Fundamental subjects of quantum mechanics and general relativity are presented
in a unitary framework. Based on the fundamental quantum laws of PlanckEinstein and De Broglie, a quantum particle is described by wave packets in the
conjugate spaces of the coordinates and momentum. With the time-dependent
phases proportional to the Lagrangian, the group velocities of these wave packets
are in agreement with the fundamental Hamilton equations. When the relativistic
Lagrangian, as a function of the metric tensor and the matter velocity field, is
considered, the wave velocities are equal to the wavefunction coordinate velocity,
which means that these waves describe the matter propagation. The equality of the
integrals of the matter densities over the coordinate and momentum spaces, with
the mass in the Lagrangian of the time-dependent phases, which describes the
particle dynamics, represents the mass quantization rule. Describing the
interaction of a quantum particle with the electromagnetic field by a modification
of the particle dynamics determined by additional terms in the time-dependent
phases, with an electric potential conjugated to time and a vector potential
conjugated to the coordinates, Lorentz’s force and Maxwell’s equations are
obtained. With Dirac’s Hamiltonian and operators satisfying the Clifford algebra,
dynamic equations similar to those used in the quantum field theory are obtained,
but with an additional relativistic function, depending on the velocity and the
matter-field momentum. We obtain particle and antiparticle wavefunctions
describing matter and anti-mater distributions. Unlike the conventional Fermi’s
golden rule, in the new theory, the particle transitions are described by the
Lagrangian matrix elements over the Lagrangian eigenstates and the densities of
these states. Transition rates are obtained for the two possible processes, with the
spin conservation or with the spin inversion. In this framework, we consider
Dirac’s formalism of general relativity, with the basic concepts of the Christoffel
symbols, covariant derivative, scalar density and matter conservation, the
geodesic dynamics, curvature tensor, Bianci equations, Ricci tensor, Einstein’s
gravitation law, and the Schwarzschild metric tensor. From the action integrals for
the gravitational field, matter, electromagnetic field, and electric charge, we
obtain the generalized Lorentz force and Maxwell equations for general relativity.
It is shown that the gravitation equation is not modified by the electromagnetic
field. For a black hole, the velocity and the acceleration of a particle are obtained.
At the formation of a black hole, as a perfectly spherical object of matter
gravitationally concentrated inside the Schwarzschild boundary, the central matter
explodes, and the inside matter is carried out towards this boundary, reaching there only in an infinite time. Based on this model, we conceive our universe as a
huge black hole, with its essential properties, such as the Big Bang, inflation, low
large-scale density, redshift, quasi-inertial behavior of the distant bodies, dark
matter, and dark energy, entirely explained by the general relativity. For a
quantum particle in a gravitational wave, we obtained a rotation of the metric
tensor perpendicular to the propagation direction of this wave, with the angular
momentum 2, which we call the graviton spin, and a rotation of the particle
matter, with a half-integer spin for Fermions and an integer spin for Bosons. We
apply this theory to a two-particle and a particle-antiparticle collision, as well as a
two-body decay of a quantum particle. In this framework, we also obtain a unitary
description of the four forces acting in nature. A system of equations for the quark
coordinates in a proton is obtained.
Keywords: Antiparticle, Black hole, Big bang, Bianci equations, Blue quark, Blue gluon, Covariant derivative, Clifford algebra, Contravariant coordinate, Christoffel symbol, Covariant coordinate, Curvature, Colour space, Dirac hamiltonian, Density of states, Dirac spin operators, Down quark, Einstein’s equation of gravitation, Fermi's golden rule, Feynman diagram, Four-vector, Flavour space, Group velocity, Geodesic equation, Graviton spin, Green quark, Green gluon, Gell-mann operators, Grand unified theory, Heisenberg picture, Hamiltonian, Schwarzschild metric tensor, Lorentz force, Lagrange equations, Lagrangian, Metric tensor, Maxwell equations, Nucleon, Pauli spin operators, Quantum electrodynamics, Quantum flavour-dynamics, Quantum chromodynamics, Redshift, Ricci tensor, Red quark, Red gluon, Schrödinger picture, Scalar potential, Spin, Spinor, Schwarzschild singularities, Schwarzschild boundary, Strong interaction, Two-body collision, Two-body decay, Time-space interval, The least action, Up quark, Vector potential, Vertex, Inflation, Vacuum impedance, Virtual photon, Wave packet, Wave velocity, Weak interaction.