This paper introduces a novel ontological framework, termed the Ze model, which reframes the foundations of Einstein's relativity. It posits a unified vectorial substance, the state vector Ψ, as the fundamental entity, with its invariant norm ‖Ψ‖² serving as the primary conserved quantity. Space and time are not independent dimensions but emerge as antiparallel projections of Ψ. I demonstrate that Special Relativity (STR)—its invariant interval, time dilation, and the role of the speed of light c—arises as the kinematic limit of the dynamics governing the reallocation of Ψ's magnitude. General Relativity (GR) is recovered as the classical continuum limit, where spacetime curvature is reinterpreted as a smooth gradient in the orientation field of Ψ vectors, effectively unifying matter and geometry into manifestations of a single substrate. The framework exhibits deep conceptual affinities with pre-geometric approaches: it shares the primacy of a deeper space with Twistor Theory and grounds causality in vector directionality, paralleling Causal Set Theory. This synthesis suggests that STR and GR are not fundamental descriptions of an arena but are highly effective theories emergent from a monistic, vector-based reality. The model provides a new pathway for conceptualizing quantum gravity through the proposed quantization of Ψ's orientation.

Abstract The gravity in the context of General Relativity (GR) as dynamical curvature of spacetime remains a principal impediment not only to its unification with the other fundamental interactions, but also to the formulation of quantum gravity. One possible resolution involves considering gravity in the context of Special Relativity (SR). This paper presents a procedure, which correlates the GR metrics of curved spacetime and the SR Gravitational Scalar Generalized Potential (GSGP). The GR time dilation is the key-point for the correlation of the two gravities, which implies the corresponding SR Lagrangian. Previous papers have already demonstrated the procedure and the results in cases of FLRW metric, wormholes with spherical symmetry, and Schwarzschild metric (where not only the gravitational motions (free falls) in the context of SR are exactly the same as those in the context of GR with stationary metric, but also the SR and GR Gravitational Red Shift). This paper analytically derives the general formulae of Equations of Motion in Spacetime endowed with Stationary metric in the context of GR and the ones in the context of SR, proving that they are exactly the same. Finally, it presents the case studies of gravitational motions around Schwarzschild blackhole, Kerr rotating blackhole and Standard Ellis-Bronnikov wormhole. Thus, it is shown that these motions have an equivalent SR viewpoint.

This study presents an optimization framework for designing a 50-storey steel high-rise building subjected to dynamic wind and seismic loading. The goal is to minimize total structural weight while meeting code-based limits on drift, displacement, stress, panel-zone shear and strong column–weak beam behaviour. A discrete special relativity search (DSRS) algorithm is introduced by mapping continuous special relativity search update rules into a discrete selection scheme and adding adaptive coefficients to improve convergence. The algorithm is integrated with SAP2000 to perform nonlinear dynamic analyses, with constraint violations addressed through a penalty-based fitness function. The optimized design achieves a minimum weight of 2.93 × 106 kg, significantly lower than the initial configuration. Statistical evaluation over 3000 function calls yields mean, median and worst solutions of 6.42 × 106, 6.59 × 106 and 7.86 × 106 kg, demonstrating efficiency. Stress-ratio and drift checks confirm compliance with AISC 360-16 and Iranian Standard 2800, indicating that DSRS is effective for discrete structural optimization.

Abstract A renewed experimental interest in quantum vacuum fluctuations brings back the need to extend the study of electromagnetic vacuum correlations. Quantum or semi-classical models developed to understand various configurations should combine the effects of the zero-point fluctuations with those of blackbody radiation. In this paper, after a brief historical introduction and a rapid study of the electric field correlations in time domain, we propose exact and approximate expressions for the vacuum field correlations in Fourier space seen by moving points. We first present an exact computation of the electric field correlations, expressed in frequency space, between two points moving with opposite constant velocities on parallel trajectories. We also consider the electric field self-correlations, i.e. on the same moving point but at different frequencies, and comment the results related to special relativity. Then, we compute the exact main symmetrized quadratic electromagnetic field correlations between two points diametrically opposed on the same circular trajectory, with diameter r, covered at constant angular velocity Ω. We derive the expressions for the electromagnetic field correlations with itself and with its spatial derivatives, still at the locations of the moving points. Since the points we consider are accelerating, both the zero-point fluctuations and the blackbody spectrum give non-trivial results, for two-point correlations as well as for self-correlations. In both cases, results are shown at any vacuum temperature. For practical uses, we provide the first-order approximations in the small parameter Ωr/c with c being the speed of light.

