The starting point of this research is a contradiction of the conventional Schrödinger equation with one of the fundamental Hamilton equations – a minus sign, essential for the energy conservation, is missing. The full agreement of the Schrödinger equation with the Hamilton equations is obtained only when the Hamiltonian in the time dependent phases of the two wave packets representing a quantum particle in the coordinate and momentum spaces is replaced by its Lagrangian. We consider the Universe as a distribution of ‘intrinsic’ matter, characterized by curvilinear time-space coordinates, curved in a system of other coordinates, by an ‘extrinsic’ matter, with a density as another matter coordinate. According to the general theory of relativity, any acceleration of an extrinsic matter differential element in an ‘extrinsic’ (non-gravitational) field is perpendicular to the velocity. This characteristic describes a matter propagation in planes perpendicular to the velocity. This dynamics can be described by two Fourier conjugated wave packets, with a condition of quantization asserting that the space integral of the matter density is equal to the rest mass in the coefficient of the time dependent phases of these wave packets, which, according to their group velocities, appears as a Lagrangian. In this framework, fundamental physical problems are reconsidered by using the general theory of relativity in Dirac’s formulation, for the description of the quantum dynamics. Although in this paper we develop an essentially relativistic theory, in the proper system of a quantum particle we consider only small velocities of its differential matter elements, otherwise this particle being shattered in space, as the notion of ‘particle’ has no more any sense. We show that the Schwarzschild solution with a singularity is only an approximate one, since the dynamics of a differential matter element is always joined to the dynamics of the other matter elements of a quantum particle, and of other quantum particles always present in the realistic cases. These matter elements perturb the gravitational field considered for the Schwarzschild solution, leading to a penetrability of the boundary of a black hole, from the outside for an absorption rate, and from the inside, for an evaporation rate. We consider black particles with phases including only relativistic Lagrangians depending on the rest masses, and ‘visible’ particles, including other interaction terms depending on ‘charges’. We obtain the Lorentz force and the Maxwell equations as properties of a field interacting with a quantum particle, relativistic quantum equations with spin interaction, the spin of the extrinsic matter of a quantum particle, and the spin of the intrinsic component of this particle, we call ‘graviton’.
