The notion of diffeomorphism invariance and general covariance are conceptually delicate issues for the field equations and the actions. A thorough study on the original Einstein field equation and its two modifications by Einstein is presented. It is concluded that the cosmological constant and the unimodular condition are independent concepts, and the unimodular condition has no direct role in the derivation of the traceless field equation. Unimodular gravity with unambiguous action does not exist, and the derivation of traceless equation from the action principle is an open question.

A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schr\"odinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial evolution of the wavefunction, and the latter is used to calculate the radial probability density for different measurements. The obtained results show that Born's position measurement postulates naturally emerge from the theory and its first principles. Experimental verification of the theory and its predictions is also proposed.

A new proof of the geodesic character of all motions of bodies that interact only gravitationally - and a detailed illustration of the real meaning of the linearized approximation of general relativity.

Finite element simulations of four pile static tests were performed using Plaxis 3D. In addition, calculations of pile settlements according to Ukrainian and USSR building codes were performed. These results compared to full-scale pile tests. In order to determine the influence of reaction piles on the test pile response in a static load test were performed simulations with group of reaction piles around tested pile and applied respective negative loads. Plaxis and in situ measured load-displacement curves showed good correlation. Recommendations for Plaxis modeling were given.

We propose a heuristic model of the universe as a growing quasicrystal projected from a higher-dimensional lattice. This quasicrystalline framework offers a novel perspective on cosmic expansion, where the intrinsic growth dynamics naturally give rise to the observed large-scale expansion of the universe. Motivated by this model, we explore the Schrödinger equation for a particle in a box with time-dependent boundaries, representing the expanding underlying space. By introducing a constraint that links microscale quantum phenomena with macroscale cosmological quantities, we derive an equation resembling the Friedmann equation, providing potential insights into the Hubble tension. Our model incorporates phonons and phasons-quasiparticles inherent in quasicrystalline structures-that play critical roles in cosmic-scale dynamics and the universe's expansion. This framework suggests that the necessity for an inflationary period may be obviated. Furthermore, phonons arising from the quasicrystalline structure may serve as dark matter candidates, influencing the dynamics of ordinary matter while remaining largely undetectable through electromagnetic interactions. Drawing parallels with crystalline matter at atomic scales, which is fundamentally quantum in nature, we explore how the notion of tiling space can support continuous symmetry atop a discrete structure. This provides a novel framework for understanding the universe's expansion and underlying structure. Consequently, our approach suggests that further development could enhance our understanding of cosmic expansion and the universe's structure, bridging concepts from quantum mechanics, condensed matter physics, and cosmology.

In this article we discuss a peculiar regime of Compton Scattering that assures the maximum transfer of energy and momentum from free electrons propagating in vacuum to the scattered photons. We name this regime Full Inverse Compton Scattering (FICS) because it is characterized by the maximum and full energy loss of the electrons in collision with photons: up to 100 % of the electron kinetic energy is indeed transferred to the photon. In the case of relativistic electrons, characterized by a large Lorentz factor (gamma >> 1), FICS regime corresponds to an incident photon energy equal to mec^2/2 . We interpret such an astonishing result as FICS being the time reversal of direct Compton Scattering of very energetic photons (of energy much greater than mec2) onto atomic electrons. Although the cross section of Compton scattering is decreasing with the energy of the incident photon, making the process less probable with respect to other reactions (pair production, nuclear reactions, etc) when high energetic photons are bombarding a target, the kinematics straightforwardly implies that the back-scattered photons would have an energy reaching asymptotically me^2c^2 . FICS is instead the unique suitable working point in Compton scattering for achieving the total transfer of (kinetic) energy exactly from the electron to the photon. Experiencing transitions from the initial momentum to zero in the laboratory system, in FICS the electron is also subject to very large negative acceleration; this fact can lead to possible experiments of sensing the Unruh temperature and related photon bath. On the other side of the energy dynamic range, low relativistic electrons can be completely stopped by moderate energy photons (tens of keV), leading to full exchange of temperature between electron clouds and photon baths.

Aftershock sequences are of particular interest in seismic research since they may condition seismic activity in a given region over long time spans. While they are typically identified with periods of enhanced seismic activity after a large earthquake as characterized by the Omori law, our knowledge of the spatiotemporal correlations between events in an aftershock sequence is limited. Here, we study the spatiotemporal correlations of two aftershock sequences form California (Parkfield and Hector Mine) using the recently introduced concept of "recurrent" events. We find that both sequences have very similar properties and that most of them are captured by the space-time epidemic-type aftershock sequence (ETAS) model if one takes into account catalog incompleteness. However, the stochastic model does not capture the spatiotemporal correlations leading to the observed structure of seismicity on small spatial scales.

