Gravitational self-regularization of quantum fields at Planck scales

Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.

Diffusion gravity and its consequences

Diffusion quantum mechanics (DQM), proposed recently (Zakir, 2020-21), describes a conservative diffusion of classical particles in a fluctuating classical scalar field and, in a homogeneous field, derives the formalism of quantum mechanics. In an inhomogeneous scalar field, DQM reproduces gravitation, and in the present paper, the following theory of diffusion gravity and its various consequences are considered. In DQM a part of the energy of the scalar field is transferred to particles as their fluctuation energy (“thermal” energy), appearing as their rest energy (mass). The resulting local decrease in the field’s energy density around a macroscopic body generates “thermal” diffusion flux of particles to this region. The properties of this “thermal” part of conservative diffusion are similar to gravitation. A high matter concentration in some region reduces the local energy density of scalar field sufficiently to reduce the local intensity of fluctuations. Due to the conservativity of diffusion, the increments in the drift velocity of particles are cumulative, and “thermal” diffusion acceleration arises, independent on the particle’s mass. The world lines become curved, and all processes with particles slowdown, which means time dilation. On hypersurfaces of simultaneity t = const, where the scalar field is defined, effective metrics, connection, and curvature arise. They obey to Einstein’s equations following from balance between energies of matter and background scalar field.

Diffusion treatment of quantum mechanics and its consequences

Localized ensemble of free microparticles spreads out as in a frictionless diffusion satisfying the principle of relativity. An ensemble of classical particles in a fluctuating classical scalar field diffuses in a similar way, and this analogy is used to formulate diffusion quantum mechanics (DQM). DQM reproduces quantum mechanics for homogeneous and gravity for inhomogeneous scalar field. Diffusion flux and probability density are related by Fick’s law, diffusion coefficient is constant and invariant. Hamiltonian includes a “thermal” energy, kinetic energies of drift and diffusion flux. The probability density and the action function of drift form a canonical pair and canonical equations for them lead to the Hamilton-Jacobi-Madelung and continuity equations. At canonical transformation to a complex probability amplitude they form a linear Schrödinger equation. DQM explains appearance of quantum statistics, rest energy (“thermal” energy) and gravity (“thermal” diffusion) and leads to a low mass mechanism for composite particles.

Global and local gravitational redshifts in cosmology and their consequences for theory and observations

A consistent theory of gravitational redshift in cosmology (GRC) is formulated. The global GRC arises due to weakening of gravitational time dilation due to decreasing of matter density during the propagation time of photons. In the expanding world the local GRC arises due to the weakening of gravity of the sphere between observer and source, since photons emitted at a smaller radius arrive at a larger one. In static world there is no GRC at the exchange of photons at the periphery of this sphere. In any case photons from observer to source have the same GRC as photons from source to observer, which is in agreement with the cosmological principle. Consequences of the local and global GRC for cosmological models and their parameters, as well as corrections to data on distant objects and CMB, are considered. In Appendix the inconsistency of two former treatments of the gravitational frequency shift in cosmology is shown. They: a) did not take into account the global GRC; b) derived the local GRC not from the field of the sphere between the source and observer, but from the field of spheres around one of them; c) contradicted each other (the signs of shifts are opposite); d) violated cosmological principle (changing the propagation direction changes the sign of shift) and e) were based on the delusion that the Friedmann model supposedly contains the gravitational shift.

Local and global theories of relativity in flat and curved spacetimes

Special and general theories of relativity consist in describing both local and global phenomena - the first in flat, and the second in curved spacetime. In the paper it is shown that each of these two classes of relativistic effects, local and global, is universal and is the subject of a separate theory. First, descriptions in local frames of reference, related by the local Lorentz transformations, form the local theory of relativity, or local relativity (LR). The locality principle allows to apply LR to non-inertial local frames, and the equivalence principle to the local frames in gravitational field. Secondly, descriptions in global frames of reference, constructed from local frames coexisting on a common hypersurface of simultaneity, form the global theory of relativity, or global relativity (GlR). LR and GlR are based on physical coordinates and complement each other, the special and general theories of relativity were hybrids of these two theories. LR and GlR describe the local and global properties of gravity, separating the field effects from the effects of motion by different methods, such as bimetric formalism, where one metric describes geometry of the global frames, and other describes spacetime geometry. It is shown that GlR leads to a picture of collapse with formation of frozars, and also leads to a cutoff of the loop integrals of quantum fields at the Planck length. In GlR, cosmological models are built on hypersurfaces of simultaneity, where both stretching and the Doppler effect contribute to redshifts, and aberration is also taken into account. Predicted an initial violetshift removing the double redshift paradox, and this leads to the slowing time cosmology consistent with observational data.