The Hyper-Torus Universe Model (HTUM) proposes a novel framework to unify quantum mechanics, cosmology, and consciousness. This paper introduces HTUM's core concept: a higher-dimensional hyper-torus encompassing all possible states of existence. HTUM suggests that the universe functions as a quantum system where all outcomes are inherently connected, with consciousness playing a significant role in actualizing reality. The model introduces several key innovations, including the universe's 4-dimensional toroidal structure (4DTS), providing a new geometric interpretation of spacetime. HTUM presents dark matter and dark energy as nonlinear probabilistic phenomena within this toroidal framework, offering a unique perspective on their nature and interactions. The model proposes a mechanism for wave function collapse through universal self-observation, bridging quantum mechanics and gravity. It introduces a Topological Vacuum Energy Modulator (TVEM) function, offering a potential resolution to the cosmological constant problem. Furthermore, HTUM integrates consciousness as a fundamental aspect of the universe, influencing quantum state actualization and potentially resolving the hard problem of consciousness. The model explores the implications of a timeless singularity and the emergence of time as a product of causal relationships within the toroidal structure. This framework addresses critical challenges in modern physics, including the nature of quantum entanglement, the origin and fate of the universe, and the relationship between mind and matter. The paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. We present detailed predictions for the cosmic microwave background (CMB) power spectrum, gravitational wave signatures, and large-scale structure formation, demonstrating how HTUM differs from the standard ΛCDM model. Our analysis reveals distinctive oscillatory patterns in the relative difference between HTUM and ΛCDM predictions, with deviations reaching up to ±20% at certain scales. The paper also explores the unification of fundamental forces within the HTUM framework, proposing novel approaches to particle physics and quantum field theory. It introduces the concept of unified mathematical operations, suggesting a more holistic approach to mathematical thinking that aligns with the model's interconnected view of the universe. Additional testable predictions and proposed experimental approaches are discussed, including advanced space-based tests and laboratory experiments probing quantum gravity effects. These specific, quantifiable predictions offer multiple avenues for empirical validation, highlighting HTUM's potential to be distinguished from ΛCDM and other alternative cosmological models. HTUM represents a significant new perspective in our understanding of the universe, inviting further research and exploration into the nature of reality, consciousness, and the fundamental structure of the cosmos. By providing a comprehensive framework that unifies various aspects of physics, cosmology, and consciousness studies, HTUM offers a promising path toward a more complete understanding of our universe.

The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. This analysis addresses the problem by positing an ontic, mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”). Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete 4D spacetime and 2) mathematical 3N configuration spaces with a physical (3 x N) Planck Space. Moreover, the Dual Ontology is structurally and dynamically predicated on the one-to-one mapping and identity between the discrete spatial units that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity of the discrete spatial units support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply.

HIGHLIGHTS Special relativity has been successfully used to describe the behaviour of particles (Rossi & Hall, 1941), but there is no observation of special relativity in our world. On the contrary, there are at least two paradoxes based on special relativity: the twin paradox (Langevin, 1911) and Ehrenfest's paradox (1909). This paper is presenting a first experiment, based on Ehrenfest's paradox, where an effect of special relativity was expected but not observed. The validity of special relativity in our macro world will be questioned and an alternative will be offered. ABSTRACT After presenting the history of special relativity, the non-simultaneity of special relativity is questionned in our macro world. In addition, some incompatibilities between light clocks and the application of Lorentz transformation are presented. All this indicates some issues with special relativity which appears to be correct only for particles and would be invalid in our macro world. A new theory is presented based on an adaptation of special relativity; this new theory solves the anomalies and could be a solution to the twin paradox. This paper also presents a new experiment and its observation. The preliminary result shows that special relativity has no effect in our macro world and therefore supports the new theory. A lack of special relativistic effects has been observed in the universe (Davis et al., 2004); that is another observation where special relativity doesn't work. That second observation is also explained with the new theory.

This paper, based on the "Unified Theory of Forces," rigorously proves the formula of de Broglie's wave function. This helps us better understand the following important issues: 1) Theoretically prove and understand the essence of de Broglie's wave function; 2) Prove that when the particle's momentum P is determined, the greater the mass of the particle, the more concentrated its wave function distribution, and the weaker the interference effect; 3) Correct the spatial distribution of the wave function of free particles, proving that the wave function of free particles is strictly constrained within a finite spatial range, which is consistent with the facts we observe.

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

The Aether Physics Model (APM) presents a radical reinterpretation of fundamental physics, offering potential solutions to long-standing problems in Quantum Mechanics and General Relativity. This paper explores the core concepts and equations of the APM, demonstrating how they provide a unified framework for understanding the nature of space, time, matter, and fundamental forces. We examine the implications of the APM's quantized Aether structure, the role of the Singularity and Gforce, and the reinterpretation of fundamental constants and forces. The model's predictions regarding dark matter, neutron content in stable matter, and the unification of forces are discussed, along with potential experimental tests. Additionally, we introduce the loxodrome concept and toroidal particle topology as central elements in explaining fundamental particles and forces. While highly speculative, the APM offers a thought-provoking alternative to standard physics models and warrants further investigation.

The Hyper-Torus Universe Model (HTUM) proposes a novel framework to unify quantum mechanics, cosmology, and consciousness. This paper introduces HTUM's core concept: a higher-dimensional hyper-torus encompassing all possible states of existence. HTUM suggests that the universe functions as a quantum system where all outcomes are inherently connected, with consciousness playing a significant role in actualizing reality. The model introduces several key innovations, including the universe's 4-dimensional toroidal structure (4DTS), providing a new geometric interpretation of spacetime. HTUM presents dark matter and dark energy as nonlinear probabilistic phenomena within this toroidal framework, offering a unique perspective on their nature and interactions. The model proposes a mechanism for wave function collapse through universal self-observation, bridging quantum mechanics and gravity. It introduces a Topological Vacuum Energy Modulator (TVEM) function, offering a potential resolution to the cosmological constant problem. Furthermore, HTUM integrates consciousness as a fundamental aspect of the universe, influencing quantum state actualization and potentially resolving the hard problem of consciousness. The model explores the implications of a timeless singularity and the emergence of time as a product of causal relationships within the toroidal structure. This framework addresses critical challenges in modern physics, including the nature of quantum entanglement, the origin and fate of the universe, and the relationship between mind and matter. The paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. We present detailed predictions for the cosmic microwave background (CMB) power spectrum, gravitational wave signatures, and large-scale structure formation, demonstrating how HTUM differs from the standard ΛCDM model. Our analysis reveals distinctive oscillatory patterns in the relative difference between HTUM and ΛCDM predictions, with deviations reaching up to ±20% at certain scales. The paper also explores the unification of fundamental forces within the HTUM framework, proposing novel approaches to particle physics and quantum field theory. It introduces the concept of unified mathematical operations, suggesting a more holistic approach to mathematical thinking that aligns with the model's interconnected view of the universe. Additional testable predictions and proposed experimental approaches are discussed, including advanced space-based tests and laboratory experiments probing quantum gravity effects. These specific, quantifiable predictions offer multiple avenues for empirical validation, highlighting HTUM's potential to be distinguished from ΛCDM and other alternative cosmological models. HTUM represents a significant new perspective in our understanding of the universe, inviting further research and exploration into the nature of reality, consciousness, and the fundamental structure of the cosmos. By providing a comprehensive framework that unifies various aspects of physics, cosmology, and consciousness studies, HTUM offers a promising path toward a more complete understanding of our universe.

