This paper presents research within the topic of special relativity. First, we show that time dilation and length contraction do not necessarily require that the speed of light be the same in all reference frames. It is only necessary to require that the speed of light be finite in any particular frame. Next, we demonstrate that the relativistic Doppler shift for electromagnetic waves has an analogue for extended material objects, and furnish an expression for the relative velocity of such objects in terms of what we call their "rest length shift''. An alternative velocity, which we call "rest velocity'', is then introduced to simplify the Lorentz transformation formulas. We also show that regular velocity can be regarded as the geometric average of the "rest velocity'' and another type of velocity we term "contracted velocity". We conclude by formulating the relationship between regular and "rest'' velocity for non-uniform motion in one, two, and three dimensions.

In this research article, we are going to study the concept of the theory of relativity and after extracting the essential information, we will try to find a relation between the theory of relativity and the results we are obtaining through contemporary physics experiments. It has been investigated that traveling in time is not a dream anymore and time can pass at a different rate for some people.

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein's research regarding general relativity and attempt to link general relativity to quantum laws.

This is the second in a series of two articles introducing the Gravitas computational general relativity framework, in which we now focus upon the design and capabilities of Gravitas's numerical subsystem, including its ability to perform general 3+1 decompositions of spacetime via the ADM formalism, its support for the definition and construction of arbitrary Cauchy surfaces as initial data, its support for the definition and enforcement of arbitrary gauge and coordinate conditions, its various algorithms for ensuring the satisfaction of the ADM Hamiltonian and momentum constraints, and its unique (totally-unstructured) adaptive refinement algorithms based on hypergraph rewriting via Wolfram model evolution. Particular attention will be paid to the seamless integration between Gravitas's symbolic and numerical subsystems, its ability to configure, run, analyze and visualize complex numerical relativity simulations and their outputs within a single notebook environment, and its capabilities for handling generic curvilinear coordinate systems and spacetimes with general (and often highly non-trivial) topologies using its specialized and highly efficient hypergraph-based numerical algorithms. We also provide illustrations of Gravitas's functionality for the visualization of hypergraph geometries and spacetime embedding diagrams in two and three dimensions, the ability for Gravitas's symbolic and numerical subsystems to be used in concert for the extraction of gravitational wave signals and other crucial simulation data, and Gravitas's in-built library of standard initial data, matter distributions and gauge conditions. We conclude by demonstrating how the numerical subsystem can be used to set up, run, visualize and analyze a standard yet nevertheless reasonably challenging numerical relativity test case: a binary black hole collision and merger within a vacuum spacetime (including the extraction of its outgoing gravitational wave profile).

In this paper, inspired by quantum field theory, or more specifically QED, we propose a dynamical model for relativity. By adopting the approach provided by this dynamical model, we provide a dynamical explanation for relativistic phenomena such as length contraction, time dilation and clock desynchronization. The result of the dynamical approach for clock desynchronization is especially interesting. Our dynamical approach exhausts the freedom for different clock synchronizations on frames accelerated from an initial reference frame, which is allowed by Einstein’s principle approach. Furthermore, our dynamical approach arrives at the interesting conclusion that Einstein’s equivalence principle and gravitational redshift are necessary to explain special relativistic clock desynchronization. This result shows that special relativity by itself is an incomplete theory. If our dynamical model assumptions are assumed to be valid at a fundamental level, it implies some modifications to quantum field theory and general relativity via the equivalence principle. These modifications have been discussed.

Recent efforts to conceptually design a technologically meaningful electromagnetic retarded engine indicated that this can only be done using the immense charge and current densities which exist in the atomic scale. However, this scale cannot be described by Newtonian physics, and only a quantum description will suffice to describe the dynamics of an electron on this scale properly. Here we study the retarded field quantum engine and highlight the differences between the quantum and the classical retarded engines.

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model (ΛCDM), which endorses a positively curved early Universe with a confidence level greater than 99%. Although General Relativity (GR) performs accurately in the local/present Universe where spacetime is almost flat, its lost boundary term, incompatibility with Quantum Mechanics and the necessity of dark matter/energy could indicate its incompleteness. By utilising the Einstein–Hilbert action, this letter presents extended field equations by considering the pre-existing/background curvature and the boundary contribution. The extended field equations consist of Einstein field equations with a conformal transformation feature in addition to the boundary term, which can remove singularities, satisfy a conformal invariance theory and facilitate its quantisation.

Origin, mechanics and properties of the Solar System are analysed in the framework of the Complete Relativity theory (by the same author). According to Complete Relativity, everything is relative. Any apparent absolutism (notably invariance to scale of dimensional constants, absolute elementariness, invariance to time) is an illusion stemming from limits imposed by [or on] polarized observers that will inevitably lead to misinterpretation of phenomena (another illusion) occurring on non-directly observable scales or even on observable but distant scales in space or time. If everything is relative, reference frames will exist where particles are planets and where planets are living beings. Earth is, therefore, analysed here in more detail, both as a particle and, as a living evolving being (of, hypothesized, extremely introverted intelligence). The analysis confirms the postulates and hypotheses of the theory (ie. existence of discrete vertical energy levels) with a significant degree of confidence. During the analysis, some new hypotheses have emerged. These are discussed and confirmed with various degrees of confidence. To increase confidence or refute some hypotheses, experimental verification is necessary. Main conclusions that stem from my research and are further confirmed in this paper are: universes are, indeed, completely relative; Solar System is a scaled (inflated, in some interpretations) Carbon isotope with a nucleus in a condensed (bosonic) state and components in various vertically excited states; life is common everywhere, albeit extroverted complex forms are present on planetary surfaces only during planetary neurogenesis; anthropogenic climate change is only a part (trigger from one perspective) of bigger global changes; major extinction events on a surface of a planet are relative extinctions, a regular part of transformation and transfer of life in the process of planetary neurogenesis.

Loop quantum gravity (LQG) quantizes gravity through the quantization of the space-time. It begins with general relativity (GR) and brings some concepts from quantum field theory to quantize the space-time. The conceptual background of GR is necessary to comprehend the LQG framework. Therefore, in this paper, prerequisite concepts such as special relativity, general relativity, covariant electromagnetism, tensor analysis, Lagrangian formulation, Hamiltonian formulation and basics of quantum mechanics are briefly introduced; that, are needed to study loop quantum gravity(LQG).