We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all electroweak gauge bosons interact with each other prior to symmetry breaking. This represents a crucial shift in the identification of physical gauge bosons: Unlike the Standard Model which posits a change of Lie algebra basis induced by spontaneous symmetry breaking, here the basis is unaltered and $A,\,Z^0,\,W^\pm$ represent the physical bosons both before and after spontaneous symmetry breaking. Our choice of $\mathfrak{u}_{EW}(2)$ requires some modification of the matter field representation of the Standard Model. For $U_{EW}(2)$, there are two pertinent representations ${\mathbf{2}}$ and its $U(2)$-conjugate ${\mathbf{2^c}}$ related by a global gauge transformation that squares to minus the identity. The product group structure calls for strong-electroweak degrees of freedom in the $(\mathbf{3},\mathbf{2})$ and the $(\mathbf{3},{\mathbf{2^c}})$ of $SU_C(3)\times U_{EW}(2)$ that possess integer electric charge just like leptons. These degrees of freedom play the role of quarks, and they lead to a modified Lagrangian that nevertheless reproduces transition rates and cross sections equivalent to the Standard Model. The close resemblance between quark and lepton electroweak doublets suggests a mechanism for a speculative phase transition between quarks and leptons that stems from the product structure of the symmetry group. Our hypothesis is that the strong and electroweak bosons see each other as a source of decoherence. In effect, lepton representations get identified with the $SU(3)$-trace-reduced quark representations. This mechanism allows for possible extensions of the Standard Model that don't require large inclusive multiplets of matter fields.

While our natural intuition suggests us that we live in 3D space evolving in time, modern physics presents fundamentally different picture: 4D spacetime, Einstein's block universe, in which we travel in thermodynamically emphasized direction: arrow of time. Arguments for such nonintuitive and nonlocal living in kind of "4D jello" come among others from: Lagrangian mechanics we use from QFT to GR saying that history between fixed past and future situation is the one optimizing action, special relativity saying that different velocity observers have different own time directions, general relativity deforming shape of the entire spacetime up to switching time and space below the black hole event horizon, or the CPT theorem concluding fundamental symmetry between past and future for example in the Feynman-Stueckelberg interpretation of antiparticles as propagating back in time. Accepting this nonintuitive living in 4D spacetime: with present moment being in equilibrium between past and future - minimizing tension as action of Lagrangian, leads to crucial surprising differences from intuitive "evolving 3D" picture - allowing to conclude Bell inequalities, violated by the real physics. Specifically, particle in spacetime becomes own trajectory: 1D submanifold of 4D, making that statistical physics should consider ensembles like Boltzmann distribution among entire paths (like in Ising model), what leads to quantum behavior as we know from Feynman's Euclidean path integrals or similar Maximal Entropy Random Walk (MERW).

From the recently observed propagation of gravitational waves through space-time an upper limit can be deduced for the stiffness of space-time through which the gravitational wave propagates. The upper limit is extremely weak, implying that the stiffness of space-time is at least 14 orders of magnitude weaker than that of jello.

What is the nature of reality? How should be an answer to this question? At this level, we are so deep that all our concepts are obscure. Quantum theory (QT) is at this level. The quest for interpreting it fails because the clarity of our actual fundamental concepts in ordinary language cannot match the precision of the theory's mathematical formalism. The interpretation of quantum mechanics should define and bring clarity to fundamental concepts; not simply rely over them. Quantum theory requires a new worldview, the one that will make it understandable. We discuss on the formulation and interpretation of closed, and final theories, in other words, completely axiomatic theories that define their own conceptual framework, and closed theories that cannot be made simpler. We claim that everything we can properly say about a theory follows from its interpretation, and that interpreting is saying the meaning of each of its mathematical statements. We argue that quantum mechanics is a closed theory; and, therefore, that part of it is part of the final or fundamental theory of physics (FTP). We propose a new entirely axiomatic formulation of part of quantum theory (including all its mathematical framework) in which new powerful and useful elements are added to the existing formalism. Our interpretation is straightforward: it allows us reading or saying the meaning of each of the theory's axiom, theorem or element. We state that the proposed theory is the FTP. Its interpretation may dissolve most of the existing paradoxes around QT. The principle of excluded middle is not valid in general. Both epistemic and ontic elements are present in the theory since it is a theory of knowledge and truth. This and other fundamental concepts are defined by the theory, which can represent both reality and our knowledge about it. Aesthetics is one of its key features.

