The dialectical approach, excluding mechanical principles of identity, is used to reveal the structure of "elementary" particles and the nature of electromagnetic and gravitational waves. The unknown nature of mass and electric charge is revealed on the basis of the accepted dynamic model of elementary particles. All kinds of interactions of such particles are considered in terms of the exchange of motion and matter with surrounding objects and fields at the characteristic frequencies. Theoretical notions related to the wave behavior of the particles at the atomic and subatomic levels are developed. An elementary equation of kinematic exchange is presented. Dynamic exchange is described by exchange active-reactive charges. Exchange parameters of an electron, proton, neutron, and a field of exchange at atomic and subatomic levels are derived from the presented equations.

A brief introduction to the theory of the dialectical field of binary real numbers, which makes possible the expression of the contradictoriness of discontinuous and continuous features of objects of study, is considered. A wave character of physical processes is presented by the wave binumerical field of real numbers repeating the geometry of these processes in three dimensional space, which is impossible to express by the conventional field of complex numbers localized in the plane of real and "imaginary" components. The advantage and completeness of nonconventional description by the dialectical field of binumbers is demonstrated by an analysis of harmonic oscillations.

Interrelation between the fundamental period-quantum of the dialectical binumerical wave field of decimal base D=2plge and the base units of matter, space, and time (the gram, the centimeter, and the second) is considered. Fundamental constants of physics (such as the electron mass and charge, the gravitational wave radius and period, etc.) are examined on the consistency with the universal formula of measures, which are directly connected with the fundamental period-quantum. The last and the universal spectrum of measures are regarded as manifestation of the Law of Decimal Base.

For the first time, fundamentals of physical, phase and energetic, probability are stated. A new theory of the internal structure of atoms as the atoms of matter and space is proposed. On this basis, a wave theory of atomic spectra and other related questions are presented. In particular, the possible structure of carbon and its compounds, the structure of Al2O3 and H2O, which are determined by the wave equation solutions, are presented. The real possibility to predict theoretically the molecular and crystal structures on the basis of obtained solutions, which are still hardly predictable by quantum-mechanical method, is stated.