This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

In 1922, Albert Einstein visited Paris and interacted extensively with an illustrious section of the French academia. In overfilled sessions at the Coll\`{e}ge de France and the Sorbonne, Einstein explained his theories of relativity, and prominent physicists, mathematicians and philosophers listened, debated, questioned and explored facets of relativity. The 1922 visit had its echoes in the life and works of many who participated, particularly decisive for Einstein and the philosopher Henri Bergson. This essay examines that eventful visit, focusing on the physical and logical aspects of Bergson's critique, with physics commentaries, linking prominent French physicists and mathematicians Langevin, Painlev\'{e}, Hadamard, Becquerel, Sagnac, and Kastler. I give particular attention to the logical and empirical accuracy of the physics issues involved, delineating Bergson's exact reasoning for his philosophical enthusiasm in Einstein's theory and for the ensuing critique. Bergson's philosophical stand on duration and simultaneity is reassessed in the context of later developments in cosmological physics as well as the wealth of empirical data involving comparison of atomic clocks. Finally we are led naturally to a surprising completion of the philosopher's program on universal time, duration and simultaneity, in harmony with the time of the physicist. In the appendices after the main text I also give the physics background and easily verifiable proofs for the assertions made in the text, pertaining to relativity, simultaneity and time dilation, clearly distinguishing beliefs and facts.

This article presents a novel approach to understanding the influence of electric Energy on space-time curvature. EFE actual calculations refer solely to gravitational charges. In this article, I expand them to include the electric charge with calculations carried specifically for electric charges, with exciting results. The article leverages the universal consistency of physical laws, applying the known effects of gravitational charges on space-time curvature to electric charges. The research focuses on calculating the specific impact of electric charges on space-time curvature, rooted in the principle that space-time curvature is omnipresent. The findings reveal that space-time curvature's alteration due to an electric charge is influenced by various factors, including the charge's location, magnitude, mass, density, associated electric field, and its motion through space-time. Notably, the conversion factor for electric charges differs from the conversion factor for gravitational charges. These insights significantly enhance our understanding of electromagnetism and general relativity, paving the way for a more profound comprehension of electric charges.

In previous works we have developed the concept of a relativistic engine taking into account the phenomena of retardation of electromagnetic fields. We have shown that Newton’n third law cannot strictly hold in a distributed system, where the different parts are at a finite distance from each other and thus force imbalance is created at the system’s center of mass. As the system is affected by a total force for a finite period, mechanical momentum and energy are acquired by the system. In previous works we relied on the fact that the bodies were macroscopically natural. Lately we relaxed this assumption and studied charged bodies, thus analyzing the consequences on a possible electric relativistic engine. On the first paper on this subject we investigated this phenomena in general but gave an example of a system only at the stage of reaching a stationary state, a second paper was devoted to the same but on the atomic scale, here we shall analyze the charge relativistic engine in a general time dependent setting.

In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. A preliminary analysis of this option denoted "nano relativistic scale" is studied in the current paper.

Newton's third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is thus zero. However, according to the principles of relativity, a signal cannot propagate at speeds exceeding the speed of light. Hence the action and reaction cannot be generated at the same time due to the relativity of simultaneity. Thus, the total force cannot be null at a given time. In a previous paper \cite{MTAY1}, we have shown that Newt\-on'n third law cannot strictly hold in a distributed system, where the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation, which cannot exceed the speed of light in the vacuum. A specific example of two current loops with time dependent currents demonstrated that the summing of the total force in the system does not add up to zero. This analysis led to the suggestion of a relativistic engine \cite{MTAY3,AY1}. As the system is affected by a total force for a finite period, the system acquires mechanical momentum and energy. Now the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in \cite{MTAY4}, while preliminary results regarding energy conservation were discussed in \cite{AY2,RY,RY2}. Previous analysis relied on the fact that the bodies were macroscopically natural, which means that the number of electrons and ions is equal in every volume element. Here we relax this assumption and study charged bodies, thus analyzing the consequences on a possible electric relativistic engine.

The purpose of this paper is to show a new approach to unify the theory of general relativity and quantum physics. For this, we rely on thermodynamics, fluid mechanics and the theory of information. We will then see that the Shannon entropy, Boltzmann and Von Neumann can be the source of gravity, which would be a form emerging. For this, we will study at first what is lacking for the unification of general relativity and physics. Secondly, we will explain the concept of entropic gravity by introducing calculations Erik Verlinde. Then we will explain the concept of entropy Boltzmann, Shannon, Von Neumann and the links between them. Then, we will modify Einstein's equations by transforming the tensor of perfect fluid in terms of entropy. Finally, we will link our theory with experience already carried out as part of a link between gravity and quantum theory.

One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant H_0 using the time delay Delta t between multiple images of lensed quasars. This method has already been applied, obtaining a value of H_0 compatible with that obtained from the SNe 1A, but non compatible with that obtained studying the anisotropies of the CMB. This difference could be a statistical fluctuation or an indication of new physics beyond the Standard Model of Cosmology, so it desirable to improve the precision of the measurements. At the current technological capabilities it is possible to obtain H_0 to a percent level uncertainty, so a more accurate theoretical model could be necessary in order to increase the precision about the determination of H_0. The actual formula which relates Delta t with H_0 is approximated; in this paper we expose a proposal to go beyond the previous analysis and, within the context of a new model, we obtain a more precise formula than that present in the Literature.

The Universe has a gravitational horizon with a radius R_h = c/H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaitre-Robertson-Walker spacetime, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model R_h = ct. As of today, this cosmology has passed over 20 observational tests, often better than LCDM. The gravitational radius R_h therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to mc². This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches R_h. In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.

This paper examines radially infalling worldlines in both Schwarzschild and Kruskal-Szekeres coordinates. A new Schwarzschild coordinate chart is presented which emphasizes the curvature of both the time and space coordinates and makes clear not only the mechanism by which the inertial observer is accelerated relative to the rest observers, but also clearly shows the light-like nature of the inertial worldline at the event horizon. The light-like nature of the falling frame is then supported by examining the falling worldlines in Kruskal-Szekeres coordinates. The effect of length contraction in the falling frame is also analyzed in both Schwarzschild and Kruskal-Szekeres coordinates.

Disk galaxies have a typical dimension of few tens of thousands of light years. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect is absent in modelling used to calculate rotation curves throughout the entire galaxy and its external gas. The considerable differences between Newtonian action at a distance predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that applying general relativity in a rigorous fashion without mindlessly neglecting retardation, one can explain the radial velocities of galactic matter without modifying gravity or adding unseen matter. Moreover, it was shown that dark matter effects as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. In the original main paper on the subject only one galaxy (M33) was analysed in detail. This was later amended somewhat with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain an excellent fit without postulating dark matter or modifying general relativity.

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi–hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric, and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them to reach the center. However in the present case this behavior is affected by the parameter γ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the θ−r subspace. Possible relevance of these results in the explanation of extragalactic jets, is brought out. .