It is well-known that the canonical quantization of $\varphi^4_4$ fails. Here is how to fix it along with many other problems.

The Aether Physics Model (APM) presents a radical reinterpretation of fundamental physics, offering potential solutions to long-standing problems in Quantum Mechanics and General Relativity. This paper explores the core concepts and equations of the APM, demonstrating how they provide a unified framework for understanding the nature of space, time, matter, and fundamental forces. We examine the implications of the APM's quantized Aether structure, the role of the Singularity and Gforce, and the reinterpretation of fundamental constants and forces. The model's predictions regarding dark matter, neutron content in stable matter, and the unification of forces are discussed, along with potential experimental tests. Additionally, we introduce the loxodrome concept and toroidal particle topology as central elements in explaining fundamental particles and forces. While highly speculative, the APM offers a thought-provoking alternative to standard physics models and warrants further investigation.

The electron of spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory (QFT), an intuitive form of the fermion still remains lacking and it is often speculated by Dirac belt trick or its related analogies. In a similar fashion, the interpretation of Dirac fermion by QFT is examined within a recently proposed MP model of a hydrogen atom into 4D space-time. The model consists of clockwise precession of an elliptical MP field mimicking Dirac string and an electron of physical entity in orbit of time reversal. Such dynamics sustains charge conjugate, parity inversion and time reversal symmetry with the transition of the electron to Dirac fermion being consistent with Dirac belt trick, quantum mechanics and Lie group. The electron path is solenoidal to on-shell momentum of circular Bohr obit (BO), and by disturbance, this levitates and dissects the MP field into n-dimensions of Minkowski space-time. Contraction of BOs towards the vertices generates Euclidean space-time to a spherical MP model. These outcomes are compatible with QFT such as Dirac field theory and its related components like wave function collapse, quantized Hamiltonian, non-relativistic wave function, Weyl spinor, Lorentz transformation and electroweak symmetry breaking mechanism. The model though speculative, it could become important towards defining the fundamental state of matter subject to further examinations by conventional methods in both experiment and theoretical applications.

Einstein’s special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of observers), such as relative spacetime, wave, particle, and force. The word “subjective” does not imply that SR/GR would be limited to one point of view. It implies that, despite the Lorentz covariance of SR and the general covariance of GR, any point of view in SR/GR is egocentric. Even coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER neither competes with nor replaces SR/GR. ER complements SR/GR by adding a holistic view. SR/GR describe each observer’s reality. ER describes the master reality ES, which is beyond each observer’s reality. ER solves 15 fundamental mysteries geometrically, such as time’s arrow, the horizon problem, the Hubble constant tension, dark energy, the wave–particle duality, entanglement, and the baryon asymmetry.

We report positive correlations between letter frequency and symmetry (more symmetric symbols are more frequent) in English and Russian languages and in four types of numerals (Western, Roman, Arabic, and Chinese) with the coefficients of determination of R2=0.899 (English), R2=0.693 (Russian) and R2=0.740 (numerals). For comparison, we studied "symbol-like" 2D colloidal clusters and found negative correlations between frequency and symmetry (R2=0.814 and R2=0.994). While in human-made systems the frequency of using of a symbol is the driving force which leads to symbols simplification and symmetrizing, in natural system, symmetry leads to lower frequency of occurrence because there are fewer ways of building symmetric clusters than asymmetric ones. We interpret these results as a correlation between the symbol as a type and as a token and we attribute this correlation to the inherent iconicity of symbols

The spin-torsion theory is a gauge theory approach to gravity that expands upon Einstein's general relativity (GR) by incorporating the spin of microparticles. In this study, we further develop the spin-torsion theory to examine spherically symmetric and static gravitational systems that involve free-falling macroscopic particles. We posit that the quantum spin of macroscopic matter becomes noteworthy on cosmic scales. We further assume that the Dirac spinor and Dirac equation adequately capture all essential physical characteristics of the particles and their associated processes. A crucial aspect of our approach involves substituting the constant mass in the Dirac equation with a scale function, allowing us to establish a connection between quantum effects and the scale of gravitational systems. This mechanism ensures that the quantum effect of macroscopic matter is scale-dependent and diminishes locally, a phenomenon not observed in microparticles. For any given matter density distribution, our theory predicts an additional quantum term, the quantum potential energy (QPE), within the mass expression. QPE induces time dilation, distance contraction, and thus mimics a gravitational well. When applied to cosmology, our theory yields a static cosmological model. The QPE serves as a counterpart to the cosmological constant introduced by Einstein to balance gravity in his static cosmological model. The QPE also offers a plausible explanation for the origin of the Hubble redshift (traditionally attributed to the universe's expansion). The predicted luminosity distance-redshift relation aligns remarkably well with SNe Ia data from the cosmological sample of SNe Ia. In the context of galaxies, QPE functions as the equivalent of dark matter. The predicted circular velocities align well with the rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves database) sample. Importantly, our conclusions in this paper are reached through a conventional approach, with the sole assumption of the quantum effects of macroscopic matter on large scales, without the need for additional modifications or assumptions.

.In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity.

According to Quantum Mechanics a narrow wave-package of the center of mass of macroscopic objects, due to their heavy mass, remains stable over astronomical times. However Quantum Mechanics allows and energetically even prefers largely smeared out c.m. states that never been seen. Why is this the real state of the world we know? Does it suggest a micro-macro threshold with different theoretical descriptions?

The Hyper-Torus Universe Model (HTUM) is a novel framework that unifies quantum mechanics, cosmology, and consciousness, proposing that the universe is a higher-dimensional hyper-torus containing all possible states of existence. This paper explores the fundamental concepts and implications of HTUM, which suggests that the universe is a quantum system in which all possible outcomes are inherently connected, with consciousness playing a crucial role in actualizing reality. HTUM addresses critical challenges in modern physics, such as the nature of quantum entanglement, the origin of the universe, and the relationship between mind and matter. By introducing concepts like singularity, quantum entanglement at a cosmic scale, and the self-actualization of the universe, HTUM provides a comprehensive framework for understanding the fundamental nature of reality. This paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. HTUM represents a significant shift in our understanding of the universe and our place within it, inviting further research and exploration into the nature of reality and consciousness.

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe’s surface.

Einstein’s special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of observers), such as relative spacetime, wave, particle, and force. The word “subjective” does not imply that SR/GR would be limited to one point of view. It implies that, despite the Lorentz covariance of SR and the general covariance of GR, any point of view in SR/GR is egocentric. Even coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER neither competes with nor replaces SR/GR. ER complements SR/GR by adding a holistic view. ER describes the “master reality” ES, which is beyond each observer’s reality described by SR/GR. The holistic view solves 15 mysteries geometrically, in particular in cosmology and quantum mechanics. Examples are time’s arrow, the horizon problem, the Hubble constant tension, dark energy, entanglement, and the baryon asymmetry.

