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.

A novel geometric interpretation of the Minkowski metric is provided, which offers a different and more intuitive approach to phenomena in special relativity. First it is shown that a change of basis in Minkowski space is the equivalent of a change of basis in Euclidean space if a basis element is replaced by its dual element, constituting a mixed basis set. The methodology of the proof includes infinitesimal changes of basis using the Lie-algebras of the involved groups. As a consequence, a direct mapping between Euclidean and Minkowski space is defined. Second, a measuring device called a local, flat observer is defined in Euclidean space and it is shown, that this device uses a mixed basis when measuring distances. Combining these steps, it is concluded that a local, flat observer in a four-dimensional Euclidean spacetime measures a Minkowski spacetime.

For more than one hundred years, scientists dispute the correct interpretation of Lorentz transformations within the framework of the special theory of relativity of Albert Einstein. On the one hand, the changes in length, time and mass with increasing velocity are interpreted as apparent due to the observer dependence within special relativity. On the other hand, real changes are described corresponding to the experimental evidence of mass increase in particle accelerators or of clock delay. This ambiguity is accompanied by an ongoing controversy about valid Lorentz-transformed thermodynamic quantities such as entropy, pressure and temperature. In this paper is shown that the interpretation problem of the Lorentz transformations is genuinely anchored within the postulates of special relativity and can be solved on the basis of the thermodynamic approach of matter-energy equivalence, i.e. an energetic distinction between matter and mass. It is suggested that the velocity-dependent changes in state quantities are real in each case, in full agreement with the experimental evidence.

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.

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.

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.

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.

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.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides a mathematical framework in which the description of a physical system in curved spacetime and its description in a flat spacetime with fields are equivalent. As demonstrated in previous publications, in curved spacetime this tensor reproduces Einstein Field Equations and in flat Minkowski spacetime, it describes physical system with fields that can be widely configured. Thanks to the obtained compliance with QM and QED, the use of the discussed tensor may significantly simplify Quantum Field Theory equations and a new interpretation of the Schrödinger equation is possible. In the article it has also been shown that the use of Alena Tensor for the electromagnetic field takes into account effects related to the particle's spin, Abraham–Lorentz effect and, in the curvilinear description, this excludes non-physical phenomena such as the black hole singularity. The article contains a method for verifying Alena Tensor within QM, proposing an explanation for the discrepancy between the Dirac and Klein-Gordon solutions. It also discusses prospects for the application of Alena Tensor in unification theories against the background of existing research directions.

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.

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.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=t_q). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

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.

A single photon inside a gravitational field defined by the accelerates $g$ is found to have a gravitational mass given by $m_g=(\hbar/2c^3)g$, where $\hbar$ is the reduced Planck's constant, and $c$ is the speed of light in vacuum. This force is equivalent to the curvature force introduced by Einstein's general relativity. These photons behave like the radiation emitted by a black hole. A black hole emitting such a radiation develops an entropy that is found to increase linearly with black hole mass, and inversely with the photon mass. Based on this, the entropy of a solar black hole emitting photons of mass $\sim 10^{-33}eV$ amounts to $\sim 10^{77}\,k_B$. The created photons could be seen as resulting from quantum fluctuation during an uncertainty time given by $\Delta t=c/g$. The gravitational force on the photon is that of an entropic nature, and varies inversely with the square of the entropy. The power of the massive photon radiation is found to be analogous to Larmor power of an accelerating charge.

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.

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.

In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

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.

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.

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

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.

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.

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.

Time is a component quantity of various measurements and is also used on its own to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience [1]. The measuring equipment well might happen to be a clock. By making a presupposition that clock is Time, it is perceived experimentally that “Time exhibits wave-like properties”

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

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.

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

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.

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.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

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.

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modication that assumes Haug's maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton's gravitational constant or the Planck constant. After a long period of slow progress in theoretical physics, we are now in a Klondike "gold rush" period where many of the essential pieces are falling in place.

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.

Several mathematicians and physicists are working all over the globe to get a unified theory. However, most of them are discarding Einstein’s view at the very first step of their theories. This article provides a brief description about this. Also, on the basis of Koga’s theory we point out two reasons which might have caused Einstein’s failure to get a unified theory.

The paper discusses the 2022 Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by the 2022 Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview.

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.