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. However, the proofs of these theorems traditionally depend upon a collection of assumptions about the continuum spacetime (and, in the physical case, the stress-energy distribution defined over it), including its global structure, its energy conditions, the existence of trapped null surfaces and the various volume/intersection properties of geodesic congruences, that are inherently difficult to translate to the case of discrete spacetime formalisms, such as causal set theory or the Wolfram model. Some, such as the discrete analog of Raychaudhuri's equation for the volumes of geodesic congruences, are subtle to formulate due to intrinsic differences in the behavior of discrete vs. continuous geodesics; for others, such as the definition of a trapped null surface, no appropriate translation is known for the general discrete case due to a lack of a priori coordinate information. It is therefore a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previous work, in which the conformal and covariant Z4 (CCZ4) formulation of the Cauchy problem for the Einstein field equations, with constraint-violation damping, was defined in terms of Wolfram model evolution over discrete (spatial) hypergraphs for the case of vacuum spacetimes, and proceeds to consider a minimal extension to the non-vacuum case by introducing a massive scalar field distribution, defined in either spherical or axial symmetry. Under appropriate assumptions, this scalar field distribution admits a physical interpretation as a collapsing (and, in the axially-symmetric case, uniformly rotating) dust, and we are able to show, through a combination of rigorous mathematical analysis and explicit numerical simulation, that the resulting discrete spacetimes converge asymptotically to either non-rotating Schwarzschild black hole solutions or maximally-rotating (extremal) Kerr black hole solutions, respectively. Although the assumptions used in obtaining these preliminary results are very strong, they nevertheless offer hope that a more general, perhaps ultimately ``Penrose-like'', singularity theorem may be provable in the discrete spacetime case too.

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translate into a gradient expansion that, at the leading order, can recover the BKL solution. We solve exactly the leading order equations in a spherical symmetric case and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

In this work, we try to find a way to describe the physical law of micro-world under the frame of a space-time theory. By introducing the scalar fields $\mathcal{D}\left( x\right)$ and $\zeta\left( x\right) $, we rewrite the action of conventional field theory and the Lagrangian describing the motion of the particle, where a modified space-time relation is obtained. To test the correctness of this attempt, we demonstrate the Klein-Gordon equation by the Hamilton-Jacobi method in four dimensional form and present a time delay for the ground state of hydrogen atom.

It is well known that a sequence of two non-collinear Lorentz boosts (pure Lorentz transformations) does not correspond to a Lorentz boost, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. We visualize the interrelation between this rotation and the relativity of distant simultaneity by moving a Born-rigid object on a closed trajectory in several steps of uniform proper acceleration. Born-rigidity implies that the stern of the boosted object accelerates faster than its bow. It is shown that at least five boost steps are required to return the object's center to its starting position, if in each step the center is assumed to accelerate uniformly and for the same proper time duration. With these assumptions, the Thomas-Wigner rotation angle depends on a single parameter only. Furthermore, it is illustrated that accelerated motion implies the formation of an event horizon. The event horizons associated with the five boosts constitute a natural boundary to the rotated Born-rigid object and ensure its finite size.

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life's origin. Non-biological and biological entities obey the universal laws of nature grounded on space-time symmetry (STS) transformations. The fabric of STS is the immense subject of our review. The symmetry, encompassing behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. Objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation - mirror reflection. Chirality as a symmetry element reflecting the property of asymmetry (or dissymmetry) is the critical structural feature of natural systems, including sub-atomic particles and living matter. The inheritance of molecular symmetry from the symmetry of elementary particles points to the bi-directional causal pathway of prevalent bio-chirality. We assume that both extremities of spatial dimension naturally influence this transitional state of biological matter. The current review promotes an integrative holistic approach to the new experimental results in fast-developing and divergent branches of STS and biological chirality. The generalized view on biological chirality is a necessary and promising avenue for adequately understanding the link between protein folding, cell morphology, neuronal signaling, and laterality of cognitive functions.

We study the effect of the generation of the mechanical transverse wave (MTW)　travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter q_E representing the acceleration experienced between observers within the light cone. By comparing q_E to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that q_E aligns more closely with these data. The core argument of the paper is that Λ—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective q_E in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.

We have shown that Newton’s third law does not strictly hold in a system with remote elements, due the finite speed of signal propagation and thus force imbalance occurs at the system’s center of mass. As the said system is affected by a total force for a finite duration, mechanical energy and momentums are gained by the system. In early works we assumed that the bodies were macroscopically charge neutral. Later we removed this restriction, thus analyzing the consequences on a possible electric charged relativistic motor. On the first published paper on this subject we studied this phenomena in general but gave only an example of a system reaching a stationary state, in this paper we shall analyze a charged retarded electromagnetic motor in a more general time dependent setting giving specific examples in which the system never reaches a stationary state yet produces steady linear momentum non the less.

In recent years retarded gravity has explained many of the mysteries surrounding the "missing mass" related to galactic rotation curves, the Tully-Fisher relations, and gravitational lensing phenomena. Indeed a recent paper analyzing 143 galaxies, has demonstrated that retarded gravity will suffice to explain the galaxies rotation curves without the need to postulate dark matter for multiple types of galaxies. Moreover, it also demystified the "missing mass" related to galactic clusters and elliptic galaxies in which excess matter wad derived through the virial theorem. Here we give a mathematical criterion which specifies the cases for which retardation is important for gravity (and when it is not). The criterion takes the form of an "uncertainty" relation.

In this paper, the Hafele‐Keating experiment and the geostationary orbit satellite of related physics problems of are analyzed and discussed in detail. If researchers read the paper and think about it, It will be found that the Hafele‐Keating experiment and the geostationary satellite problem prove that some of the core ideas and theories of relativity are seriously wrong. Isnʹt that a very serious problem in physics? Canʹt this cause the academic circles to pay great attention to it? Isnʹt this worthy of in‐depth analysis and research? The core of the paper is to point out that there are problems with the space concept and the reference system theory of classical physics and relativity, And that would bring up a whole host of physics problems. It takes a concerted effort from the academic community, Do furtherin‐depth analysis and research. Strive forthe further discovery and perfection of physics theory.

In this work, the conceptions of the electrodynamics of action-at-a-distance and of electromagnetic fields are reviewed and confronted, with the aim of clarifying whether it is possible to propose a Weberian theory of action-at-a-distance, which together with a renewed mechanics (both re-specting the existence of a limiting velocity c) could constitute a framework capable of yielding predictions equivalent to those of the conventional Maxwell-Lorentz and SRT framework. In this work, it is shown that, considering basic assumptions about the interaction process, understanding it as an action exchange process, it is possible to derive the expression of the electrodynamic Phipps’ potential energy between two interacting charges. It is also shown that, with the same assumptions and the additional hypothesis that the interaction is supported by a mediating agent (aether or field) which is perturbed by the transmission of action, this perturbation obeys the wave equation (one of the main drawbacks of Weberian electrodynamics). Another aim of the work is to confront the relational electrodynamic formulations (supported by Galilean transformations that assume a universal time) with the Maxwell-Lorentz formulation of electromagnetism (linked to Lorentz transformations that entail local times), in order to elucidate whether the space-time to which the SRT leads us is a mere mathematical artifice or an inescapable reality.