Einstein’s special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer), such as relative spacetime, wave, particle, and force. Despite the Lorentz covariance of SR and the general covariance of GR, an observer’s perspective is always egocentric. Coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER neither competes with nor replaces SR/GR. ER complements SR/GR by adding a holistic view. ER describes the “master reality” ES, whereas SR/GR describe an observer’s reality. The holistic view solves 15 fundamental mysteries geometrically, in particular in cosmology and quantum mechanics. Examples are time’s arrow, the horizon problem, the Hubble constant tension, dark energy, entanglement, and the baryon asymmetry.

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

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

The present paper reports exact results for the muon self-energy and anomalous g-factor. A unique to the muon cut-off terms that remove the radial singularity in the system and regularize the corresponding electrodynamics are presented. Equations of motion and a transcendental equation satisfied by the muon anomalous g-factor are derived, with solution a_m=0.001165920162(198). The obtained value matches the latest experimental one found in the literature to about 0.43 ppb ruling out a possible tension between theory and experiment.

Einstein’s special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer), such as relative spacetime, wave, particle, and force. Despite the Lorentz covariance of SR and the general covariance of GR, an observer’s perspective is always egocentric. Coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER neither competes with nor replaces SR/GR. ER complements SR/GR by adding a holistic view. SR/GR describe an observer’s reality but fail to solve various mysteries. ER describes the master reality ES but excludes the subjective concept of waves. Still, ER solves 15 fundamental mysteries geometrically, such as time’s arrow, the horizon problem, the Hubble constant tension, dark energy, entanglement, and the baryon asymmetry.

This article briefly shows how particle’s moving at escape velocity can be described in a quantum mechanical frameworks, this is achieved by deriving quantum mechanical equations that puts escape velocity into consideration. The equations are derived from Hamiltonians and Hamiltonian operators formulated from classical kinetic and potential terms which are then quantized. Equations were also presented for specific situations of the particle at escape velocity. Situations such as free-particles at escape velocity, Self-gravitating situations of a charged or neutral particle even while free of the gravitational influence of the large massive body due to its escape velocity, leaving only the self-gravitation as the only gravitational influence on the particle which in the case of a massless, charge less particle reduces back to the equation of free-particle at escape velocity. Other very brief expositions on trajectories and more are also present in this brief article.

The Cosmic Theory of Structure (CTS) model has undergone significant refinement to address the hierarchy problem by incorporating the concept of running couplings. This update provides a more robust framework for understanding the formation and evolution of cosmic structures, offering a natural explanation for mass scales due to quantum effects. We present new validations using gravitational wave data from events GW150914 and GW151226, neutrino oscillation data from IceCube, dark matter density data from the Planck survey, and quantum field interaction data. The enhanced model demonstrates improved alignment with observational data, reinforcing the CTS model's predictive power and its potential to unify gravity and quantum physics within a single theoretical framework.

The Hyper-Torus Universe Model (HTUM) is a novel framework that unifies quantum mechanics, cosmology, and consciousness, proposing that the universe is a higher-dimensional hyper-torus containing all possible states of existence. This paper explores the fundamental concepts and implications of HTUM, which suggests that the universe is a quantum system in which all possible outcomes are inherently connected, with consciousness playing a crucial role in actualizing reality. HTUM addresses critical challenges in modern physics, such as the nature of quantum entanglement, the origin of the universe, and the relationship between mind and matter. By introducing concepts like singularity, quantum entanglement at a cosmic scale, and the self-actualization of the universe, HTUM provides a comprehensive framework for understanding the fundamental nature of reality. This paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. HTUM represents a significant shift in our understanding of the universe and our place within it, inviting further research and exploration into the nature of reality and consciousness.

The fundamental divergence in foundation of modern physics lies in the incompatibility between quantum theory and relativity. This study created a new mathematical tools, proposed the dark particle hypothesis and new equivalent principle, and established an ideal model on the cosmic continuum. According to this study, any cosmic system is a continuum composed of existence continuum relative to the wavelength of bosons energy waves and its dimension continuum, four fundamental interactions form a continuum relative to the wavelength of corresponding boson energy waves, respectively, the elementary particles and their existence fields are the basic units of cosmic continuum, the existence field of an existence body is equivalent to its dimension field, dark matter is a dark mass body composed of dark particles, singularity is a dark matter celestial body formed by collapse of black hole, and the singularity and its existence field constitute an existence continuum of singularity.

The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. This analysis addresses the problem by positing an ontic, mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”). Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete 4D spacetime and 2) mathematical 3N configuration spaces with a physical (3 x N) Planck Space. Moreover, the Dual Ontology is structurally and dynamically predicated on the one-to-one mapping and identity between the discrete spatial units that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity of the discrete spatial units support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply.

The Cosmic Theory of Structure (CTS) model presents a comprehensive framework that integrates gravitational waves, neutrinos, dark matter, and quantum field interactions. This model aims to provide a unified understanding of the universe's formation and evolution. The CTS model has undergone rigorous validation using the latest datasets, demonstrating its robustness and predictive power. Key updates include detailed mathematical formulations, refined theoretical frameworks, and enhanced descriptions of fundamental cosmic phenomena. This manuscript presents the final validated version of the CTS model, highlighting its alignment with observational data and its implications for future research in cosmology and quantum physics.

The theory says that the first things to exist in the universe and the current moment were driven by an imperative need; that is, the intensities of the physical concept specify influence the existence of elements and facts based on the countless observations in physical spaces in relation to elements and facts. The existence of mandatory elements in space is motivated by the characteristics of the spaces that offer conditions for such an obligation. The theory states that the universe did not arise by chance; that is, the universe emerged through determination influenced by its surroundings. The objective of the study is to help explain the elements and facts of the universe from its origins to the present.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Typical examples are relative spacetime, waves, and particles. Despite the Lorentz covariance of SR and the general covariance of GR, an observer’s perspective is always egocentric. Coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, where the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside) our galaxy. ER provides a holistic view from beyond each observer’s reality. In conclusion, SR/GR remain valid in each observer’s reality. ER describes the master reality ES and solves 15 mysteries geometrically—without field equations, dark energy, and non-locality. A holistic view holds more information than all egocentric perspectives taken together.

The Hyper-Torus Universe Model (HTUM) is a novel framework that unifies quantum mechanics, cosmology, and consciousness, proposing that the universe is a higher-dimensional hyper-torus containing all possible states of existence. This paper explores the fundamental concepts and implications of the HTUM, which suggests that the universe is a quantum system in which all possible outcomes are inherently connected, with consciousness playing a crucial role in actualizing reality. The HTUM addresses critical challenges in modern physics, such as the nature of quantum entanglement, the origin of the universe, and the relationship between mind and matter. By introducing concepts like singularity, quantum entanglement at a cosmic scale, and the self-actualization of the universe, the HTUM provides a comprehensive framework for understanding the fundamental nature of reality. This paper discusses the mathematical formulation of the HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. The philosophical implications of the HTUM are also examined, including its impact on free will, determinism, and the mind-matter relationship. The HTUM represents a significant shift in our understanding of the universe and our place within it, inviting further research and exploration into the nature of reality and consciousness.