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

Quantum loops are processes that constitute quantum objects. In the causal model of quantum loops and quantum objects presented here, the nonlinear processes involve the elementary units of spacetime and the associated elementary units of quantum fields. As such, quantum loop processes are the sources of gravitational fields (i.e., spacetime curvature) and of the quantum objects wave function. The model may be viewed as a derivative of loop quantum gravity, spin networks and causal dynamical triangulation, although significant deviations to these theories exist. The causal model of quantum loops is based on a causal model of spacetime dynamics where space(-time) consists of interconnected space points, each of which is connected to a small number of neighboring space points. The curvature of spacetime is expressed by the density of these space points and by the arrangement of the connections between them. The quantum loop emerges in a nonlinear collective behavioral process from a collection of space points that carry energy and quantum field attributes.

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.

Physics and neuroscience share overlapping objectives, the major of which is probably the attempt to reduce the observed universe to a set of rules. The approaches are complementary, attempting to find a reduced description of the universe or of the observer, respectively. We propose here that combining the two approaches within an observer-inclusive physical scheme, bears significant advantages. In such a scheme, the same set of rules applies to the universe and its observers, and the two descriptions are entangled. We show here that analyzing special relativity in an observer-inclusive framework can resolve its contradiction with the observed non-locality of physical interactions. The contradiction is resolved by reducing the universe (including the observer) to a dynamic distribution of closed strings (“ceons”) whose vibration waves travel at c. This ceons model is consistent with general relativity, non-locality, the holographic principle and loop quantum gravity; it also eliminates Zeno’s motion paradoxes. Yet, the model entails several new empirical predictions. Finally, the ceons model suggests a fundamental physical implementation of active biological perception. Paraphrasing Torricelli, this paper suggests that we live submerged in a c of light.

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.

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural explanation for the famous, more than a century old, 4/3 factor in the electromagnetic mass.

This paper seeks to investigate the questions of: How does the constancy of the speed of light come about? Why does time dilation and length contraction occur? Are they physical effects with a mechanism? Does mass have a role is in these effects? Is Relativity an emergent phenomenon? The enquiry is along a different tact than the standard Lorentzian invariance canon but in the realm of readily known experimental facts or analogies and theory in the domain of wave propagation and solid state physics. These analogies, to almost prosaic physics, have a small following and are called Ether Theories, which modern physics has implicitly reinstated by General Relativity and Quantum Field Theories. In the category of Ether Theories based on analogies to solid state physics, this presentation is unique in not being Lorentz invariant; it is based on earlier papers by the author enquiring into the speed of coincidence counting of the Bell Inequality and a communication protocol. It is believed that Lorentz invariance emerges from the Ether and all Relativistic Mechanics can be built from the bottom up. The conclusion is that space-time is not really curved but the effects are all ascribable to mass gain.

We explore the possibility to form a physical theory in $C^4$. We argue that the expansion of our usual 4-d real space-time to a 4-d complex space-time, can serve us to describe geometrically electromagnetism and nuclear fields and unify it with gravity, in a different way that Kaluza-Klein theories do. Specifically, the electromagnetic field $A_\mu$, is included in the free geodesic equation of $C^4$. By embedding our usual 4-d real space-time in the symplectic 8-d real space-time (symplectic $R^8$ is algebraically isomorphic to $C^4$), we derive the usual geodesic equation of a charged particle in gravitational field, plus new information which is interpreted. Afterwards, we formulate and explore the extended special relativity and extended general relativity an $C^4$ or$R^8$. After embedding our usual 4-d space-time in $R^8$, two new phenomena rise naturally, that are interpreted as "dark matter" and "dark energy". A new cosmological model is presented, while the geometrical terms associated with "dark matter" and "dark energy" are investigated. Similarities, patterns and differences between "dark matter", "dark energy", ordinary matter and radiation are presented, where "dark energy" is a dynamic entity and "dark matter" reveal itself as a "mediator" betwen ordinary matter and "dark energy". Moreover, "dark matter" is deeply connected with "dark energy". Furthermore, the extended Hamilton-Jacobi equation of the extended space-time, is transformed naturally as an extended Klein-Gordon equation, in order to get in contact with quantum theories. By solving the Klein-Gordon equation analytically, we derive an eigenvalue for Higg's boson mass value at 125,173945 $Gev/c^{2}$. The extended Klein-Gordon equation, also connects Higg's boson (or vacuum) with Cosmology, due to the existence of our second "time" T (cosmological time), which serve us to connect quantum theories with Cosmology. Afterwards, in the general case, we explore the symmetries of the curved Hamilton-Jacobi equation locally, in order to investigate the consequences of a $C^4$ space-time in Standard Model. An extension to Standard Model is revealed, especially in the sector of strong nuclear field. The Stiefel manifold $SU(4)/SU(2)$ seems capable not only to describe the strong nuclear field but give us,as well, enough room to explore in the future, the possibility to explain quark confinment. Our extension, flavors firstly the unification of nuclear fields and afterwards the unification of nuclear fields with electromagnetic field. The desired grand unification, is achieved locally, through the symmetry group $GL(4,C)\simeq SO(4,4)\cap U(4)$ and we present a potential mechanism to reduce the existing particle numbers to just six. Afterwards,23 present the extended Dirac equation in $C^4$ space-time (Majorana-Weyl representation) plus a preliminary attempt to introduce a pure geometric structure for fermions. Finally, we consider a new geometric structure through n-linear forms in order to give geometric explanation for quantisation