In Einstein’s Special Relativity(SR), time is treated as one of the four dimensions within spacetime and is relative in nature. Typically, a photon clock serves as the illustrative device in the time dilation thought experiment, featuring a single photon bouncing between two mirrors. However, the present paper identifies a fundamental flaw in this thought experiment, hence challenging its validity. Contrary to SR, this paper asserts that time is a consequence of motion. Space and time should be treated differently as proposed by classical mechanics. Importantly, this stance does not challenge the concept of curved space in General Relativity (GR), but rather questions the idea of relative time, as employed in both SR and GR. The absence of time dilation also dispels the twin paradox, prompting a necessary reassessment of the second postulate of relativity to ensure a more precise depiction of relativistic effects.

We elucidate the versatility of intriguing symmetry and asymmetry phenomena outside and inside black holes. For description of the test particle (planet and photon) motion it is used the Kerr-Newman metric of the rotating and electrically charged black hole. In particular, it is demonstrated the symmetry and asymmetry of the one-way Einstein-Rosen bridge inside black hole toward and through the plethora of endless and infinite universes.

Galaxies are rather big physical systems having a typical size of tens of kilo parsecs. Thus any change at the center of the galaxy will affect the outskirts only tens of thousand of years afterwards. Retardation seems to be neglected in current calculations of rotational velocities in the far edges of the galaxy and its surrounding gas. The differences between the velocities predicted by Newtonian theory and observational derivations are accommodated by either assuming "dark matter" or by introducing modifications to the laws of gravity in which MOdified Newtonian Dynamics (MOND) is one of the typical examples, celebrating now forty years since its inception. We show that there are overlapping conditions for retardation corrections in the weak approximation to general relativity and the low acceleration conditions for MOND corrections. We will also show that MOND interpolation formula is useful for calculating retardation effects provided an appropriate interpolation function is chosen.

Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation gives a relationship between the mass ratio and the final velocity in multiples of the exhaust speed, and dictates a high mass ration for current exhaust speeds. A relativistic motor exchanging momentum and energy with the electromagnetic field may mitigate such considerations, enabling efficient interplanetary travel. In this paper we will discuss the advantages and challenges of this novel mover for space transportation.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

The standard Cosmological model (LCDM) assumes that the expanding spacetime around us is infinite, which is inconsistent with the observed cosmic acceleration unless we include Dark Energy (DE) or a Cosmological Constant ($\Lambda$). But the observed cosmic expansion can also be explained with a finite mass $M$, inside a uniform expanding sphere, with empty space outside. An object with mass $M$ has a gravitation radius $r_S=2GM$. When $M$ is all contained within $r_S$, this is a Black Hole (BH). Nothing can escape from $r_S$, which becomes a boundary for the inside dynamics. In the limit where there is nothing outside, the inside corresponds to a local isolated Universe. The $r_S$ boundary condition corresponds to an effective force which is mathematically equivalent to $\Lambda=3/r_S^2$. We can therefore interpret cosmic acceleration as a measurement of the gravitational boundary of our Universe, with a mass $M = \frac{c^2}{2G}\sqrt{3/\Lambda} \simeq 6 \times 10^{22} M_{\odot}$. Such BH Universe (BHU) is observationally very similar to the LCDM, except for the very large scale perturbations, which are bounded by $r_S$.

In classical General Relativity, White Holes (WH) refer to the time reverse Schwarzschild (SW) Black Hole (BH) solution of a point mass $M$ and gravitational radius $r_S=2GM$. The SW metric is static so that a time reverse WH solution simply corresponds to a violation of causality. The WH solution does not make any physical sense here. For a more physical model, such as the Lemaitre-Tolman-Bondi (LTB) metric with finite mass inside $r_S$, we show that both the expanding and collapsing solutions correspond to a BH and not to a WH.

In paper I, we showed that the observed (LCDM) Universe can be modeled as a local Black Hole (BH) Universe (BHU) of fixed mass M, without Dark Energy (DE): cosmic acceleration is caused by the BH event horizon rS=2GM. %The same BHU solution can be used to model the interior of a stellar or galactic BHs. Here, we propose that our BHU could form from the hierarchical free-fall collapse of regular matter. We argue that the singularity could be avoided with a Big Bounce explosion, caused by neutron degeneracy pressure (Pauli exclusion principle). This happens at GeV energies, like in core collapse supernova, well before the collapse reaches Planck energies (1E19 GeV). If our universe formed this way, there is no need for cosmic Inflation or a singular start (The Big Bang). Nucleosynthesis and recombination follow a hot expansion, like in LCDM, but cosmological measurements, which are free parameters in LCDM, could be estimated from first principles. Dark Matter could be made up of a wide mass range of primordial compact objects (BHs and Neutron stars), remnants of the collapse and bounce, which can provide a faster start for galaxy formation. We present a simple prediction to explain the observed value of Lambda and the coincidence problem.

We propose that the Big Bang does not have a singular start, but that it originates from gravitational collapse of a low density cloud that collapsed 25 Gyrs ago to form a Black Hole (BH) of mass M ≃ 6 × 1022M⊙. The collapse continued inside the BH for 11Gyrs until the density achieves neutron degeneracy and the collapse bounces into expansion like a core collapse supernova. From observations today, this model is very similar to the standard Big Bang cosmology but there is no need for Inflation or Dark Energy (DE). The observed cosmological constant Λ is not a new form of DE, but results from the dynamics of the Big Bang expansion inside the BH event horizon rS = 2GM = √3/Λ. Why our Universe has such a large mass M (or small Λ value)? If τO(≃ 10Gyr) is the astronomical timescale needed for observers like us to exist, we find a simple anthropic prediction, based only on gravitational collapse from Gaussian fluctuations, that the maximum probability for M is MO < M < 3MO where MO = τO/3G. This agrees well with the measured values for τO and M in our Universe.

In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and also suggest a rapid expansion of the matter density, thus making mechanism such as inflation (which demands invoking and ad-hoc scalar field) redundant. This is in accordance with Occam’s razor.

The standard model of cosmology assumes that our Universe began 14 Gyrs (billion years) ago with a hot Big Bang expansion out of nothing. It can explain a vast range of different astrophysical data from a handful of free cosmological parameters. However successful this model is, we have no direct evidence or fundamental understanding of some key assumptions: low entropy start, Inflation, Dark Matter and Dark Energy. Here we present a simpler and more physical explanation for the same observations that do not require such assumptions or new laws of Physics. It is based on the evidence that we live inside a Black Hole (BH) of mass $ M \simeq 5 \times 10^{22} M_{\odot}$, which we observed as cosmic acceleration. How did the Big Bang end up inside such a BH? We propose that 25 Gyrs ago, a very low density dust cloud collapsed and form such BH. As there was no pressure support, the collapse continued inside until it reached neutron energy densities (GeV). Causal regions of solar mass size rebound by neutron degeneracy, like a supernovae, producing the Big Bang expansion and compact dark matter remnants. During collapse, perturbations exit the horizon to re-enter during expansion, given rise to the observed universe. We review the evidence for such BH Universe.

