The Mechanics of Spacetime - A Solid Mechanics Perspective on the Theory of General Relativity

We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the "cosmic fabric" and spacetime with the fabric's world volume. Using a Lagrangian formulation, we show that the fabric's behavior as derived from Hooke's Law is analogous to that of spacetime per the Field Equations of General Relativity. The study is conducted in the limit of small strains, or analogously, in the limit of weak and nearly static gravitational fields. The Fabric's Lagrangian outside of inclusions is shown to have the same form as the Einstein-Hilbert Lagrangian for free space. Properties of the fabric such as strain, stress, vibrations, and elastic moduli are related to properties of gravity and space, such as the gravitational potential, gravitational acceleration, gravitational waves, and the energy density of free space. By introducing a mechanical analogy of General Relativity, we enable the application of Solid Mechanics tools to address problems in Cosmology

Recovering the Principle of Relativity from the Cosmic Fabric Model of Space

We extend the descriptive power of the Cosmic Fabric model of space developed by Tenev and Horstemeyer (2018) to include moving observers by demonstrating that all reference frames are phenomenologically equivalent with one another and transform between each other via the Lorentz transformations. Our approach is similar to that of Lorentz (1892), which was used to explain the negative outcome of the Michelson-Morley {\ae}ther detection experiment (Michelson and Morley 1887), except that we deduce the notions of length contraction and time dilation from the postulates of the Cosmic Fabric model. Our result is valid for the continuum length scale at which, by definition, the cosmic fabric can be described mathematically as a continuum. Herein, we also discuss the length-scale dependent nature of the Cosmic Fabric model as a possible way to relate gravitational and quantum theories

Zitterbewegung of neutral relativistic particles in static longitudinal fields

Zitterbewegung of neutral relativistic particles propagating along a constant magnetic and/or electric field is studied. It is shown that spin Zitterbewegung, when superimposed on the Larmor precession frequency, leads to a beating pattern. The existence of a forbidden frequency of spin precession is predicted. Modifications of position and velocity Zitterbewegung due to lifted spin degeneracy manifested in the appearance of longitudinal and transversal Zitterbewegung, each with two Zitterbewegung frequencies and resulting beating patterns, are reported

Circumstance and choice : the role of initial conditions and policies in transition economies

The experience of countries in transition from a planned to a market-oriented economy has varied greatly. The clearest differences are between the East Asian countries, China and Vietnam, and the countries of Central and Eastern Europe (CEE) and the former Soviet Union (FSU). China and Vietnam have contained inflation and benefited from continued high growth in GDP since the beginning of their reforms, while all CEE and FSU countries have experienced large declines in output, and most have experienced hyperinflation. But even in CEE and the FSU, differences are marked. Some countries have lost over half of their GDP, and growth performance in a number of countries is still poor, while others are growing strongly. Some are still suffering from high inflation while others have successfully reduced annual inflation. What determines this divergence of outcomes across transition countries? No study so far has analyzed the interaction of all factors, including initial conditions, political change, and reforms, in a unified framework including CEE, the FSU, China, and Vietnam. The authors examine these broader interactions, but focus first on the role of initial conditions, such as initial macroeconomic distortions and differences in economic structure and institutions, which have been emphasized less in the literature. They find that initial conditions and economic policy jointly determine the large differences in economic performance among the 28 transition economies in the sample. Initial conditions dominate in explaining inflation, but economic liberalization is the most important factor determining differences in growth. But reform policy choices are not exogenous. They depend, in turn, on both initial conditions and political reform, with political reform the most important determinant of the speed and comprehensiveness of economic liberalization. Other findings provide additional insight into these relationships. Results show that liberalization has a negative contemporaneous impact, but a stronger positive effect on performance over time. The results also show that macroeconomic and structural distortions are negatively related to both policy and performance. Regarding the former, unfavorable initial conditions discourage policy reforms but do not diminish their effectiveness once they are implemented. The authors find some evidence that the influence of initial conditions diminishes over time. This is in part because many of the initial conditions are themselves modified in the course of transition. Monetary overhangs are dissipated through inflation, industrial overhang is eroded as plants shut down, and market memory returns through experience.Economic Conditions and Volatility,Economic Theory&Research,Enterprise Development&Reform,Environmental Economics&Policies,Banks&Banking Reform,Economic Theory&Research,Environmental Economics&Policies,Governance Indicators,Economic Conditions and Volatility,Achieving Shared Growth

Trapped ion emulation of electric dipole moment of neutral relativistic particles

The electric dipole moments of various neutral elementary particles, such as neutron, neutrinos, certain hypothetical dark matter particles and others, are predicted to exist by the standard model of high energy physics and various extensions of it. However, the predicted values are beyond the present experimental capabilities. We propose to simulate and emulate the electric dipole moment of neutral relativistic particles and the ensuing effects in the presence of electrostatic field by emulation of an extended Dirac equation in ion traps

De-Biasing Models of Biased Decisions: A Comparison of Methods Using Mortgage Application Data

Prediction models can improve efficiency by automating decisions such as the approval of loan applications. However, they may inherit bias against protected groups from the data they are trained on. This paper adds counterfactual (simulated) ethnic bias to real data on mortgage application decisions, and shows that this bias is replicated by a machine learning model (XGBoost) even when ethnicity is not used as a predictive variable. Next, several other de-biasing methods are compared: averaging over prohibited variables, taking the most favorable prediction over prohibited variables (a novel method), and jointly minimizing errors as well as the association between predictions and prohibited variables. De-biasing can recover some of the original decisions, but the results are sensitive to whether the bias is effected through a proxy