On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main approximation of the relativistic self-consistent field model, in which the influence of vacuum field fluctuations is taken into account when constructing the one-particle states. The solutions of the self-consistent equations determine possible states, which also include the states with broken symmetries. Different states of the field are matched to particles, whose masses are determined by both parameters of the Lagrangian and vacuum fluctuations. The density of the vacuum energy in these states is calculated. It is shown that the concept of Bogolubov's quasi-averages can naturally be applied for definition of exact Green functions in the states with broken symmetries. Equations for exact one- and two-point Green functions are obtained.

The modified $F(R)$ gravity theory with the function $F(R)=-(1/\beta)\ln(1-\beta R)$ is studied. The action at small coupling $\beta$ becomes Einstein--Hilbert action. The bound on the parameter $\beta$ from local tests is $\beta\leq 2\times 10^{-6}$ cm$^2$. We find the constant curvature solutions and it was shown that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. The potential and the mass of the scalar field (scalaron) are obtained in the Einstein's frame. The slow-roll cosmological parameters are studied and e-folds number is evaluated. The critical points of autonomous equations are analyzed. The function $m(r)$ that describes the deviation from the $\Lambda$CDM model is calculated.

It is shown how the time-dependent Schrödinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrödinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi equation, are also reviewed. The derivation of the time-dependent equation is based on an {\it a priori} assumption equivalent to Feynman's dynamical postulate. De Broglie's concepts of 'matter waves' and their phase and group velocities are also critically discussed.

High-Tc Type-II ceramic-superconductor at temperature T < Tc, under presence of magnetic-field B becomes non-superconducting if B exceeds a critical value Bc2. Thus at T < Tc, by application/absence of critical magnetic- field as a controlling device, these non-superconducting/superconductor states can be achieved for current-flow to two corresponding states of block/pass or off/on or 0/1. Thus it appears that there is a possibility of a new breed of transistors purely with high-Tc Type-II ceramic-superconductor; compact and without junctions & complexities. The proposed ceramic-superconductor-transistor (CST) seems in-principle to work well for switching purpose, but its use could also be extended for other electronic/computer devices too. The CST, being junction-less thus diffusion-less, could possibly be packed more closely (at nano-level) than the semi-conductor devices which has a limitation due to diffusion-layer-overlapping. A similar superconductor-device named Cryotron was invented at MIT half-a-century ago, but could not survive against semiconductor. CST is a rebirth of cryotron in different disguise & in new perspective.

It has been known for over 100 years that there is a discrepancy between Maxwell's electrodynamics and the idea of a classical electron as the ``atom'' of electricity. This incompatibility is known under the terms 4/3 problem of the classical electron and radiation reaction force and was circumvented in the currently most successful theories, the quantum field theories, by limit value considerations, by the mutual subtraction of infinities, i.e., by purely mathematical methods that eliminate obvious contradictions but are not really based on an intuitive understanding of its physical causes. The actual origin of the problems mentioned lies in the instability of the classical electron. Stabilization cannot be achieved within the framework of Maxwell's electrodynamics. This raises the question of what a minimal change to the fundamentals of electrodynamics should look like, which contains Maxwell's theory as a limiting case. A detailed analysis of the 4/3 problem points to models that fulfill these requirements.

In this paper, we explore the field propagator with a structure that is general enough to encompass both the case of newly-defined mass-dimension $1$ fermions and spin-$1/2$ bosons. The method we employ is to define a map between spinors of different Lounesto classes, and then write the propagator in terms of the corresponding dual structures.

This paper presents a BPD (Balanced Power Dissipation) heuristic scheduling algorithm applied to VLSI CMOS digital circuits/systems in order to reduce the global computational demand and provide balanced power dissipation of computational units of the designed digital VLSI CMOS system during the task assignment stage. It results in reduction of the average and peak temperatures of VLSI CMOS digital circuits. The elaborated algorithm is based on balanced power dissipation of local computational (processing) units and does not deteriorate the throughput of the whole VLSI CMOS digital system.

The classic "Bell's Theorem" of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka "hidden variables"); (2) locality; or (3) time-forwards macroscopic statistics (aka "causality"). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP has two major variations -- a many-worlds version, and a neoclassical version of partial differential equations (PDE) in the spirit of Einstein. Section 2 discusses quantum measurement according to BTP, focusing on how we represent condensed matter objects like polarizers in a Bell's Theorem experiment or in tests of Hawking's cosmology. The Backwards Time Telegraph, though speculative, is discussed.

In this review of Dark Matter we review dark matter as sterile neutrinos, fermions, with their present and possibly future detection via neutrino Oscillations. We review the creation of Dark Matter via interactions with the Dark Energy (quintesence) field. We also review bosons as dark matter, discussing a proposed search for dark photons. Since photons are vector bosons, if dark photons exist at least part of dark matter are vector bosons. Ongoing experimental detection of Dark Matter is reviewed.