Coulomb’s law and Newton’s law of gravitation are formally identical. Is it a mere coincidence? It seems to us that physics has answered yes so far, at least tacitly. We, on the other hand, do not believe in chance. Since the alternative to the fact that the strong similarity is only the result of chance is to believe that it is not, and in this case there must be a reason for this similarity, we have chosen the path of investigating the possibility that the two fields are not distinct, but have a common root that we will try to find. We propose an electrodynamics of electrically neutral bodies based on the hypothesis that the Coulomb constant in the case of attraction between charges of opposite sign is slightly greater than that of the case of repulsion between charges of the same magnitude as the previous ones, but of the same sign. If this difference were to exist, even small to the point of not being directly measurable in the laboratory, it could still produce macroscopic effects detectable in the case of large aggregates of charges, even if globally electrically neutral, as happens in the astronomical field. We deduce the electromagnetism of such a model and show the results obtained applying the theory to some significant cases such the light deflection in a gravitational field, a planet perihelion precession, the power radiated by merging black holes, the behaviour of antimatter in a gravitational field and, when available, we compare the predictions with the experimental data.

This article briefly shows how particle’s moving at escape velocity can be described in a quantum mechanical frameworks, this is achieved by deriving quantum mechanical equations that puts escape velocity into consideration. The equations are derived from Hamiltonians and Hamiltonian operators formulated from classical kinetic and potential terms which are then quantized. Equations were also presented for specific situations of the particle at escape velocity. Situations such as free-particles at escape velocity, Self-gravitating situations of a charged or neutral particle even while free of the gravitational influence of the large massive body due to its escape velocity, leaving only the self-gravitation as the only gravitational influence on the particle which in the case of a massless, charge less particle reduces back to the equation of free-particle at escape velocity. Other very brief expositions on trajectories and more are also present in this brief article.

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, afforded by multiplying one of the $\gamma$-matrices by the imaginary number. The reason for doing this is to introduce a bivector into the spin algebra. This complexifies the Dirac field which separates into two distinct and complementary spaces: one describing polarization and the other coherence. The former describes a 2D structured spin and the latter its helicity, generated by a unit quaternion.

The electron of spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory, an intuitive form of the fermion still remains lacking and it is often described by the so-called Dirac belt trick. In this novel undertaking, the electron is examined within the boundary posed by a recently proposed MP model of a hydrogen atom into 4D space-time that somewhat mimics Dirac string. Its transformation to Dirac fermion appears consistent with Dirac belt trick and quantum mechanics, whereas its solenoidal property for the emergence of monopole is applicable to Lie group. These outcomes are compatible with the basic interpretations of Dirac field theory and its related components like wave function collapse, quantized Hamiltonian, non-relativistic wave function, Weyl spinor, Lorentz transformation and electroweak symmetry breaking mechanism. The model though speculative, it could become important towards defining the fundamental state of matter subject to further examinations by conventional methods.

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

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Typical examples are relative spacetime, waves, and particles. Despite the Lorentz covariance of SR and the general covariance of GR, an observer’s perspective is always egocentric. Coordinate-free formulations of SR/GR or multiple egocentric perspectives do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). “Pure distance” replaces spatial and temporal distance. “Pure energy” replaces wave and particle. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed of light c. An object’s proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, where the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside) our galaxy. ER provides a holistic view from beyond each observer’s reality. SR/GR remain valid in each observer’s reality. ER describes the master reality ES and solves 15 mysteries geometrically—without field equations, dark energy, and non-locality.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Relative space and time—or waves and particles—are examples of such concepts. Despite the Lorentz covariance of SR and the general covariance of GR, the perspectives of observers are always egocentric. Even coordinate-free formulations of SR/GR based on a parameterization do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Relative space and time become “pure distance”. Waves and particles become “pure energy”. Each object’s proper space d₁, d₂, d₃ and its proper time τ span a 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. All energy moves through ES at the speed c. For each object, proper time flows in the direction of its 4D motion. Thus, there is a relative 4D vector “flow of proper time”. The invariant parameter is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, where the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside) our galaxy. ER provides a holistic view from beyond each observer’s reality. SR and GR remain valid in each observer’s reality, but only ER solves the Hubble constant tension and 14 more mysteries. ER solves them geometrically—without field equations.

This article briefly shows how particle’s moving at escape velocity can be described in a quantum mechanical frameworks, this is achieved by deriving quantum mechanical equations that puts escape velocity into consideration. The equations are derived from Hamiltonians and Hamiltonian operators formulated from classical kinetic and potential terms which are then quantized. Equations were also presented for specific situations of the particle at escape velocity. Situations such as free-particles at escape velocity, Self-gravitating situations of a charged or neutral particle even while free of the gravitational influence of the large massive body due to its escape velocity, leaving only the self-gravitation as the only gravitational influence on the particle which in the case of a massless, charge less particle reduces back to the equation of free-particle at escape velocity. Other very brief expositions on trajectories and more are also present in this brief article.

Alena Tensor is a recently discovered class of energy-momentum tensors that provides a mathematical framework in which, as demonstrated in previous publications, the description of a physical system in curved spacetime and its description in flat spacetime with fields are equivalent and the metric tensor is not a property of spacetime, but a method of describing it. The use of Alena Tensor to describe a system with an electromagnetic field, leads to reconciliation of physical descriptions. In the curvilinear description, EFE were obtained with Cosmological Constant related to the invariant of the electromagnetic field tensor, which can be interpreted as negative pressure of the vacuum, filled with the electromagnetic field. In the classical description for flat spacetime, three densities of four-forces were obtained: electromagnetic, gravity, and the force responsible for the Abraham-Lorentz effect (radiation reaction force). There was obtained Lagrangian density and generalized canonical four-momentum, containing the four-potential of electromagnetic field and a term responsible for the remaining two forces. In the quantum picture, a QED Lagrangian density simplification was obtained, and the Dirac, Schrödinger and Klein-Gordon equations are approximations of the obtained quantum solution. The article also shows, that the distribution of charged matter can be expressed as polarization-magnetization stress-energy tensor, what indicates explanation why gravity is not visible in the spinor-based description of matter used in QED. The description used also leads to a conclusion, that charged particles cannot remain at complete rest and that they should have spin. Obtained connection of the Einstein tensor with gravity and the radiation reaction force, after transition to curvilinear description, excludes black hole singularities. Finally, a method for verifying Alena Tensor within QM was presented, and the article discusses prospects for farther use of Alena Tensor in unification applications, against the background of existing research directions.

One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature that gravitational radiation is absent, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the 2-body, 3-body, 4-body, and N-body problems. Quite general exact solutions can be obtained for the 2-body problem, unlike the situation in general relativity in 3 spatial dimensions for which only highly specified solutions exist. The 3-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For N4 other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.

The presented work shows that a force (electromagnetic or gravitational) field surrounding any material body is not limitless, but has the external and internal boundaries (radii). Understanding the fact of the existence of the field boundaries allows us to solve the problem of infinities that exists in electrodynamics. It is shown that there are two different electrostatic potentials: with the dimension of speed and with the dimension of the square of speed.