An axiomatic theory is proposed that reconciles the existence of an absolute scale for time (Planck time) and special relativity. According to this theory speed of light c becomes a variable which is proposed to be taken as the fifth dimension.

In this paper we investigate into the possible resurrection for the aether and it’s compatibility with the theory of relativity. We revisit the Michelson-Morley experiment and expose some of the major inadequacies. In this regard, we have presented the true/corrected form of the Michelson-Morley experiment. We have tried to revise the interpretational aspect of the mathematical formalism regarding the metric of Minkowskian space-time in addendum with it’s relationship to the two theories of time. We herein have also tried to restrain some of the quantum mechanical issues arising from the mainstream understanding of the mathematical formalism of the Minkowskian manifold. Essentially, we have argued in favour of aether to be incorporated into our mathematical formalism as well the physical understanding of the universe.

Similarly to his special theory of relativity, Einstein's special principle of relativity extends beyond the limits currently known to it. Up to now, the principle has not been suspected to have the potential to translate laws. However, the principle holds an inherent capacity to translate physical laws and, in so doing, speeds up our understanding and control of physical reality. Such a translation of laws leads to the faster discovery of other laws, such as the Laws of Electronic Motion, characterizing the motion of electrons around the atomic nucleus, and the Third Law of Biological Resistance, facilitating the successful control of drug resistance in medicine. The ability of the special principle of relativity to translate laws shines forth once the said principle is duly interpreted. This interpretation exposes a parallelism between experimental frames of reference and justifies the applicability of the laws of one frame of reference in other parallel frames of reference. This process opens the door to our faster discovery of the laws governing a multiplicity of frames parallel to a frame we already know the laws of. In practice, the interpretation of Einstein's special principle of relativity speeds up our understanding of the workings of physical reality and strengthens our capacity to subdue matter.

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the apparent excess matter leading to gravitational lensing in both galaxies and galaxy clusters.

In this paper, we investigate how Rindler observer measures the universe in the ADM formalism. We compute his measurements in each slice of the space-time in terms of gravitational red-shift which is a property of general covariance. In this way, we found special relativity preferred frames to match with the general relativity Rindler frame in ADM formalism. This may resolve the widely known incompatibility between special relativity and general relativity on how each theory sees the red-shift. We found a geometric interpretation of the speed of light and mass.

Visual imagery, i.e., the mental experience of an object occurring in the absence of external visual stimulus, might encompass diverse content according to different observers. Further, subjectively experienced time is encoded in the later entorhinal cortex. Starting from these two observations, and considering Einstein’s account of spacetime, we show how, in terms of special relativity, the content of visual imagery is not stationary and fixed, rather depends on the standpoint of the observer. We elucidate how the subjective definition of time (perceived by our mind as static) might give rise to modifications in the length of the imagined object which are experimentally assessable and quantifiable. In particular, based on recent neuroscientific literature, we show how changes in our mental time windows are able to squeeze the visual content of mental imagery.

The Landauer principle supplies the estimation of the minimal mass of a particle which is capable to record/erase information within a thermal bath at the temperature of T. Particles lighter than ${\tilde{m}}_0=\frac{k_{B}Tln2}{c^2}$will not transform the information to the surrounding bodies and are well expected to be undetectable. The relation of the Landauer principle to the problem of “dark matter” is discussed. The maximal informational content of a particle at rest, estimated as $I_{max}=\frac{m_0{c}^2}{k_{B}Tkn2}$ is introduced. The Landauer principle also allows the estimation of minimal energy of the field which is capable to record/erase 1 bit of information in the surrounding at the temperature of T. The relativistic aspects of the Landauer principle and its relation to the relativistic transformation of temperature are addressed.

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

We received an Honorable Mention at the Gravity Research Foundation 2018 Awards for Essays on Gravitation by showing that a correct general relativistic interpretation of the Mössbauer rotor experiment represents a new, strong and independent, proof of Einstein's general theory relativity (GTR). Here we correct a mistake which was present in our previous computations on this important issue by deriving a rigorous computation of the additional effect of clock synchronization. Finally, we show that some recent criticisms on our general relativistic approach to the Mössbauer rotor experiment are incorrect, by ultimately confirming our important result.

The fact that real dissipative (entropy producing) processes may be detected by non–comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information theory, in analogy with the explanation of the Maxwell's demon paradox.

Using four field equations, a recently proposed theory that covers the phenomenology of classical physics at the level of the Maxwell and Einstein Field Equations (M&EFEs) but then goes further by unifying electromagnetic and gravitational phenomena in a fundamentally new way is reviewed. Predictions of the field equations are shown to be consistent with those of the M&EFEs through specific solutions; a particle-like solution representing a point charge, and two radiative solutions representing electromagnetic and gravitational waves. A unique feature of the full set of field equations is that charge and mass are treated as dynamic fields instead of being introduced as external parameters as is done with the classical M&EFEs, a feature that enables a procedure for quantizing the mass, charge and angular momentum of particle-like solutions. Finally, antimatter is naturally accommodated by the theory and definite predictions regarding the interactions of matter and antimatter with gravitational fields are made.

In physics, thought experiments are impressive heuristic tools. They are valuable instruments to help scientists find new results and to teach students the known ones. However, as we shall show, they should always be received with prudence, even when they are a shortcut to 'prove' well-established results. Here, we show that the most widely known thought experiments devised to derive the gravitational frequency shift from energy conservation are, in fact, problematic. When properly set and correctly read, those thought experiments reveal that the existence of the gravitational frequency shift is, in fact, at odds with energy conservation. We also propose two new simple thought experiments, one using the conservation of energy and the other the conservation of linear momentum, that corroborate that conclusion, showing that those conservation principles do not imply the gravitational frequency shift. We think that our results may be of some epistemological interest and could serve as a warning sign on how thought experiments should be received and trusted.

n this article a first attempt at formalizing a new approach to the grand unified theory is introduced. This theory named NUVO is based primarily on considering two aspects of inertia. The first aspect is how a mass couples to space, introducing definitions to distinguish massive particles from massless particles. The second aspect is space’s availability to couple to massive particles. In essence these are the two contributions of inertia; mass and space. Postulates, clarifications, and a mathematical structure are introduced. Part 1 covers the physics of the very large (cos- mic), laying ground work for part two which applies the structure to the very small (quantum). The cosmic application of the theory will show a strong correlation to empirical data and correspondence to General Rela- tivity, including; time dilation, length contraction, and orbital advances. Departing from the canonical findings of General Relativity by predicting a quantization of physical units under the effect of acceleration and or gravity.

