Fermat’s principle and the effect of jerk on light motion near the Sun

In classical mechanics, in the case of gravitational and electromagnetic interactions, the force on a particle is usually proportional to its acceleration: The force acts locally on the particle. However, there are situations possible-if the particle moves through a suitable medium, for example, in which the force depends also on the first-time derivative of its acceleration, the jerk, and on its second-time derivative, the snap, and possibly also on higher-time derivatives. Such forces are called nonlocal, and this work investigates such nonlocal forces, mainly those depending on the jerk. In particular, we implement jerk and acceleration in geodesics by means of the nonlocal-in-time kinetic energy approach to spacetime physics. We describe a framework that can be used to estimate the quantum nonlocal time parameter by studying the deflection of light around the Sun. Comparing our results with long baseline interferometry (VLBI) observations, we concluded that the nonlocal time parameter [Formula: see text] s.

Editorial for the Special Issue “Relativistic Astrophysics”

Relativistic Astrophysics is the branch of astrophysics that studies astronomical phenomena and celestial bodies, for which classical mechanics and Newton’s law of gravitation are inapplicable to creation of suitable models and we have to generalize these approaches following general relativistic prescriptions [...]

АЛГОРИТМ ПРОЕКТУВАННЯ АВТОМАТИЗОВАНИХ ЗМІШУВАЛЬНИХ КОМПЛЕКСІВ БЕЗПЕРЕРВНОЇ ДІЇ ДЛЯ СИПКИХ МАТЕРІАЛІВ

Purpose. Creation of design algorithm of continuous action mixing complexes that will allow defining parameters of the equipment proceeding from requirements to quality, productivity and the set compounding of mixture.Methodology. The method of discrete elements, classical mechanics positions, theory of solids contact interaction, method of mathematical modeling are used in the work.Findings. The paper proposes a generalized algorithm for designing a continuous mixing complex for bulk materials. The procedure for designing a centrifugal mixer, the flow shapers, plate feeders and conical-cylindrical hoppers are presented. Calculations of design and technological parameters are carried out on the basis of information about the physical and mechanical properties of bulk components particles, requirements for equipment performance and the mixture homogeneity. The results of calculations of the mixing complex for the three-component mixture used for the production of polyethylene film are presented. To test the proposed algorithm, a mathematical model based on the discrete elements method is created. The mixing process is modeled and the coefficients of inhomogeneity of each of the components in the finished mixture are determined. The obtained results confirmed that the proposed algorithm allows to determine the parameters of the mixing complex, which ensure compliance with the specified requirements for the quality and the equipment performance.Originality. Mathematical models of bulk motion dynamics in mixing complexes are improved, which include bunker devices, plate feeders, flow shapers and continuous centrifugal mixer, taking into account the bulk motion discrete nature.Practical value. The obtained results allow calculating the design and technological parameters of the equipment that is a part of the continuous mixing complex according to the set productivity, recipe and requirements to the mixture homogeneity.

Topology optimization design for buckling analysis related to the size effect

Owing to the excellent performance of microstructures or nanomaterials with well-designed topological configuration, the characteristic scale of structural design is gradually shifting from macroscopic to nanoscale or microscale structural design. However, the size effect that emerges from the small-scale structures may not be explained effectively with the hypothesis of classical mechanics owing to the lack of microscopic parameters in the classical constitutive model. In addition, slender beams within such small-scale structures are prone to buckling failure, which puts forward additional requirements for the stability design of the structure except for the overall compliance of the structure. Therefore, a topology optimization framework combining the modified couple stress theory with the solid isotropic material penalization (SIMP) model is constructed to illustrate the size effect on topology optimization. Numerical results show that the size effect affects the compliance, buckling performance, and topological configurations of the evolutionary structures.

Time and Causality: A Thermocontextual Perspective

The thermocontextual interpretation (TCI) is an alternative to the existing interpretations of physical states and time. The prevailing interpretations are based on assumptions rooted in classical mechanics, the logical implications of which include determinism, time symmetry, and a paradox: determinism implies that effects follow causes and an arrow of causality, and this conflicts with time symmetry. The prevailing interpretations also fail to explain the empirical irreversibility of wavefunction collapse without invoking untestable and untenable metaphysical implications. They fail to reconcile nonlocality and relativistic causality without invoking superdeterminism or unexplained superluminal correlations. The TCI defines a system’s state with respect to its actual surroundings at a positive ambient temperature. It recognizes the existing physical interpretations as special cases which either define a state with respect to an absolute zero reference (classical and relativistic states) or with respect to an equilibrium reference (quantum states). Between these special case extremes is where thermodynamic irreversibility and randomness exist. The TCI distinguishes between a system’s internal time and the reference time of relativity and causality as measured by an external observer’s clock. It defines system time as a complex property of state spanning both reversible mechanical time and irreversible thermodynamic time. Additionally, it provides a physical explanation for nonlocality that is consistent with relativistic causality without hidden variables, superdeterminism, or “spooky action”.

Inductive Warrant

But Hertz’s suggestions did not address his original “small metaphysics” conflicts in a credible manner. The alternative resolution that material scientists currently favor supplies an alternative paradigm upon which this book will later elaborate. To this end, the present chapter reviews the intellectual circumstances that Hertz confronted and why they were important to him. He displayed a keen eye for delicate detail in his diagnostic work, in a manner that should serve as a sterling model of conceptual detective work whenever it is wanted. But the depth of his insights has been frequently misunderstood by later generations, largely due to a greatly diminished form of “classical mechanics” that became popular in the twentieth century because of the parochial requirements of quantum theory. Within this reduced setting, Hertz’s motivating problems disappear, not because they have been solved, but because they have been ignored. As an aftereffect, many philosophers writing today confidently believe that they understand what “the worlds of classical mechanics are like,” although these rash presumptions embody a significant degree of simplistic misrepresentation. The present chapter outlines the forgotten background required to appreciate Hertz’s conceptual puzzles as he confronted them. These details are not required for the central argument of the book, but they nicely illustrate the natural contexts from which “small metaphysics” puzzles characteristically emerge within a gradually evolving discourse.