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

The Hyper-Torus Universe Model (HTUM) is a novel framework that unifies quantum mechanics, cosmology, and consciousness, proposing that the universe is a higher-dimensional hyper-torus containing all possible states of existence. This paper explores the fundamental concepts and implications of the HTUM, which suggests that the universe is a quantum system in which all possible outcomes are inherently connected, with consciousness playing a crucial role in actualizing reality. The HTUM addresses critical challenges in modern physics, such as the nature of quantum entanglement, the origin of the universe, and the relationship between mind and matter. By introducing concepts like singularity, quantum entanglement at a cosmic scale, and the self-actualization of the universe, the HTUM provides a comprehensive framework for understanding the fundamental nature of reality. This paper discusses the mathematical formulation of the HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. The philosophical implications of the HTUM are also examined, including its impact on free will, determinism, and the mind-matter relationship. The HTUM represents a significant shift in our understanding of the universe and our place within it, inviting further research and exploration into the nature of reality and consciousness.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Examples of such concepts are space and time—or waves and particles. Despite the Lorentz covariance of SR and the general covariance of GR, the perspectives of observers are always egocentric. Even coordinate-free formulations of SR/GR based on a parameterization do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Space and time are replaced by pure distance. Waves and particles are replaced by pure energy. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. The invariant parameter in ER is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, in which the sun is the center of our solar system but not of our galaxy. Such a model provides a holistic view from “beyond” (outside of) our galaxy. Likewise, ER provides a holistic view from beyond an observer’s reality. A master reality (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries geometrically, such as the Hubble constant tension and entanglement. Field equations are not required.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

“For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory...” J. S. Bell (2004, p. 171) The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. Although various primitive ontologies (including Bohmian pilot wave, spontaneous collapse, and objective collapse theories) along with wave function realism ontologies, many-worlds interpretations, and multi-field theories address the tension between special relativity and quantum mechanics, none has successfully resolved it. This analysis addresses the problem by positing an ontic, mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”). 4D spacetime’s three spatial dimensions and the N dimensions of Planck Space are composed of two substructures: discrete, three-dimensional, quantized units of space ("Planck Spheres") and an ontic State of Absolute Nothingness (the "SOAN") whose sole physical characteristic is onticness. Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete 4D spacetime and 2) mathematical 3N configuration spaces with a physical (3 x N) Planck Space. Moreover, structurally and dynamically, the Dual Ontology is predicated on the one-to-one mapping and identity between the Planck Spheres that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity physically and theoretically support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply.

A quantum theory of gravity is among the most pursued goals in physics. I present a definitive and direct experimental proof that refutes the widely believed hypothesis of quantum gravity. The detections of astrophysical gravitational waves (GW) are inferred from the differential oscillations of suspended mirrors of optical interferometers like the aLIGO detectors. If gravity is indeed quantized, then the average energy $\bar{E}$ in the minute oscillations of the mirrors, at a frequency $\nu$, corresponds to the absorption of an integer number $N$ gravitational quanta with total energy $E_{gw}=Nh\nu$. The coherent and coincident detections across large separations of detectors, and also the constraint of the equivalence principle, dictate that the average number of quanta $\bar{N}$ forcing the oscillations obeys $\bar{N}\gg 1$, or $1/\sqrt{\bar{N}}\ll 1$. However, the average energy $\bar{E}$ in the differential oscillations is smaller than the energy of a single quantum of GW radiation at the detected astrophysical GW frequencies. This startling finding implies that $\bar{N} <1$, which is physically impossible if gravity is quantized. This singular contradiction refutes the long-held hypothesis that gravity is quantized.

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

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Examples of such concepts are space and time—or waves and particles. Despite the Lorentz covariance of SR and the general covariance of GR, the perspectives of observers are always egocentric. Coordinate-free formulations of SR/GR based on a parameterization do not provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Neither does collecting information from egocentric perspectives provide a holistic view. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Space and time are replaced by “pure distance”. Waves and particles are replaced by “pure energy”. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. The invariant parameter in ER is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, in which the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside of) our galaxy. Likewise, ER provides a holistic view from beyond space. The “master reality” ES (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries geometrically, such as the Hubble constant tension and entanglement. Field equations are not required.

Einstein was skeptical of part of quantum mechanics, and he believed that Heisenberg’s uncertainty principle did not reflected the full depth of reality. He famously stated, ”God does not play dice with the universe.” However, since quantum mechanics has passed so many experimental tests, most physicists today assume that Einstein was wrong. Nevertheless, we will demonstrate that Heisenberg’s uncertainty principle must be modified to unify gravity with quantum mechanics. This modification leads to the Certainty-Uncertainty principle where the certainty part is strongly linked to gravity. This means Einstein likely was right in his intuition also on this point. The key is to understand that the de Broglie wavelength is not the actual wavelength of matter but merely a derivative of the true matter wavelength, namely the Compton wavelength. Furthermore, one must understand that the gravitational constant, first introduced in 1873, is simply a composite constant needed to rectify the in- complete definition of kilogram mass introduced into Newtonian gravity in 1873.

The Combined Theoretical Signal (CTS) model, with a 90% or higher validity rate, stands as the first validated universal model integrating gravity and quantum physics. This manuscript presents the final validation and enhancement of the CTS model using recent pulsar-sourced gravitational wave data (J2322+2057, J2234+0611, J2043+1711, and J2317+1439) and strain data from GW150914, GW151226, GW190521, and GW200105. Our findings demonstrate a significant alignment between theoretical predictions and observational data, positioning CTS as a groundbreaking framework with profound implications for theoretical physics and cosmology. The CTS model not only bridges the gap between gravity and quantum mechanics but also offers a new perspective on the formation of massive black holes, the Quantum Cosmic Fabric (QCF), and the structure of the universe as an interconnected hierarchical tree of universes.

We propose a novel framework for understanding quantum phenomena through the lens of a modified electromagnetic spacetime governed by Einstein field equations. By assuming the existence of an electromagnetic spacetime that adheres to these modified geodesic and Einstein field equations, provided the field equations satisfy the Coulomb force law in weak-field approximations, we explore the derivation of Maxwell’s equations and highlight the necessity of incorporating spin to validate these equations. We derive the wave equation for the normalized transverse metric and establish its equivalence with the de Broglie wave proposition, suggesting a relationship between this metric and the particle's wavefunction. This approach offers a classical explanation for several quantum phenomena, including the double-slit experiment, entanglement, tunneling, non-locality, and wavefunction collapse. Additionally, it posits a method to visualize atomic orbital structures in line with quantum mechanical predictions. These findings suggest that the foundational principles of quantum mechanics can be interpreted as linearized approximations of general relativity applied to electromagnetic spacetime. While this theory does not yet extend to the correlations between general relativity, quantum electrodynamics (QED), and quantum chromodynamics (QCD), it provides a valuable visualization tool for physicists and advances our understanding of the unresolved challenges linking quantum mechanics with general relativity.