Abstract In this paper, we first show that it is possible to establish, by rescaling the proper time axis of inertial reference frames in a space-proper time, a new geometric framework for special relativity – equivalent to the standard framework – allowing the construction of kinetic distortion diagrams which directly visualize time dilation and length contraction for inertial motions. We then show that in the presence of a Newtonian gravitational field, the curvature of spacetime given by the Schwarzschild solution can be translated into the new geometric framework by gravitational distortions, allowing the construction of gravitational distortion diagrams to directly represent Newtonian gravitational field effects on space and time. Finally, we discuss the pedagogical value of this approach, particularly through its diagrammatic representations, for teaching relativity to undergraduate students.

Abstract The formulation of quantum field theory in Minkowski spacetime, which emerges from the unification of special relativity and quantum mechanics, is based on treating time as a parameter, assuming a fixed arrow of time, and requiring that field operators commute for spacelike distances. This procedure is questioned here in the context of quantum field theory in curved spacetime (QFTCS).
In 1935, Einstein and Rosen (ER), in their seminal paper [1] proposed that "a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime" which involved two arrows of time. Recently proposed direct-sum quantum theory reconciles this ER's vision by introducing geometric superselection sectors associated with the regions of spacetime related by discrete transformations. We further establish that the quantum effects at gravitational horizons involve the physics of quantum inverted harmonic oscillators that have phase space horizons. This new understanding of the ER bridges is not related to classical wormholes, it addresses the original ER puzzle and promises a unitary description of QFTCS, along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background, which is statistically 650 times stronger than the standard scale-invariant power spectrum from the typical understanding of inflationary quantum fluctuations when compared with the posterior probabilities associated with the model given the data. We finally discuss the implications of this new understanding in combining gravity and quantum mechanics.

The inertial frames are the frames moving with a uniform velocity in any direction. The second postulate of Special Relativity speaks of constancy of light speed (in vacuum) in all inertial frames, with no riders. However, it is taken to implicitly mean only those inertial frames that are moving along the line from origin to the event’s location, or of light propagation. For the inertial frames moving otherwise i.e. in directions oblique to the latter, the setup is converted back to the same (i.e. parallel moving observer), by taking up the distance component parallel to observer’s motion for transformation, and ignoring the rest of its components. The Wigner-Thomas rotation arises only on account of this limited interpretation. It disappears when obliquely moving (with respect to direction of event from origin) inertial frames are given recognition. The two non-collinear boosts are equivalent to one boost in the resultant direction that is oblique to the directions of both the boosts. The example presented in the article amply demonstrates it. Therefore, to give sanctity to the Wigner-Thomas rotation, the second postulate needs to be supplemented by specifying the “Inertial Frames” with a rider “that are moving along the Line of its (light’s) motion”. Further, the Lorentz Transformation have not been and also cannot be derived for events other than those of light. However, these are universally applied to such events e.g. those of non-collinearly moving frames in this case. Thus, another (third) postulate is required to be added, and i.e. “The transformation arrived at for light applies to other events also, where the distance-time ratio is not equal to c”. Addition of the postulate will provide the much needed authorization for working out of Wigner-Thomas rotation, along with numerous other cases such as length contraction and time dilation on moving bodies, though with errors. The error would obviously be proportional to the difference between the distance-time ratio of the event and c.

Some well known scientists – John Wheeler, Erik Verlinde, Max Tegmark, Edward Fredkin, Melvin Vopson - suggest that information is fundamental to the physics of the universe, and that computer-generated / mathematical formulas create reality. In the case of waves being digital, the waves would not merely be described by mathematics but would literally be the result of maths. Digital waves then propose a modification of the theory that dark matter consists of ultralight particles. They’re hypothesised to be so light that they’re no longer particles but are digital collections of binary digits produced by the Electric Dipole Moment decomposing ordinary matter. The gravitational waves which Einstein speculated to be involved in composing mass would rotate from their normal position on the x-axis and leak into the extra-dimensional y-axis, initially in its positive aspect (hyperspace) then in its negative portion (subspace). When it returns to the positive x-axis, the binary digits constituting gravity interact with those making up electromagnetism to refresh the universe’s particles (returning them to their previous, original state and preventing entropy). The quantities of dark matter and dark energy in the universe are calculated using cosmology’s standard Lambda-CDM model plus the concept of enthalpy (the enthalpy H of a thermodynamic system is defined as the sum of its internal energy and the product of its pressure and volume). There are also consequences for Special Relativity’s non-simultaneity, Quantum Mechanics’ quantum superposition, and Lambda-CDM’s concept of an expanding universe. To paraphrase H. G. Wells from his novel “The First Men in the Moon”, “If the world will not have (this article as valid hypothesis), then the world may take it as fiction.”

In the present paper, I dispel the belief that the transformation developed by F. Selleri is equivalent to the Lorentz transformation, thus dispelling the misconception that his alternative theory is equivalent to Einstein’s special theory of relativity. In the current paper I present an argument that has not been shown before aimed at settling the dispute. I demonstrate that the Selleri transformation is not equivalent to the Lorentz transformation by reasons of predicting different results for relativistic aberration.

