformations of the sub-geometric fractal surface.
The fractal equations of mechanics (quantum and classical) are clearly demonstrated to be definitions of an arbitrary potential on a fractal complex number valued surface. The developed approach helps us to show that a translational motion of any rotating compact object (point-like particle) can be equivalently represented by a specific rotation of a virtual ring described in terms of a fractal “wave function”, the model endowing the particle with a set of quantum characteristics including quantization of the ring’s space translation.
It is shown that the theory of relativity, apart from the standard format and the comparatively new quaternion formulation, can also be presented in terms of quaternion spinors. Mathematically, the spinor format is fundamental while technically it is primitive since it links transformations of reference frames (including non-inertial frames) with an instant rotation of a unique vector “about itself.” Such a rotation in its turn can be regarded as a reciprocal change of scales of two orthogonal directions on a 2D plane, in general, a complex number valued one. This allows for considering any transformation of relative groups SO(3,ℂ) and SL(2,ℂ) and the localized Lorentz group as a deformations of the fractal (pregeometric) spin surface.