The theory of special relativity has reexamined and reconstructed the concepts of space and time, which are indispensable for describing physical laws, consequently instigating a major revolution in physics in general. Although the correctness of the special theory of relativity has been con-firmed by many observations and experiments, it is unclear why the "principle of relativity" and the "principle of the constant speed of light," which form the basis of the idea, are valid. Moreo-ver, although special relativity has advanced our understanding of time, our understanding of the fundamental question, "What is time?" is still limited. The theory of special relativity regards space as a four-dimensional construct consisting of one-dimensional time and three-dimensional space. This paper proposes an alternative framework, wherein real space is uniform and isotropic four-dimensional space, and elementary particles are waves that propagate through this four-dimensional space at a constant speed. This new perspective provides evidence to support two of Einstein’s key principles—the "principle of relativity" and the "principle of the constant speed of light." Furthermore, this model clarifies what time is and why time flows at a constant rate from the past to the future.

In this paper, we will describe the general theory of relativity. The special theory of relativity is based on the ideal inertial frames. These ideal inertial frames are assumed to exist in every event in space-time. In contrast, in the general theory of relativity, we do not have to make that assumption. Additionally, the space-time is considered to be part of the solution to the motion. Moreover, interpretation of geometrical quantities is introduced.

This article investigates the fundamental principles that establish universal limits in physical phenomena, such as the uniformity of physical laws and Energy conservation, leading to the concepts of maximum speed, locality, and maximum density. These principles guide me to explore Quantum Black Holes—relativistically rotating, miniature charged black holes with a singular core at the highest possible density. Uniquely, these Quantum Black Holes maintain all quantized charges, including gravitational ones. The study further demonstrates that quarks and leptons are composed of these Quantum Black Holes, redefining them as the actual elementary particles.Exploring these particles reveals that they emit Energy outward, modifying the curvature of nearby space-time. This discovery provides new insights into local space-time dynamics, characterized by a single equation that includes the influence of all charges and hidden Energy. By the conclusion of this article, I show that Quantum Black Holes offer explanations for several Standard Model deficiencies: the nature of luminous, dark, and anti-Matter; the mass, size, and quantized charges of all elementary particles (including gravitational); the nature of neutrino oscillations; and the mechanism by which electric charges remain bound even though the same type of electric charge components must repeal each other.

This paper introduces a Unified Field Theory through the generalization of General Relativity, following the methodology outlined by Einstein for incorporating complex metrics in the pursuit of a comprehensive Unified Field Theory.

By developing the previously proposed method of combining continuum mechanics with Einstein Field Equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangian density equal to the invariant of the electromagnetic field was obtained, vanishing four-divergence of canonical four-momentum appears to be consequence of the Poyinting theorem, and explicit form of one of gauges of the electromagnetic four-potential was introduced. The proposed method allows for further development with additional fields.

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

The recent Planck Legacy release confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which prefers a positively curved early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wavefunction of the Universe is utilised to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wavefunction reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolved in opposite directions as distinct Universe sides, corroborating the axis of CMB. The wavefunction indicates that a nascent hyperbolic expansion away from early plasma is followed by a first phase of decelerating expansion during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both sides free-fall towards each other under gravitational acceleration. The predicted conformal curvature evolution demonstrates the fast orbital speed of outer stars owing to external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wavefunction predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings show that early plasma could be separated and evolved into distinct sides of the Universe that collectively inducing its evolution, physically explaining the effects attributed to dark energy and dark matter.

Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analysing the situation without neglecting Mercury's mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too large. ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a subsequent better understanding of the famous Dark Matter and Dark Energy problems.

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial reference frames, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic reference frames. There exist some differences between this theory and Einstein's theory of general relativity.

In the present paper we investigate the conservative conditions in Quadratic Gravity. It is shown explicitly that the Bianchi identities lead to the conservative condition of the left-hand-side of the (gravitational) field equation. Therefore, the total energy-momentum tensor is conservative in the bulk (like in General Relativity). However, in Quadratic Gravity it is possible to have singular hupersurfaces separating the bulk regions with different behavior of the matter energy-momentum tensor or different vacua. They require special consideration. We derived the conservative conditions on such singular hypersurfaces and demonstrated the very possibility of the matter creation. In the remaining part of the paper we considered some applications illustrating the obtained results.

In this work, we study the existence of strange star in the background of f(T,T) gravity in the Einstein spacetime geometry, where T is the torsion tensor and T is the trace of the energy-momentum tensor. The equations of motion are derived for anisotropic pressure within the spherically symmetric strange star. We explore the physical features like energy conditions, mass-radius relations, modified TOV equations, principal of causality, adiabatic index, redshift and stability analysis of our model. These features are realistic and appealing to further investigation of properties of compact objects in f(T,T) gravity as well as their observational signatures.

A dark region and a bright part of accretion disk are viewed on the first image of the supermassive black hole in the galaxy M87 obtained by the Event Horizon Telescope. We demonstrate that a viewed dark region is a silhouette of the black hole event horizon, while the outline (contour) of this silhouette is an equator of the event horizon globe. A dark silhouette of the black hole event horizon is placed within the expected position of the black hole shadow, which is not revealed on the first image. We calculate numerically a relation between the viewed position of the black hole silhouette and the brightest point in a thin accretion disk in dependence of the black hole spin. A spin of the supermassive black hole in the galaxy M87, derived from this relation, is $a=0.75\pm0.15$.

We consider the conjecture of the relationship between the entanglement entropy of spacetime, matter and the action in Einstein's general relativity. Our analysis suggests the possibility of regarding the entanglement entropy of spacetime and matter as the dimensionless action in general relativity by using Planck units. In this case, the action principle originates from the maximization of the entanglement entropy. We also show that the fundamental property of entanglement entropy leads to attractive characteristic of gravitational force for classical particles.

A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes.

In the weak-field approximation of covariant theory of gravitation the problem of 4/3 is formulated for internal and external gravitational fields of a body in the form of a ball. The dependence of the energy and the mass of the moving substance on the energy of field accompanying the substance, as well as the dependence on the characteristic size of the volume occupied by the substance are described. Additives in the energy and the momentum of the body, defined by energy and momentum of the gravitational and electromagnetic fields associated with the body are explicitly calculated. The conclusion is made that the energy and the mass of the body can be described by the energy of ordinary and strong gravitation, and through the energies of electromagnetic fields of particles that compose the body.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and masses can be rewritten in terms of their densities and the integral over the curved space-time volume element. The idea find its place in quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores these concepts and runs through various frameworks and equations relevant to this idea including the quantum stress energy tensor, and expressing Schrodinger’s equation in ways that are tied to general relativity it also discusses the cosmological constant and the cosmological constant problem.

We proposed an equation of motion as a constraint condition on the gauge degree of freedom in general relativity theory based on a co-moving framework. This constraint equation transformed the gauge degree freedom of general relativity theory into an natural equation of motion, and provide an explicit theoretical understanding on the Mach's principle and rotating bucket experiment. The galaxy rotation curves is derived directly from general relativity theory under this constraints equation. This work may inspires different understanding on dark matter, dark energy, and the quantization of gravity.

