Volume 74, Issue 5

Virtual particles are expected to occur in microscopic processes, as they are introduced, for instance, by Feynman in quantum electrodynamics as photons performing in an unknown way in the interaction between two electrons. This note describes macroscopic virtual particles as they appear in classical evanescent modes and in quantum mechanical tunnelling particles. Remarkably, these large virtual particles are present in wave mechanics of elastic, electromagnetic, and Schrödinger fields.

In this paper, we show that both the general product-connectivity index χ α and the general sum-connectivity index χαs\({}^{s}{\chi_{\alpha}}\) are closely related molecular descriptors when the real number α is in some interval. By comparing these two kinds of indices, we show that the sum-connectivity index χ−0.5601s\({}^{s}{\chi_{-0.5601}}\) is the best one for measuring the π -electronic energies of lower benzenoid hydrocarbons. These improve the earlier results.

We show by direct numerical simulations that spatiotemporally localised waveforms, strongly reminiscent of the Peregrine rogue wave, can be excited by vanishing initial conditions for the periodically driven nonlinear Schrödinger equation. The emergence of the Peregrine-type waveforms can be potentially justified, in terms of the existence and modulational instability of spatially homogeneous solutions of the model and the continuous dependence of the localised initial data for small time intervals. We also comment on the persistence of the above dynamics, under the presence of small damping effects, and justify that this behaviour should be considered as far from approximations of the corresponding integrable limit.

By invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four-dimensional non-commutative curvature scalar (which is torsion dependent), which is sourced by the Nambu–Goto world-sheet action for a string plus the Kalb–Ramond string action. This ‘quantum gravity’ is actually a non-commutative classical matrix dynamics, and the only two fundamental constants in the theory are the square of the Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and ℏ) and quantum general relativity (and G ) emerge from the underlying matrix dynamics in the thermodynamic limit. Statistical fluctuations, which are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope to highlight here the deep connection between quantum foundations and the sought-for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!

This article attempts to explain the underlying physics of several recent experiments and astrophysical observations that have been mystifying the physics community for quite some time. So far, none of the advanced theories beyond the standard models of particle physics and cosmology have shown sufficient potential to resolve these mysteries. The reason for this failure may lie in the fact that these theories are based on the concept of extra space dimensions that appears to be in conflict with numerous experiments, in particular with recent Large Hadron Collider data. Therefore, the novel idea of extra number systems is introduced, replacing the idea of extra space dimensions. This approach is complemented by a set of fundamental physical principles that provide the constraints and guidelines for a modified physical formulation in agreement with known experimental reality. However, such a theory requires novel physical concepts in conjunction with novel symmetry groups. These groups give rise to additional types of matter, termed hypercomplex masses (which are responsible for the extreme hypercomplex gravitational fields, see below, and are also denoted as matter flavour ), including, for instance, particles of negative mass, identified with dark matter. Furthermore, four-dimensional Minkowski spacetime, assumed to be a quasi de Sitter space dS1,3$dS^{1,3}$ dual spacetime , DdS1,3$DdS^{1,3}$, with imaginary time coordinate; that is, time is a complex quantity . The three spatial coordinates are shared by the two spacetimes. Dark matter is assumed to reside in DdS1,3$DdS^{1,3}$ and therefore is principally invisible. On the other hand, its gravitational interaction with ordinary matter ( m ≥ 0) in spacetime dS1,3$dS^{1,3}$ is directly perceptible. The novel group structure predicts the existence of a fourth particle family of negative masses; that is, besides the dark matter particle χ of mass mχ≈−80.77$m_{\chi}\approx-80.77$ GeV/c 2 , there is the dark neutrino ν χ of mass mνχ≈−3.23$m_{\nu_{\chi}}\approx-3.23$ eV/c 2 . Moreover, the hypercomplex group structure of gravity (SU(2)×SU(2)$SU(2)\times SU(2)$) postulates three gravitational bosons for cosmological fields [resulting from Einstein’s theory of general relativity (GR)], the graviton νGN$\nu_{G_{N}}$ with spin 2, the novel gravitophoton νgp$\nu_{gp}$ with spin 1 (existence of weak gravitomagnetic fields of GR), and the quintessence particle ν q with spin 0, which, when present, mediates an interaction between ordinary matter ( m ≥ 0) and the ubiquitous scalar field of dark energy. In addition, the existence of extreme gravity fields (hypercomplex gravity) is postulated, based on the second group SU (2), and an interaction between electromagnetism and hypercomplex gravity is predicted, mediated by three additional hypercomplex-gravity bosons. Some long-standing problems of cosmology will be addressed; namely, the Big Bang scenario and the origin of dark energy and the nature of dark matter and their relation to the modified Newtonian dynamics hypothesis will be discussed.

High-pressure third-order elastic constants of materials have rarely been investigated experimentally and theoretically to date, so the predictive ability of the method of the volume-conserving, homogeneous deformations based on the first-principles total-energy calculations is tested for the first time in this work. Using this approach, the high-pressure third-order elastic constants C111−3C112+2C123${C_{111}}-3{C_{112}}+2{C_{123}}$, C111/2+3C112+C123${C_{111}}/2+3{C_{112}}+{C_{123}}$, C144−C155${C_{144}}-{C_{155}}$, and C 456 of the MgO single crystal are obtained successfully. Meanwhile, the reliability of this method is also verified by comparing the calculated structural properties and high-pressure second-order elastic constants of the MgO single crystal with the available experimental results and other theoretical predications. Results not only indicate the accuracy of our calculations but also reveal the feasibility of the present theoretical method. It is hoped that the present theoretical method and predictions on the high-pressure third-order elastic constants of the MgO single crystal would serve as a valuable guidance or reference for further related investigations.