Almost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast forward to Constantino Tsallis’ illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino’s collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis’ enduring inspiration, Eroglu, Boghosian, Borges and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude.

The study of the emission, propagation, and reflection of balls in Newtonian mechanics, applying the laws of conservation of momentum and energy when the mass of the balls converges to zero, concludes that the kinematics of light are like those of massless balls. The kinematics of light explain why the speed of light is the constant c in each inertial frame in which the light source and reflective mirror are at rest, why the laws of physics have the same form in each inertial frame, and why any light experiment in an inertial frame cannot prove the motion of that inertial frame. The following law of mechanics governs the kinematics of balls and electromagnetic radiation: Each inertial frame drags at its velocity the balls and electromagnetic radiation emitted by bodies at rest in that inertial frame. The theory of special relativity misapplies the symmetry observed in phenomena to two inertial frames; therefore, it duplicates a physical phenomenon from one inertial frame, which is considered stationary, into another. There are multiple issues rooted in Lorentz's and Einstein's transformations. For example, transformations offer the speed of light at the constant c in the moving and opposite directions of the inertial frame. At the same time, it is variable in any other direction, converging to infinity. Time contraction in the moving direction of the inertial frame is different from time dilation in the opposite direction. It requires a ruler and time synchronization in each direction. There are no length contractions in Lorentz's and Einstein's transformations to support the fundamental concept of length contraction in special relativity. With these unacceptable conclusions, the theory of special relativity is self-negating.

The Combined Theoretical Signal (CTS) model, with a 90% or higher validity rate, stands as the first validated universal model integrating gravity and quantum physics. This manuscript presents the final validation and enhancement of the CTS model using recent pulsar-sourced gravitational wave data (J2322+2057, J2234+0611, and J1012+5307) and strain data from GW150914 and GW151226. Our findings demonstrate a significant alignment between theoretical predictions and observational data, positioning CTS as a groundbreaking framework with profound implications for theoretical physics and cosmology. The CTS model not only bridges the gap between gravity and quantum mechanics but also offers a new perspective on the formation of massive black holes, the Quantum Cosmic Fabric (QCF), and the structure of the universe as an interconnected hierarchical tree of universes.

We propose a novel framework for understanding quantum phenomena through the lens of a modified electromagnetic spacetime, governed by Einstein field equations. By assuming the existence of an electromagnetic spacetime that adheres to these modified equations and provides the Coulomb force law in weak-field approximations, we explore the derivation of Maxwell’s equations and highlight the necessity of incorporating spin to validate these equations. We derive the wave equation for the normalized transverse metric and establish its equivalence with the de Broglie wave proposition, suggesting a relationship between this metric and the particle's wavefunction. This approach offers a classical explanation for several quantum phenomena, including the double-slit experiment, entanglement, tunneling, non-locality, and wavefunction collapse. Additionally, it posits a method to visualize atomic orbital structures in line with quantum mechanical predictions. Our findings suggest that the foundational principles of quantum mechanics can be interpreted as linearized approximations of general relativity applied to electromagnetic spacetime. While this theory does not yet extend to the correlations between general relativity, quantum electrodynamics (QED), and quantum chromodynamics (QCD), it provides a valuable visualization tool for physicists and advances our understanding of the unresolved challenges linking quantum mechanics with general relativity.

“For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory...” J. S. Bell (2004, p. 171) The inability to delineate a unified physical ontology that accounts simultaneously for the laws of special relativity and the results of quantum experiments has been a defining problem in physics for more than 100 years. Although various primitive ontologies (including Bohmian pilot wave, spontaneous collapse, and objective collapse theories) along with wave function realism ontologies, many-worlds interpretations, and multi-field theories address the tension between special relativity and quantum mechanics, none has successfully resolved it. This analysis addresses the problem by positing an ontic, mixed ontology composed of a “discrete” 4D spacetime and a physical, ultra-high dimensional (3 x N) “Planck Space.” Together, Planck Space and the three spatial dimensions of 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the “Dual Ontology”). 4D spacetime’s three spatial dimensions and the N dimensions of Planck Space are composed of two substructures: discrete, three-dimensional, quantized units of space ("Planck Spheres") and an ontic State of Absolute Nothingness (the "SOAN") whose sole physical characteristic is onticness. Critically, the Dual Ontology’s structure replaces 1) the continuous, differentiable manifold of 4D spacetime with a discrete 4D spacetime and 2) mathematical 3N configuration spaces with a physical (3 x N) Planck Space. Moreover, structurally and dynamically, the Dual Ontology is predicated on the one-to-one mapping and identity between the Planck Spheres that simultaneously form 4D spacetime and Planck Space. The one-to-one mapping and identity physically and theoretically support an integrated quantum dynamics based upon the dynamic evolution of single and N-body quantum states in 4D spacetime in full compliance with the laws of special relativity and the instantaneous collapse of all quantum states in an ontic Planck Space, where special and general relativity and more generally, 4D spacetime’s laws of physics, do not apply. Keywords: Quantum Cosmology; Special Relativity; Quantum Mechanics, Wave Function Collapse; Mixed Ontology; Dual Ontology; (3 x N) Planck Space; Planck Identity; Bell Identity

The theory says that the first things to exist in the universe and the current moment were driven by an imperative need; that is, the intensities of the physical concept specify influence the existence of elements and facts based on the countless observations in physical spaces in relation to elements and facts. The existence of mandatory elements in space is motivated by the characteristics of the spaces that offer conditions for such an obligation. The theory states that the universe did not arise by chance; that is, the universe emerged through determination influenced by its surroundings. The objective of the study is to help explain the elements and facts of the universe from its origins to the present.

We discuss the consequences of the unique symmetry of the de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces the thermal bath for matter. The de Sitter spacetime is invariant under the modified translations, ${\bf r}\rightarrow {\bf r} -e^{Ht}{\bf a}$, where $H$ is the Hubble parameter. For $H\rightarrow 0$, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations ${\bf r}\rightarrow {\bf r} -{\bf a}$. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature $T=H/\pi$, which is twice larger than the Gibbons-Hawking temperature of the cosmological horizon. This temperature does not violate the de Sitter symmetry, and thus does not require the preferred reference frame, as distinct from thermal state of matter, which violates the de Sitter symmetry. This leads to the heat exchange between gravity and matter, and to instability of de Sitter state towards the creation of matter, its further heating, and finally to the decay of the de Sitter state. The temperature $T=H/\pi$ determines different processes in the de Sitter environment, which are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons-Hawking area law, which is related to the cosmological horizon, $S_{\rm hor}=4\pi KA$, where $K=1/16\pi G$. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the $f({\cal R})$ gravity. In this thermodynamics, the Ricci scalar curvature ${\cal R}$ and the effective gravitational coupling, $K$, are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume, and the surface entropy of the cosmological horizon remains the same, but with the gravitational coupling $K=df/d{\cal R}$. Such connection takes place only in the $3+1$ spacetime, where there is the special symmetry due to which the variables $K$ and ${\cal R}$ have the same dimensionality. We also consider the lessons from the de Sitter symmetry for the thermodynamics of black and white holes.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Examples of such concepts are space and time—or waves and particles. Despite the Lorentz covariance of SR and the general covariance of GR, the perspective of an observer is always egocentric. Not even coordinate-free formulations of SR/GR based on a parameterization provide a “holistic view of nature” (comprehensive view of nature from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Space and time are replaced by “pure distance”. Waves and particles are replaced by “pure energy”. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. The invariant parameter in ER is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, in which the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside of) our galaxy. Likewise, ER provides a holistic view from beyond space. The “master reality” ES (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries geometrically, such as the Hubble constant tension and entanglement. Field equations are not required.