Abstract: Experiments conducted to date to verify the relativistic gravitational time dilation have limited scientific significance because the basic postulate of Einstein’s relativistic GR that the same time (t0) is measured in all non-inertial frames of reference, because all non-inertial frames of reference must be equal, has not yet been verified by time measurements. According to Einstein's relativistic GR, a correlation between time and different gravitational potentials must be the result of a relative relation between non-inertial frames of reference and must not the result of any other physical influence. An experiment that can differentiate between a causal correlation (relative relation) and an apparent correlation (relativistic relation) between time and gravitational potentials is still outstanding. The expressions "relative" and "relativistic" are often used as synonyms. However, Einstein's GR is a relativistic theory. In the case of general relativity, relativistic means that time depends only on the relative relation between non-inertial frames of reference and not on other physical factors. The author proposes an easy-to-realize experiment that is able to distinguish between a causal correlation (relative relation) and an apparent correlation (relativistic relation) between time and gravitational potentials, which can confirm or falsify Einstein's relativistic GR. .

The Theory of differences between elements explains the reasons for the differences in physical concepts between different elements, such as quantum physics and the Theory of general relativity, being explained through observations. Thus, it is possible to conclude from the observations that the differences are motivated by the reactions between the elements, by the composition of the elements, and by the influence of the spaces that promote losses and gains of characteristics; therefore, there is no general similarity between quantum physics and the general Theory of relativity. The study aims to understand the elements and their physical concepts that make up the Universe.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

In this paper, we investigate an exact Universe which is observational viable and filled with binary mixture of perfect fluid and cosmological constant $\Lambda$. Owning the non-uniform expansion of cosmos, we have considered redshift drift $\dot{z} = -(1+z)H_{0}+H(z)$ and performed statistical test to obtain the best fit value of model parameters of derived Universe with its observed values. Here $H_{0}$ and $z$ denote the present value of Hubble constant and redshift respectively. We estimate the best fit values of Hubble constant and density parameters are $H_{0} = 68.58 \pm 0.84$ km/s/Mpc, $(\Omega_{m})_{0} = 0.26 \pm 0.010$ and $(\Omega_{\Lambda})_{0} = 0.71 \pm 0.025$ by bounding the derived model with latest observational Hubble data (OHD) while with joint Pantheon data and OHD, its values are $H_{0} = 71.93 \pm 0.58$ km/s/Mpc, $(\Omega_{m})_{0} = 0.272 \pm 0.06$ and $(\Omega_{\Lambda})_{0} = 0.74 \pm 0.09$. The analysis of deceleration parameter and jerk parameter show that the Universe in derived model is compatible with $\Lambda$CDM model.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. The deviation, compared to the classical case, is important close to the horizon, but small in the box, and the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

In this paper, we investigate the ontological hypothesis, which implies that the spacetime is not the ultimate structure in our universe, and its existence emerges from a deeper physical entity. By using a very simple approach based on a classical problem, regarding the propagation of electromagnetic waves in empty vacuum. We were able to deduce that this deeper entity is just an omnipresent multi-rest states physical structure; aether. After that, we try to see how this aether fits in the universe that we exist in. The outcome is that its existence causes the emergence of some basic phenomena that our universe is built on. At the microscopic scale it turned out to be a source of the essential quantum phenomenon, which is currently known as the wave – particle duality. On the other hand, at the macroscopic scale it causes the emergence of spacetime curvature, around huge, massive objects like Earth, and finally, we try to visualize the prospects of aether, and how it can be a promising alternative for the dark matter.

Parallel lives is a model which provides an interpretation of quantum theory that is both local and realistic. This model assumes that all quantum fields are composed of point beings called ”lives”. Lives interact locally and have a memory of their previous interactions. The reduction of the state vector is not included in this model: lives can be divided into different worlds. This feature resembles many worlds interpretation. However in the parallel lives model, the division of lives into different worlds takes place locally. The parallel lives model is expected to be compatible with special relativity, as the lives propagate at a speed that does not exceed the speed of light and interact locally. On the other hand, it is open to paradoxes based on counterfactual propositions, as it provides a realistic interpretation of quantum theory. In this paper, we confront the parallel lives model with the paradox proposed by Hardy. We show that the parallel lives model cannot overcome the dilemma in Hardy’s paradox. We discuss implications of this confrontation on special theory of relativity, and speculate a solution that we believe, fits the spirit of the parallel lives model.

The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space ←→ time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (‘framespaces’), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck’s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck’s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.

Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term 'stochastic' to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term 'stochastic'. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein's general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein's speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.

The existence of semantic inaccuracy §2 articles by A. Einstein “On the electrodynamics of moving bodies”, illustrating the principle of the relativity of simultaneity. In a sentence “The observers co-moving with the moving rod would thus find that the two clocks do not run synchronously while the observers in the system at rest would declare them synchronous”, the preposition “not” must be moved and placed before the word “synchronous”, at the end of the sentence. The criterion for synchronism of the clocks on the rod is the time it takes for the beam to travel from clock A to clock B and back, and for observers on the rod it will be the same both when the rod is at rest and when the rod is moving. Otherwise, observers on the rod would have had at their disposal an experiment that would allow them to determine whether the rod is moving or at rest, which contradicts the first postulate of the Special Theory of Relativity. The inaccuracy is found unchanged in modern editions in English and Russian, and can become a source of difficulties when teaching the basics of the Special Theory of Relativity based on primary sources, as well as make it difficult to understand the author’s logic when studying independently. Nobel laureate R. Feynman, having expanded and modified A. Einstein's thought experiment, eliminated the inaccuracy described in the article.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides mathematical framework in which, as demonstrated in previous publications, the description of a physical system in curved spacetime and its description in flat spacetime with fields are equivalent. The description of a system with electromagnetic field based on Alena Tensor can be used to reconcile physical descriptions. 1) In curvilinear description, Einstein Field Equations were obtained with Cosmological Constant related to the invariant of the electromagnetic field tensor, which can be interpreted as negative pressure of vacuum, filled with electromagnetic field. 2) In classical description for flat spacetime, three densities of four-forces were obtained: electromagnetic, gravity, and the force responsible for the Abraham-Lorentz effect (radiation reaction force). Obtained connection of Einstein tensor with gravity and radiation reaction force, after transition to curvilinear description, excludes black hole singularities. There was obtained Lagrangian density and generalized canonical four-momentum, containing electromagnetic four-potential and a term responsible for other two forces. In this description charged particles cannot remain at complete rest and should have spin, their energy results from the existence of the energy of the magnetic moment and the density of this energy is part of the Poyting four-vector. The distribution of charged matter was expressed as polarization-magnetization stress-energy tensor, what may explain why gravity is invisible in QED. 3) In quantum picture, QED Lagrangian density simplification was obtained, and the Dirac, Schrödinger and Klein-Gordon equations may be considered as approximations of the obtained quantum solution. Farther use of Alena Tensor in unification applications was also discussed.

