Isolated Objects and Their Evolution: A Derivation of the Propagator’s Path Integral for Spinless Elementary Particles

We formalize the notion of isolated objects (units), and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects.

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.

CONSTANTS OF SPIN-SPIN INTERACTION BETWEEN CARBON NUCLEI IN STERICALLY STRESSED SYSTEMS ON THE EXAMPLE OF BICYCLOPENTANES AND BICYCLOHEXANES

Within the framework of the self-consistent theory of finite perturbations SCPT INDO, the calculation of the spin-spin interaction constants 13C-13C with preliminary optimization of geometric parameters in 16 bicyclo derivatives is carried out[2.1.0] pentane and 11 bicyclo derivatives[2.2.0]hexane. According to the results of the calculations, the bridge connection in the studied series of compounds is characterized by an unusually low s-character of hybrid orbitals, amounting to 4.8-8.8 % in bicyclo derivatives[2.1.0] pentane and 11.3-12.9 % in bicyclo derivatives[2.2.0]hexane, which corresponds to the orbital hybridization from sp10. 30 to sp19. 92 in bicyclo[2.1.0]pentanes and from sp6. 76 to sp7. 89 in bicyclo[2.2.0]hexanes. The spin-spin interaction constants between bridged and non-bridged, or between two non-bridged carbon atoms in the studied series of compounds correlate with the corresponding spin-spin interaction constants 13C-13C in isostructured cyclopropanes and cyclobutanes, which indicates close hybridization

MECHANISMS OF TRANSMISSION OF THE SPIN-SPIN INTERACTION OF CARBON-CARBON IN A SERIES OF BICYCLOBUTANE DERIVATIVES

Within the framework of the self-consistent theory of finite perturbations SCPT INDO, the calculation of the spin-spin interaction constants 13C-13C with preliminary optimization of geometric parameters in 17 bicyclo derivatives is carried out[1.1.0.] of Bhutan. There is a good correspondence of the calculated constants with the experimental values known in the literature and measured in this work. Based on the results of the calculations performed, the study of hybridization effects in the considered series of compounds was carried out. All bicyclobutane derivatives are characterized by an abnormally low s-character of endocyclic hybrid orbitals forming a bond between bridging carbon atoms. Substitution effects have a weak effect on the s-order of the bridge connection. The presence of an unsaturated alcohol structure in the 2-position of the bicyclo-butane fragment leads to a sharp decrease in the s-character of the endocyclic hybrid orbitals of the bridged carbon atoms.

Consistent Theory of Alpha-Decay

In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.

Entropy bound and unitarity of scattering amplitudes

We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling α evaluated at the scale R. The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2 → N particle scattering amplitudes at the point of optimal truncation. These bounds are more stringent than Bekenstein’s bound and in a consistent theory all three get saturated simultaneously. This is true for all known entropy-saturating objects such as solitons, instantons, baryons, oscillons, black holes or simply lumps of classical fields. We refer to these collectively as saturons and show that in renormalizable theories they behave in all other respects like black holes. Finally, it is argued that the confinement in SU(N) gauge theory can be understood as a direct consequence of the entropy bounds and unitarity.

Analysis of Theoretical Concepts for Interpretation the Result of the Experimental Studies of Free Groundwater Level Oscillation in Wells

A number of publications present the results of an experimental study of free oscillations of groundwater piezometric level in wells with their eigenfrequencies. The oscillations were initiated by a pulsed impact on the aquifer through the well. Also in a number of publications a theoretical interpretation was proposed for the established phenomenon. However, the existing theoretical ideas about free oscillations of the groundwater level seem to be incorrect. In the present work, a critical analysis of these available theoretical concepts is performed. The analysis served as an impetus to the development of a consistent theory of relaxation filtration of groundwater.