This paper introduces a theoretical framework that bridges the conceptual divide between quantum mechanics and relativity by proposing a fundamental building block of the universe: the “Space-Time* quantum.” The theory posits that every object possesses an inherent property, Time* — defined as the reciprocal of its intrinsic frequency. The Space-Time* quantum is a composite entity, consisting of a timeless space energy and a kinetic Time* energy. This framework provides a new perspective on wave-particle duality, the double-slit experiment, and quantum entanglement. It re-examines the principles of Special Relativity, offering a conceptual and visual explanation of phenomena such as time dilation and length contraction as a consequence of changes in the Space-Time quanta. The theory also provides an alternative view on the origin of the universe and the nature of gravity, suggesting that gravitational effects arise from an energy deficiency rather than a curvature of spacetime. This paper establishes a conceptual foundation for further mathematical development to test and validate these new insights.

Understanding the Nature of Science (NoS) is widely acknowledged as a fundamental component of scientific literacy and an essential goal in physics education. Textbooks play a pivotal role in shaping students’ and teachers’ conceptions of science, particularly in educational contexts such as Indonesia, where they serve as the primary instructional resources. This study aimed to analyze how the ten aspects of NoS: empirical, inferential, creative, theory-driven, tentative, scientific method, scientific theories, scientific laws, the social dimension of science, and the social-cultural embeddedness of science are represented and presented in Indonesian high school physics textbooks. Using a descriptive content-analysis approach, five widely used 12th-grade textbooks were examined across five comparable topics: electromagnetic induction, alternating current, electromagnetic radiation, special relativity, and quantum phenomena. Each textbook was analyzed using the Abd-El-Khalick framework and scored on a −3 to +3 rubric to assess the explicitness and informedness of NoS representation. The findings revealed that none of the textbooks entirely covered all ten NoS aspects; the social dimension of science was most frequently represented, while the creative, inferential, and tentative aspects were largely absent. The findings highlight the need for textbook authors and curriculum developers to integrate NoS aspects more explicitly to strengthen students’ understanding of scientific processes and reasoning. The results provide practical guidance for improving NoS representation in Indonesian physics textbooks and supporting the development of scientific literacy.

The comparison between Einstein's Theory of Relativity and the relativity theories proposed by Smarandache hinges on fundamental postulates regarding the speed of light, the nature of space and time, and the validity of classical versus relativistic velocity addition.

Most people believe that time is continuous, but we assume the opposite is true; moreover, by modelling time as discrete, the rules and laws of nature can be efficiently described in a unitary 4D xyzt space [1,2]. In a previous article entitled 101 Authors Against Einstein [2], we presented scathing critiques of Albert Einstein's theories of relativity, explaining and proving how Einstein's SR and GR theories are fundamentally incomplete and misleading due to a poor understanding of the underlying universal laws of physics. We also assume that the main reason for Einstein's errors in general relativity is that he started from the mathematical Riemann space where time is a continuous scalar and inadequate to demonstrate the physical laws in the unitary 4D xyzt space [3,4]. In this article, we examine the link between the discretization of time, the universal laws of physics, and Einstein's theories of special and general relativity, demonstrating that [3,4,5]:  Special Relativity is a Special Case of General Relativity. Special relativity and general relativity form a single theory.  Einstein's Theory of Gravitation in 1915 Led to the Erroneous Conclusion that Gravity is Not a Force, but a Consequence of the Curvature of Space Time. We show that gravity is a real force that curves space-time, and not the other way around. We also present and define the rules and foundations of discrete time theory. Finally, it should be clarified that this article is not intended to diminish the achievements of the great Einstein, such as the discovery of the laser theory 50 years before its practical application, but rather to dispel any misconceptions about his theories if any.  Note: If you are Not Familiar with the Universal Laws of Physics, Please Stop Reading. This article is not intended for you.

The optical reflection coefficient of a medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a function of the incident frequency and wavevector, valid in both the far- and near-field regimes. It is found that cross-polarisation appears as a consequence of the motion, except when it is directed along the plane of incidence. As an example, using a Drude model for the permittivity of the surface at rest, the dispersion relation of its surface modes is calculated. A tilting of the dispersion relation is observed, leading to movement-induced surface plasmon unidirectionality and non-reciprocity.

The inseparable connection of electric and magnetic interactions is shown even in the case when the formal mathematical connection between them is lost. The problem is solved in physical space, bypas-sing the curved special theory of relativity, as is still done in practice. The magnetic action is interpreted as the effect of motion in the electric. The nature of the electric field is discussed in two forms: the Coulomb field adapted to motion and radiation. The interaction of a light wave with the gravity of the Sun is simulated. The nature of such an interaction is revealed, which leads to the instability of the speed of light c in a vacuum. Theoretical results are supported by integration of differential equations of mechanical state.