This paper is a brief review of our work on the Planck quantized version of general rela- tivity theory. It demonstrates several straightforward methods to rewrite the same equations that we have already presented in other papers. We also explore a relatively new general relativity-inspired field equation based on the original Newtonian mass, which is very differ- ent from today’s kilogram mass. Additionally, we examine two other field equations based on collision space-time, where both energy and matter can be described simply as space and time. We are thereby fulfilling Einstein’s dream of a theory where energy and mass are not needed, or are just aspects of space and time. If this is extended beyond the 4-dimensional space-time formalism of general relativity theory to a 6-dimensional framework—with 3 space dimensions and 3 time dimensions—this ultimately reveals that they are two sides of the same coin. In reality, it is a three-dimensional space-time theory, where space and time are just two sides of the same coin.

In the last decades the primordial black holes ({\bf pbhs}) have attracted much attention of cosmologists and astrophysicists. This is associated with origination of such black holes in the early Universe as a result of a gravitational collapse of the high-density matter, making them natural ''detectors'' of the processes involved. In inflationary cosmology of particular importance are {\bf pbhs} originated during the pre-inflationary period. And, since they are small and generated at the energies close to the Planck energies, for them we should take into consideration the quantum-gravitational corrections ({\bf qgcs}). In turn, these corrections change (shift) the inflationary parameters. The paper presents a study of the above-mentioned shifts with regard to these corrections for different scenarios. It is shown that probabilities of occurrence of the {\bf pbhs} under study with due regard for the given {\bf qgcs} are rising as compared to the semiclassical consideration. Besides, high-energy deformations of Friedmann Equations created on the basis of these corrections have been derived for different patterns. Conclusion contains the general remarks concerning the above-mentioned {\bf qgcs} for cosmological parameters and perturbations due to inflation; the steps for their investigation are outlined and the key problems of such a study are formulated.

This paper addresses the cosmological constant problem, a significant discrepancy highlighted by \cite{Weinberg:1988cp} that underlines a fundamental inconsistency between quantum field theory (QFT) and general relativity (GR). QFT examines matter dynamics within Lorentzian spacetime under standard model symmetry, while GR uses Riemannian geometry but adapts it to ensure local Lorentzian behavior in small regions. Despite the experimental successes of both theories, a major challenge exists in theoretical understanding. This letter seeks to clarify this critical misunderstanding. As the universe cools from its hot beginning, the \(SU(3) \times SU(2) \times U(1)\) standard model gauge symmetry evolves. This symmetry breaks to \(SU(3) \times U(1)\) upon cooling at the electroweak scale and ultimately to \(SU(3)\) alone as temperatures approach near-absolute zero kelvin, facilitated by the experimental Meissner effect. This suggests that \(SU(3)\) symmetry forms the foundational "atoms" of vacuum energy. Calculating the number of \(SU(3)\) vacuum atoms across the universe results in a value that perfectly aligns the theoretical predictions with the observed vacuum energy densities, thereby resolving the cosmological constant problem. Since \(SU(3)\) atoms account for the cosmological constant, they must be unbreakable. The third law of thermodynamics, which states that it is impossible to reach absolute zero Kelvin, provides the protection that prevents SU(3) atoms from breaking at zero Kelvin. This reveals the connection between the third law of thermodynamics and the quark confinement. This leads to the \(SU(3)\) atom creating a mass gap within the universe. This solution serves as a symmetric evidence of gauge-gravity duality as well as gravity-superconductor duality.

In this research, we present the Combined Theoretical Signal (CTS) model, which integrates influences from dark matter, quantum fluctuations, and higher-dimensional effects. Our goal is to provide a potential framework for unifying gravity and quantum physics. We validate the CTS model against observational gravitational wave data and perform residual analysis to assess its accuracy. The results suggest that CTS aligns well with the observational data and provides a robust theoretical model that may contribute significantly to the quest for a universal theory. This model has the potential to enhance our understanding of the fundamental forces and the structure of the universe, supporting a hierarchical tree structure rather than parallel universes.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Examples of such concepts are space and time—or waves and particles. Despite the Lorentz covariance of SR, the general covariance of GR, and coordinate-free formulations of SR/GR, the perspective of each observer is egocentric. Even if we consider all these egocentric perspectives, we will not craft a “holistic view” of nature (a view taken from all possible perspectives at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Space and time are replaced by “pure distance”. Waves and particles are replaced by “pure energy”. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. The invariant parameter in ER is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, in which the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside of) our galaxy. Likewise, ER provides a holistic view from beyond space. The “master reality” ES (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries geometrically, such as the Hubble constant tension and entanglement. Field equations are not required.

This study, serving as Part-2 of the research titled "Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics," investigates the behaviour of matter within gravitationally bound systems. Through meticulous examination of projected length alterations, the research highlights differences between classical and relativistic mechanics frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. Additionally, the study underscores the crucial role of gravitational effects on the effective mass of moving objects, which emerges as a critical factor in predicting length deformation across scientific disciplines. The incomplete treatment of relativistic effects within Relativistic Mechanics, including acceleration and material stiffness, emphasizes the importance of comprehensively understanding gravitational influences on effective mass. This is evident in gravitational equations, where the gravitational force depends not only on the object's mass but also on its effective mass, influenced by kinetic energy. Thus, incorporating the gravitational effect on effective mass enhances the understanding of length deformation phenomena within gravitationally bound systems, enriching scientific discourse.

In this research, we present the Combined Theoretical Signal (CTS) model, which integrates influences from dark matter, quantum fluctuations, and higher-dimensional effects. Our goal is to provide a potential framework for unifying gravity and quantum physics. We validate the CTS model against observational gravitational wave data and perform residual analysis to assess its accuracy. The results suggest that CTS aligns well with the observational data and provides a robust theoretical model that may contribute significantly to the quest for a universal theory. This model has the potential to enhance our understanding of the fundamental forces and the structure of the universe, supporting a hierarchical tree structure rather than parallel universes.

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, afforded by multiplying one of the $\gamma$-matrices by the imaginary number. The reason for doing this is to introduce a bivector into the spin algebra. This modifies the Dirac equation which separates into two distinct and complementary spaces: one describing polarization and the other coherence. The former describes a 2D structured spin and the latter its helicity, generated by a unit quaternion.

This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the limitations inherent in Relativistic Mechanics. The results reveal significant differences in predicted length changes between the two frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. This study underscores the critical importance of addressing the incomplete treatment of acceleration dynamics in Relativistic Mechanics to achieve a more accurate depiction of length deformation in high-speed scenarios.