The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lema\^itre-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations.

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.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

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.

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.

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the quasinormal modes of Hayward black hole in Einstein Gauss-Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein-Lovelock gravity. By utilizing the WKB resonance technique, we examine the quasinormal modes frequencies $\omega$ by shifting the charge parameter $Q$ (it is also identified with the cosmological constant), circular harmonic index $l$, and mass of scalar field $m$. We also study the relaxation rate for those black holes and find out that the relaxation rate increases with increasing values of $Q$. We observe that real and imaginary components of the quasinormal modes are not linear functions as similar to Reisnner Nordstr\"{o}m-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller.

In this article, we calculate the deflection angle of tidal charged black hole (TCBH) in weak field limits. First we obtain the Gaussian optical curvature and then apply the Gauss-Bonnet theorem on it. With the help of Gibbons-Werner method, we are able to calculate the light's deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light's deflection angle in the presence of plasma medium and also check the graphical behavior in the presence of plasma medium. Moreover, we investigate the shadow of TCBH.For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH's shadow in the plasma medium. Hence, we discuss the shadow of the TCBH using the $M87^{*}$ parameters announced by the Event Horizon Telescope.

An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.

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.

In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self-force problem of classical electrodynamics is properly solved, it becomes a plausible ontology underlying the statistical description of quantum mechanics. In the current paper we extend this result, showing that ordinary matter, thus represented, possibly suffices in explaining the outstanding observations currently requiring for this task the contrived notions of dark-matter, dark-energy and inflation. The single mandatory 'fix' to classical electrodynamics, demystifying both very small and very large scale physics, should be contrasted with other adhoc solutions to either problems. Instrumental to our cosmological model is scale covariance (and 'spontaneous breaking' thereof), a formal symmetry of classical electrodynamics treated on equal footing with its Poincare covariance, which is incompatible with the (absolute) metrical attributes of the GR metric tensor.

We explore the field equations in a 4-d complex space-time, in the same way, that general relativity does for our usual 4-d real space-time, forming this way, a new "general relativity" in C⁴ space-time, free of sources. Afterwards, by embedding our usual 4-d real space-time in C⁴ space-time, we describe geometrically the energy-momentum tensor T_μν as the lost geometric information of this embedding. We further give possible explanation of dark eld and dark energy.

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

In this paper, we calculate the deflection angle of photon by Casimir wormhole in the weak field limit approximation. First we calculate Gaussian optical curvature with the help of optical spacetime geometry and so we use the Gauss-Bonnet theorem on the Gaussian optical metric. Then we find the deflection angle of photon by Casimir wormhole. Moreover, we calculate the photon's deflection angle in the presence of plasma medium and we also see the graphical nature of deflection angle in both cases. Second, we move towards the shadow of Casimir wormhole. After the observations of Event Horizon Telescope, the study of shadow become very important so that we plot the shapes of shadow of Casimir wormhole, and we calculate the photon geodesic around the Casimir wormhole.

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

The general theory of relativity (GR) is known to be invariant under smooth coordinate transformations (diffeomorphism). This group has a subgroup known as the Lorentz group of symmetry which is manifested 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. 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 are 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 radial velocities of galactic matter in the M33 galaxy without postulating dark matter.

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.