The article proves that the version of the special relativity theory (SRT) that is taught in all physics textbooks is incorrect, since the relativistic formulas obtained in it are incorrect and they are incorrectly explained using the incorrect principle of not exceeding the speed of light. These formulas also lead to incorrect conclusions about the physical unreality of imaginary numbers and the existence in nature of only our visible universe. A corrected version of the SRT is presented and it is explained that the argument ‘speed’ in the corrected relativistic formulas is, in accordance with Newton’s first law, the fourth spatial dimension[1]. The principle of the physical reality of imaginary numbers is experimentally proven, which refutes the principle of not exceeding the speed of light. It is shown that the SRT, on the one hand, and radio engineering, electrical engineering and computer engineering, on the other hand, mutually refute each other. It is explained that in nature, in addition to our visible universe, there are many mutually invisible, since they are in different dimensions, universes and anti-universes, which are dark matter and dark energy. This explains the well-known properties of dark matter and dark energy - their invisibility and the absence of corpuscular content. Therefore no studies at the Large Hadron Collider can explain the phenomena of dark matter and dark energy. It is explained also that in the anti-universes of such an invisible Multiverse there is anti-matter and anti-time. Therefore, time travel is possible in it. Time travel is also available to people on Earth. [1] Not to be confused with the fourth dimension in four-dimensional space-time (Minkowski space).

We present several examples showing that a significant discrepancy exists between the principle of relativity in the real physical universe and its mathematical model, especially for high relativistic velocities. According to this principle, all inertial systems are equivalent, i.e., indistinguishable. However, a fast-moving traveler in any direction in the physical universe can readily determine that his system is not equivalent with others, since there exists a preferred cosmic reference system S 0 , associated with the cosmic microwave background (CMB) radiation, which has the same temperature 2.73 K in all directions. At high velocities with respect to S 0 , the traveler will detect strong anisotropy in this radiation, which may shift the CMB into infrared or even x-ray radiation due to the Doppler effect. A similar anisotropy appears when detecting intergalactic gas and dust, as well as light from stars and galaxies. Thus, the traveler can observe that the spectrum of galaxies on one half of the celestial sphere is shifted toward blue, while on the opposite half it is shifted toward red. Moreover, all neighboring galaxies, without exception, would be moving with respect to the traveler at high relativistic velocities in nearly the same direction. The reference system S 0 is unavoidable and cannot be overridden, eliminated, or ignored, since the CMB is present everywhere. This violates the principle of relativity in the physical universe. Since this principle is a fundamental assumption in the special theory of relativity, it is essential to verify whether the theory provides an adequate approximation of reality.

The vector boson oscillator in doubly special relativity

This paper introduces a complete Framework supported by my previous works which showed the bilateral relationship between gravitational potential energy and kinetic energy, the origin of Gravity based on the relationship between matter and electromagnetic energy, the different stages of its Evolution, how General Relativity arises from Special Relativity and finally, a new Einstein’s Field Extended Equations entailing a new Cosmological Model (without the need for a cosmological constant or dark energy). Although each one of my works was based on the previous ones, given the density and prolixity of everything introduced, this paper is intended first of all as a structured summary-guide of my work related to Gravity, while refering to my previous papers to delve deeper into each and every one of the analyzed subjects. Some particularly relevant topics (e.g. the analysis of the Warping Boundary, the behavior and properties of the emergent time like a fluid, the non-existence of singularities associated with gravity or an extension of the Bekenstein-Hawking entropy law) are also added giving the whole the form of a complete Framework (which I consider in any case more an extension than a modification of Einstein’s Theory of General Relativity).

Abstract Based on the two postulates of the invariance of both the laws of physics and light speed in inertial frames, Einstein revolutionised the prevalent conceptions of space and time in the Special Theory of Relativity, which is not however without difficulties, due to gaping holes in its philosophical foundations. The first postulate is an unjustified and clumsily drafted extension of Galilean Relativity, while the second postulate, if interpreted as meaning that the speed of light will not be altered by a moving frame, does not lead to Lorentz transformations, but just reveals that a light ray is not transported by a moving frame. Reference frames involving light propagation do not exhibit the equivalence inherent in inertial frames, and hence could be classified as seemingly-inertial, being some category of non-inertial frames. Either equivalence, including simultaneity in both moving and stationary frames, is a defining characteristic of inertial frames, or else if inertial frames allow inequivalence, then they are not indistinguishable, which is a contradiction. All along, the definitions of “frames of reference,” “inertial frames,” and “simultaneity” and the “legal” drafting of the two postulates play a crucial role in the development and consistency of the Theory, almost as much as the thought experiments and the mathematics.