Sergey Siparov. On the Foundations of the Generalized Theory of Equivalence (Anisotropic Geometrodynamics)

Report was presented on the scientific seminar at the Russian University of Peoples’ Friendship, April 3, 2013. At the seminar, professor Roger Penrose was present, he also took part in the discussion. The preconditions of the geometric approach which is somewhat different from the classical approach of general relativity are discussed. The reason for its appearance is, on the one hand, the observational problems on a galactic scale, which are currently addressed through the introduction of dark concepts. The use of the dark matter concept is not free from controversy, besides, the quantitative measure of it is much larger than the measure of visible matter described by the GRT. On the other hand, the existence of the observed (gravitational) long-range interaction itself requires some adjustment in the foundations of the theory. The introduced formalism is used to interpret a number of observations that previously required dark matter and to explain other observations that previously had no explanations. Publications on this theme:

Sergey Siparov. On the Gravitation of the Moving Bodies

Report on the VII-th International Conference Finsler Extensions of Relativity Theory – FERT 2011, Braşov– Romania.. The title of the talk refers to the famous Einstein’s paper of 1905. The parallel between the situations in physics now and hundred years ago is presented. At that time the most prominent theory was Maxwell’s Electrodynamics, while unobservable ether was one of the main riddles. Now the most prominent theory is Einstein’s General Relativity while one of the main riddles is the unobservable dark matter. Anisotropic Geometrodynamics (also known as Equivalence Theory) is a new theoretical approach that provides a possibility to make a certain breakthrough and exclude the need for dark matter on the base of the use of new type of geometry. With its help, several other observations that present a problem can be also explained.

Sergey Siparov. First principles and observational back up of the Generalized Equivalence Theory (or Anisotropic Geometrodynamics)

Report at the Gamov International Conference in Odessa (2012). The talk is devoted to the role and applicability of the two fundamental principles – principle of relativity and principle of equivalence – when dealing with the galactic scale phenomena. It is shown that in order to construct a theory of gravitation, the first principle should be not the principle of relativity (as in GRT) but the principle of equivalence. Then we get the theory of equivalence (or anisotropic geometrodynamics) which is able to cope with the observational problems on the galactic scale without dark matter, and which also has important consequences both at the cosmological scale and at the planetary system scale.

Sergey Siparov. Remarks on the anisotropic geometrodynamics

Report at the International Conference – FERT 2010 in Moscow. We discuss the specific features of the previously developed approach – anisotropic geometrodynamics (the theory of equivalence), – which made it possible to cope with several problems of general relativity on a galactic scale, without the use of the concept of “dark matter” and to preserve the meaning and results of general relativity on the planetary systems scales.

Sergey Siparov. Classical GRT tests in the AGD

Report at the International Conference – FERT 2009. We discuss the applicability and the regions of applicability of various geometries in the gravitation theories. The basic concepts of the theory of equivalence (anisotropic geometrodynamics, AGD) are introduced and the first obtained results are demonstrated. We discuss the analogues of the classical GRT tests on a galactic scale. It is shown that the results, that present problems of the GRT become the natural consequences of the TE (or AGD) approach. We also discuss the hypothesis of the origin of the arms and bars in spiral galaxies, resulting from TE.

Sergey Siparov. The problem of anisotropy in geometrodynamics

Report at the International Conference – FERT 2008. For the first time, the basic concepts and definitions of the theory of equivalence (anisotropic geometrodynamics) which is based on a generalization of the equivalence principle are introduced. The role of Maxwell’s identities is emphasized. The expression for the gravitational force is obtained. The new approach is compared with the known ones, possible applications of TE are discussed.

Sergey Siparov. The choice of the space-time geometry

Report at the International Conference – FERT 2007. The problems of GRT that arise on a galactic scale, and the known attempts to overcome them by theoretical means are analyzed. It is concluded that there is a relation between the observations and the choice of geometry suitable to describe the space-time. In order to determine the geometric properties of our galaxy, a new experiment based on the effect of OMPR is suggested, and the appropriate astrophysical systems are identified.

Sergey Siparov. Dark matter – alternatives and verification

Report at the International Conference – PIRT 2007. The problems encountered in GRT on galactic scale and the attempts to overcome them by upgrading the geometric aspects of the theory are listed. We consider the hypothesis of “dark matter” and the observations related to it. It is concluded that the new observations to determine the geometric properties of our galaxy are needed. A new experiment based on the OMPR effect and appropriate astrophysical systems are suggested.

Sergey Siparov. Space-time geometric properties

Report at the сonference in Cairo, 2006. The history of the geometrization of physics is traced, and this allows to formulate the questions to the choice of geometry that have arose in connection with the observations. A new type of experiment based on the OMPR effect is proposed to register the gravitational waves from periodic sources such as pulsars or close binary systems. This experiment differs from all the known ones, because it is based on the zero-order effect and not on the first-order in the amplitude of gravitational waves effect usually regarded in this field. This allows one to remove technical problems, but creates new ones, related to the search of the suitable astrophysical systems. It is underlined that in case of detection of the specific geometric properties of space-time, there will be the need to revise the wording in the basics of classical physics.

Sergey Siparov. Hamilton canonical equations and Berwald-Moor metric (on the formalism of the Physics theories)

Report at the сonference in Cairo, 2005. The specific features of the application of Finsler geometry to construct a space-time theory are discussed. The role of the algebraic approach is emphasized. It makes it possible to obtain many of the equations of theoretical physics before the geometry is introduced. Based on the formal use of the functions associated with the Berwald-Moor metric, the canonical Hamilton’s equations are derived. They can be used for the further construction of a physical theory in Finsler space.