This paper is based on the concept of absolute airspace and its local absolute stationary reference system proposed by the author, on the premise of abandoning space concept and the relativity principle of relativity theory, It is proposed that general relativity and special relativity can be unified into Simple and practical a space-time transformation theory which fully includes other basic physical principles of relativity. And the unified and simple expression of the time transformation effect is proved and deduced. By comparing with the theoretical derivation and checking calculation of Hafele-Keating experiment in an ideal state, It is proved that the expression of time transformation effect proposed in this paper is completely correct. Compared with the theory of relativity, the calculation is simpler and more accurate. The paper also puts forward two checking prediction of physical cases about the time transformation effect, which are left for the capable competent unit or individual to verify in practice.

Through a brief analysis of the basic principle of relativity, it is found that there is a contradiction in principle between general relativity and special relativity in solving the specific problem of the clock moving around the earth, and one of them must be wrong. Through comparative analysis of five physical phenomena and experiments, it is proved that there are serious problems in the space concept of relativity theory and classical physic. At the same time, the different concept of absolute airspace is further expounded and demonstrated, and the related space-time physical phenomena and experiments are perfectly explained by this concept. According to this idea, a new time transformation relation is deduced and its correctness is demonstrated. It is proved that the principle of special relativity and special relativity are wrong, and a series of physical laws and physical explanations generated by special relativity may also be wrong, and a series of amendments or new interpretations need to be made.

We considered the hypothesis that the sources of dark energy (DE) could be black holes (BHs) or more exotic objects, such as naked singularities or gravastars. We proposed a definition of the presence of DE in the Universe and a criterion for what can be considered the source of this dark energy. It is based on the idea of the accelerated expansion of the Universe, which requires antigravity caused by large negative pressure. A recently proposed hypothesis was examined that mass of BHs increases with time according to the same law as the volume of the part of the Universe containing it and the population of BHs can mimic DE. We demonstrate the reasons why it cannot be accepted, even if all the assumptions on which this hypothesis is based are considered true.

On a rotating disk, two particles bounce at the vertices of a regular polygon in opposite directions. On the return to the entry point, a clock measures the time difference, called Sagnac effect. Due to Coriolis effects, the counterclockwise and clockwise paths are different. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The existence of a transition between a classical and a relativistic regime is proved. An experimental verification is proposed. Although the two Sagnac effects seem analogous, in detail their behavior is quite different.

In this paper a high-power and propellant-free electromagnetic propulsion is proposed based on the General Relativity and nuclear fusion technology. We find that Riemann curvature vanish and geodesic motion is free from gravitational field locally in a special space-time, which demonstrates the feasibility of propellant-free electromagnetic propulsion. To achieve high-power propulsion in Schwarzschild background, we choose current loop as axisymmetric field source and obtain exact solution of Einstein-Maxwell field equation using Killing symmetry and Ernst generation technique. An implementation with superconductor shield is given according to the Meissner effect, calculation implies that the device can be sufficiently free from gravitational field with the aid of existing nuclear fusion engineering.

Lord Kelvin believed that the electromagnetic aether must also generate gravity. Presently, we have no methods to determine the density of the electromagnetic aether, or we say the $\Omega(1)$ substratum. Thus, we also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substrata may be a possible candidate of the dark energy. According to the theory of vacuum mechanics, only those energy-momentum tensors of discrete or continuously distributed sinks in the $\Omega(0)$ substratum are permitted to act as the source terms in the generalized Einstein's equations. Thus, the zero-point energy of electromagnetic fields is not qualified for a source term in the generalized Einstein's equations. Some people believed that all kinds of energies should act as source terms in the Einstein's equations. It may be this unwarranted belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substrata is equivalent to that of around $3$ protons contained in a box with a volume of $1$ cubic metre.

Difference in two quantum states defined for a point in space time is represented by space time curvature and the superposition of these quantum states will affect the momentum of mass existed at that point. Analogy of the same with Einstein’s General relativity field equation and Einstein’s gravitational constant , indicated an equation containing ‘Hubble’s constant H , Einstein’s gravitational constant ‘H’ and Siva’s constant ‘K’. Its output is a quadratic equation. Solution to this quadratic equation predicted a fundamental force particle. This solution gives the diameter of that particle. From the fundamental principles, the diameter of this force particle gives the coupling constant of that fundamental force. Prediction and review of this particle may provide us new insights in to quantum physics and standard model of particle physics. From the first principles, it is discussed that this particle can be claimed as a force carrying particle of a fundamental force related to dark matter. This work has provided simple explanation to reconcile quantum nature of space time with smooth space time of General Relativity. This has demanded the necessity to introduce a new postulate in quantum mechanics which is beyond Hilbert space and Dirac notation. A new perspective of uncertainty principle in quantum mechanics has been elaborated.

In the present paper, the so-called Einstein’s causality is scrutinized and proven to be an illusion, a sort of mathematical fallacy. Causality as a well-established universal principle was and is absolutely valid for subluminal, luminal and superluminal signals under any natural and/or artificial circumstances. It is also shown that conceptually special relativity theory (SRT) is inapplicable to superluminality of physical phenomena since SRThas the light speed in vacuum as an upper limiting speed in its own proper domain of applications, and also because SRT is crucially based on the concept of inertial reference frames (IRFs) which are related to each other by Lorentz transformations, that is why the relative velocity of any two IRFs must be smaller than light speed.

We point out that field equations of general relativity are implied by a maximal force given by c⁴/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

Three different approaches show that, contrary to a longstanding conviction older than 160 years, the advance of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analysing the situation without neglecting Mercury's mass. General relativity remains more precise than Newtonian physics, but Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of the advance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too large for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: i) It is not correct that Newtonian theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too large. ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

Newton's kinetic energy equation delineates the laws of motion for objects travelling at speeds much less than the speed of light, an equation extensively validated at these lower velocities. Any new, more complete formulation of kinetic energy must approximate Newton's kinetic energy equation under these conditions. Einstein's special relativity, utilizing the Lorentz factor, introduces a new perspective on spacetime, adhering to the requirement that the Newtonian kinetic energy equation serves as an approximation at low velocities. In this paper, we identify all factor expressions satisfying the condition that their approximate solutions at low velocities align with Newton's kinetic energy equation. We introduce the Yuyunrui factor, incorporating two real number hyperparameters, $\alpha$ and $\beta$, encompassing all potentially correct factors, with the Lorentz factor as a specific instance where $(\alpha=0$, $\beta=1)$. We classify all potentially correct $(\alpha, \beta)$ combinations into six categories based on their distinct scaling effects and present the corresponding scaling effects. The combinations of $(\alpha, \beta)$ values applicable in the real world are necessarily included within these candidates, with the precise values requiring rigorous experimental validation. This work aims to refine our understanding of special relativity beyond the Lorentz factor.