Is immediate action at a distance, like gravitational attraction, imaginable using the contrary concept of close up, tactile, events? Tactile events, defined with the term ‘tap-tapping’ as a blind man does, described in a two-way spiritual interaction theory, are implemented in physics to understand gravitation from this respect. The quantum mechanical wave function reduction during measurements receives a new approach. Formulated is a new proof for Einstein’s Equivalence Principle, extending it beyond locality, and a sketch of how tactile interaction could explain dark energy and an accelerated expansion of the universe. Dark energy and dark matter are examples starting from which to discuss properties of matter and space and gravitation as immediate tactile action rather than mediated action such as electromagnetism.

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

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).

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.

Many models have been proposed to explain the intergalactic redshift using different observational data and different criteria for the goodness-of-fit of a model to the data. The purpose of this paper is to examine several suggested models using the same supernovae Ia data and gamma-ray burst (GRB) data with the same goodness-of-fit criterion and weigh them against the standard $\text{Λ}$ CDM model. We have used the redshift – distance modulus ( $z-\mu$ ) data for 580 supernovae Ia with $0.015\le z\le 1.414$ to determine the parameters for each model, and then use these model parameter to see how each model fits the sole SNe Ia data at $z=1.914$ and the GRB data up to $z=8.1$ . For the goodness-of-fit criterion, we have used the chi-square probability determined from the weighted least square sum through non-linear regression fit to the data relative to the values predicted by each model. We find that the standard ΛCDM model gives the highest chi-square probability in all cases albeit with a rather small margin over the next best model - the recently introduced nonadiabatic Einstein de Sitter model. We have made ( $z-\mu$ ) projections up to $z=1096$ for the best four models. The best two models differ in $\mu$ only by 0.328 at $z=1096$ , a tiny fraction of the measurement errors that are in the high redshift datasets.

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.

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.

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.

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.

The principle of the constancy of the velocity of light, which stated that the light velocity is invariant to the motion of the emitter, was well established and directly proven by experiments. Interestingly, the further assumption that the light velocity is independent of the motion of the observer was, arguably, never directly proven by any experiment for a century. This paper proposed the design of two experiments to directly test this assumption, which tried to address some perceived technical difficulty in such experiments. One is to directly measure the light speed as to moving sensors. The experiment setup is designed in such a way that the concerns of time synchronization and dilation can be avoided. Another experiment is to test the isotropy of the light speed to a moving particle in the electromagnetic accelerator by measuring the momentum to acceleration ratio. The experiment result, if positive, will provide direct and solid proof of the assumption. Otherwise, it may imply a need for further investigation. Since the light speed invariance to moving observers is a key assumption of some fundamental physical theory, either way, the experiments will have significant meanings.

Permafrost hydrology is an emerging discipline, attracting increasing attention as the Arctic region is undergoing rapid change. However, the research domain of this discipline had never been explicitly formulated. Both 'permafrost' and 'hydrology' yield differing meanings across languages and scientific domains, hence 'permafrost hydrology' serves as an example of linguistic relativity. The differing views of permafrost as either an ecosystem class or a geographical region, and hydrology as a discipline concerned with either landscapes or generic water bodies, maintain a language-specific touch in the definition of permafrost hydrology. From this point of view, the English and Russian usage of this term is explained. A universal process-based definition is further proposed, developed on a specific process assemblage, including (i) water table dynamics caused by migration of an upper aquitard through freeze–thaw processes; (ii) water migration in soil matrix, driven by phase transitions in the active layer; (iii) transient water storage in solid state in the subsurface compartment. This definition is shown to fill the niche in existing vocabulary, and other definitions from northern hydrology field are revisited.

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.

We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for perfect fluid. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. This definition helps us to explain the cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved.Part II is contained with some analysis of the lagrangian ; derived in Part I ; on the quintessence model.

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.

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.

Einstein’s theory of general relativity describes the gravitational field around massive objects ( like Earth) as a curvature in the spacetime. But it leaves the following question unanswered; why is the spacetime curved by a mass? Through a theory that has been introduced recently, regarding a medium for a light propagation, a simple answer is introduced. It depends on redefining the rest energy for a massive object ( like a planet) as new form of kinetic energy. For a static and spherically symmetric object, with a specific radius(

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

Is it possible to quantify in General Relativity, GR, the entropy generated by supermassive black holes, BHs, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere?The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of BHs of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO), and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law (GSL) that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH.This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula.The entropy of the evaporation time of BHs proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the black hole.

We present a geometric field theory in which the action and field equation are constructed from an ultra-high-density vector field and its covariant derivative and have full general covariance in a higher-dimensional spacetime. The field equation is the simplest possible generalisation of the Poisson equation for gravity consistent with general covariance and the equivalence principle. It contains the Ricci tensor and metric acting as operators on the vector field. If the covariant derivative is diagonalisable across a neighbourhood under real changes of coordinate basis, spacetime coincides with a product manifold. The dimensionalities of the factor spaces are determined by its eigenvalues and hence by its algebraic invariants. Tensors decompose into multiplets which have both Lorentz and internal symmetry indices. The field equation has a `classical vacuum' solution which is a product of Minkowski spacetime and an Einstein manifold. A worked example is provided in six dimensions. Away from this classical vacuum, connection components in appropriate coordinates include $SO(N)$ gauge fields. The Riemann tensor includes their field strength. Unitary gauge symmetries act indirectly on tensor fields and some or all of the unitary gauge fields are found amongst the $SO(N)$ gauge fields. Symmetry restoration occurs at the zero-curvature `decompactification limit', in which all dimensions appear on the same footing.

Considered is “time as an interval” including time from the past and from the future, in contrast to time as a moment. Equilibrium as the basis for a description of changing properties in physics is understood to depend on the “mean velocity theorem”, while a “time” of equilibrium resembles a center of weight. This turns out to be a good method to derive properties for any function of time t including space coordinates q(t) and expressions for the time dependent Hamiltonian. Introduced are derivatives depending on time intervals instead of time moments and with these a new relation between the Lagrangian L and the Hamiltonian H. As an application introduced is a step by step method to integrate stationary state “local” time interval measurements to beyond “locality” in General Relativity. Because of limits on the measures of the resulting time intervals and their asymmetry, this allows for a probabilistic interpretation of quantities that have these intervals as time domain in QM. Their asymmetry also questions the time reversal symmetry of GR. Another application of time intervals is the discussion of the measurement of starlight radiation energy and QM wave packet collapse as an example of a time dependent Hamiltonian. Finally a relation between starlight frequency, metric and space- and time intervals is found. Discussed is how finite and asymmetric time intervals correspond to time dependent H and symmetric infinite time intervals to a time independent H. From there, in cosmological perspective, finite time intervals can help to describe how entropy change could relate to dark energy.

Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action S_E « ħ. This is obtained through a Metropolis algorithm with weight exp(-β²S_E²) and β » ħ^-1. The squared action in the exponential allows to circumvene the problem of the non-positivity of S_E. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition S_E=0 exactly, or in certain cases even the stronger condition R(x)=0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's ''spacetime foam''.

A gravitational lens is mass-curved spacetime. Light that propagates freely, locally always on the fastest way, follows curved paths in it. The same applies to all effects propagating with the speed of light, also to gravity itself. They all have to follow the curvature of spacetime. A gravitational lens not only enhances the light from background objects but concurrently also their gravitational effect ! The "Gravitationally Lensed Gravity" (GLG) is a still scarcely noticed peculiar feature of general relativity. In [1] I presented a thought experiment to make the existence of this effect plausible. Here these considerations are described in terms of future and past light cones or null cones commonly used in relativity theory to illustrate the causal structure of spacetime. In the framework of general relativity, the GLG effect can be understood as a consequence of the folding of the past null cone by a gravitational lens. Starting from the basic ideas of the theory, the terms are introduced and applied. The extensive description on textbook level should be understandable also for beginners. In order not to obstruct the view on the essential physical relations, I avoid a mathematical formalism and use instead diagrams and figures, based on realistic numerical calculations, to reinforce my logical argumentation. Experts will recognize many long-known facts, but may still be surprised by the resulting conclusions. First, I present some particular aspects of the historical evolution of the concept of gravitational lensing and give a brief overview of the work of other authors on the subject GLG. I then explain the limitations of the applicability of the "Newtonian Limit" and move on to the key role of the speed of gravity in understanding GLG. Finally, I use a simple example to illustrate the possible significance of the GLG effect. With this work I intend to elicit greater interest in "Gravitationally Lensed Gravity" and to initiate a broader discussion about it.

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.

In this paper, we study light rays in a Kazakov-Solodukhin black hole. To this end, we use the optical geometry of the Kazakov-Solodukhin black hole within the Gauss-bonnet theorem. We first show the effect of the deformation parameter $a$ on the Gaussian optical curvature, and then we use the modern method popularized by Gibbons and Werner to calculate the weak deflection angle of light. Our calculations of deflection angle show how gravitational lensing is affected by the deformation parameter $a$. Moreover, we demonstrate the effect of a plasma medium on weak gravitational lensing by the Kazakov-Solodukhin black hole. We discuss that the increasing the deformation parameter $a$, will increase the weak deflection angle of the black hole. Our analysis also uncloak how one may find a observational evidence for a deformation parameter on the deflection angle.

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.

In this paper we will consider the cosmic fluid to be dissipating i.e it has both bulk and shearing viscosity. We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for cosmic fluid which is dissipating i.e it has both shearing and bulk viscosity. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion of Bianchi type 1 in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. By this transformation we can express the mass to be moving in a scalar potential field. This definition helps us to explain the nature of expansion of universe during cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved. In the case of bulk and shearing viscous fluid we get the solution of damped harmonic oscillator after the cosmological inflation.Part I contains the calculations of bulk viscous fluids and Part II contains the calculations of bulk and shearing viscous fluid.At the end we have also provided the relation of shearing and expansion.Part III will give the approximation of low viscosity to solve the viscous fluid problem.

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lemaî tre-Robertson-Walker (FLRW) space-time. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics—not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero dimensional) serves as the base for the holographic image of the universe. In this way our theory relates to p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans-Dicke theory. We found surprising informational interrelation between the fundamental constants, h, c, G, and their DH-analogues, h(D), c(D), G(D). DH-theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH-nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhanced the role of the Bohm potential.

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

Differences between the quantum mechanical and relativistic concepts of time observed in GPS satellites are accounted for by applying the equivalence principle to the transitioning electron of an atomic clock. It allows a differential equation of motion to be derived for the electron in the Minkowski space between electron shells. Using Hamilton’s principle we transform the differential equation relativistically into an integral equation of motion, the time integral of a Lagrangian. This newly derived equation accounts for the abstract mathematics of the more familiar non-relativistic model by means of a physical interpretation. Abstract rotations in Hilbert space are replaced by the rotations of real particle field geometries in Minkowski space. Because the properties of energy are universal the same equations are then used to describe the field geometry of galaxies despite vast differences in lifetime. They reveal a symmetry between the electromagnetic fields of atoms and the gravitational fields of galaxies due to similarities in the exchange of energy by radial and transverse fields. Our analysis reveals that the conjugate variables energy and time permit differences between atomic and galactic structure to be compared in a more intuitive way than by means of the differential equations of motion which use the conjugate variables position and momentum.

In this paper, first we use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.

Herein is introduced a simple scalar field model derived from classical based kinetic energy, gravitational potential energy, and Special Relativity’s rest mass energy. By applying a classical orbit over the scalar field, relativistic effects are predicted. The scalar field is then applied to a classical model of the Hydrogen atom resulting in a relativistic effect equal to the binding energy of the Hydrogen atom. In addition, the model derives the fine structure constant due to the gravitational effect. The relativistic effects are then discretized in increments equal to the model’s gravitational induced constant. The discretization produces the Hydrogen atom spectral emissions and an angular moment equal to Planck’s reduced constant. The model is not presented as a replacement for current theory, rather it is for inspection and illustration of how a simplistic model may offer a fundamental bridge between the more complex, time proven theories of General Relativity and Quantum Mechanics.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

Here we mathematically model black holes and the early universe following dynamics similar to RLC electrical models, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the evolution of an expanding universe as the result of a black hole collapse followed by its evaporation. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit; (3) expansion of space-time following the disintegration of the black hole, modelled by RLC-like dynamics. In updating this article, version 2, we will expand by presenting three additional examples related to the theory of the generalization Boltzmann's constant in curved space-time and the theory of general and especial relativity. We will calculate the critical mass to produce a black hole in the LHC, the existence of a high temperature Bose-Einstein condensate and finally we will demonstrate the existence of a tangential force to the repulsion force in the disintegration of subatomic particles. In the update of this article, version 3, we will expand to develop two examples. First, we will present the relationship between M-theory, extra dimensions with the theory of the generalization of Boltzmann's constant in curved space-time. Secondly, we will propose the idea of ​​updating the Lambda-CDM model, considering the primordial gravitational waves to correctly describe the evolution of the universe.

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.

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.