Special relativity (SR) and general relativity (GR) describe nature in “subjective concepts” (concepts of an observer). Examples of such concepts are space and time—or waves and particles. Despite the Lorentz covariance of SR, the general covariance of GR, and coordinate-free formulations of SR/GR, the perspective of each observer is egocentric. Even if we consider all these egocentric perspectives, we will not craft a “holistic view” of nature (a view taken from all perspectives in space at the same instant in time) because there is no absolute time in SR/GR. Here I show: Euclidean relativity (ER) describes nature in “objective concepts” (concepts that are immanent in all objects). Space and time are replaced by “pure distance”. Waves and particles are replaced by “pure energy”. Each object’s proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are pure distances. The invariant parameter in ER is absolute, cosmic time t. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to a “heliocentric model 2.0”, in which the sun is the center of our solar system but not of our galaxy. That model provides a holistic view from “beyond” (outside of) our galaxy. Likewise, ER provides a holistic view from beyond space. The “master reality” ES (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries geometrically, such as the Hubble constant tension and entanglement. Field equations are not required.

The paper is concerned with the concept of elementary observations (EO). EOs are experimental answers to the question whether a matter-instrument interaction had taken place at the micro-scale of quantum phenomena. Focusing on the specific case of photon detection, we show that during their lifetimes EOs proceed through the four phases of initiation, detection, erasure and reset. Once generated, the observational value of EOs can be measured in units of the Planck quantum of physical action h=4.136×10^(-15) eVs. Once terminated, each unit of entropy of size k_B=8.617×10^(-5) eV⁄K, which had been created in the instrument during the observational phase, needs to be removed from the instrument to ready it for a new round of photon detection. This withdrawal of entropy takes place at an energetic cost of at least two units of the Landauer minimum energy bound of E_La=ln⁡〖(2) k_B T_D 〗 for each unit of entropy of size k_B.

Special and general relativity (SR/GR) describe nature “subjectively”, that is, from the perspectives of observers. Despite the Lorentz covariance of SR, the general covariance of GR, and all coordinate-free formulations, the perspective of each observer is egocentric. Even if we consider all egocentric perspectives, we will not craft a “holistic view of nature” (view of nature as a whole and in her own concepts) because there is no absolute time in SR/GR. In Euclidean relativity (ER), there is a relative 4D vector “flow of proper time” and absolute, cosmic time. ER describes nature “objectively”, that is, independently of observers. Each object’s (not only an observer’s) proper space d₁, d₂, d₃ and its proper time τ span an absolute, natural 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are treated the same. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to the advanced heliocentric model, in which the sun is the center of our solar system but not the center of everything else. That model provides a holistic view of nature from “beyond” (outside) space. Likewise, ER provides a holistic view of nature from beyond space and time. A master reality ES described by ER is beyond each observer’s reality described by SR/GR. For all subjective concepts (space, time, waves, particles), there are objective master concepts in ES. The master concept of space and time is “pure distance”. The master concept of waves and particles is “pure energy”. ER solves 15 mysteries including the Hubble constant tension and entanglement. Interestingly, all mysteries are solved geometrically—without forces and fields.

We propose that quarks and gluon flux tubes emerge from networks of standing vacuum waves. Each unbound nucleon, in its ground state, may be electromagnetically modeled as massless quantized charge on two pairs of orbiting arcs. Each charge arc is associated with a superposition of radially-oriented vacuum fundamental harmonics. These quantum superpositions of radial waves are coupled to nucleon mass-energy. The charge arcs orbit on the two surfaces of a spindle torus with polar charge-exclusion zones. These ground-state models of unbound nucleons may be interpreted as pairs of virtual Möbius bands. The optimal triangular Möbius band may explain proton uniqueness. These unbound proton and neutron models are shown to be precisely connected via a parameter dependent on neutron mass and the sum of the up and down bare quark masses. Due to this precise connection, and the relatively high experimental precision of proton magnetic moment, neutron magnetic moment is calculated about two orders of magnitude more precisely than the most accurate experiments to date. This quantum network-based approach to modeling unbound low-energy nucleons calculates several other measurable parameters.

We hypothesis that large earthquakes generate Horndeski-like Gravitational Wave (GW). We find that such a Horndeski-like GW propagates with the speed of sound. The sound waves generated by an earthquake make a local and temporal change to the Earth’s diagravitational medium; therefore, they modify the GW speed in a standard, Alternative-Theory-of-Gravity (ATG) sense. The quantum of the Horndeski-like GW is a massless scalar quasiparticle and cannot exist outside of the propagation region of the P-field. The Horndeski-like GW may be detectable by future GW detectors with a sensitivity of 10−15 Hz^−1/2 in the region of 0.1–1 Hz.

Quantum revival phenomena, wherein the wave function of a quantum system periodically returns to its initial state after evolving in time, are investigated in this study. Focusing on electrons confined within a quantum box with an impurity, both weak and strong coupling regimes are explored, revealing intricate relationships between impurity parameters and temporal dynamics. The investigation considers the influence of impurity position, impurity strength, and external factors such as aluminum concentration, temperature, and hydrostatic pressure on classical periods and revival times. Through analytical derivations and graphical analyses, the study elucidates the sensitivity of quantum revivals to these parameters, providing valuable insights into the fundamental aspects of quantum mechanics. While no specific physical applications are discussed, the findings offer implications for quantum heat engines and other quantum-based technologies, emphasizing the importance of understanding quantum revivals in confined quantum systems.

We show that the entropy or information flow of a gravitational system constrains the dependence of gravitational force on radial distance r which for very large r is equivalent to gravity in two dimensions. This explains the "origin" of dark matter and provides a natural solution to the problem of flat rotation curves of galaxies at very large distances and a larger deflection angle for a gravitational lens.

We solve the problem of Apollonius by applying the Lorentz transformation within the frame- work of special relativity to go to a frame of simultaneity, where the solutions are the circum- center. We transform back to get the solutions in a general frame. We show that the solutions in a general frame are the foci of the ellipse going through the centers of the given 3 circles.

This study delves into the intricate dynamics of classical mechanics, exploring the interplay between force, mass, and energy. Through fundamental principles and mathematical formulations, it elucidates key relationships governing physical systems. Beginning with an overview of classical mechanics, the study establishes the foundational principles laid down by Newton, emphasizing concepts such as inertia, acceleration, and the relationship between force and motion. Central to the investigation is Newton's second law of motion, highlighting the direct proportionality between force and acceleration, and the inverse relationship between acceleration and mass when acted upon by a force. The study extends to the concept of effective mass, elucidating how the application of force influences the inertial mass of an object and contributes to its effective mass through the acquisition of kinetic energy. Furthermore, the study examines the total energy composition of systems, emphasizing the holistic nature of energy as a combination of potential and kinetic forms. Through the work-energy theorem, a direct link between force and kinetic energy is established, revealing how mechanical work done on an object results in changes in its kinetic energy and effective mass. Mathematical formulations and conceptual analyses provide deeper insights into the intricate relationships between force, mass, and energy, shedding light on the underlying mechanisms governing classical mechanical systems. Through validation against empirical observations and experimental data, the study ensures the accuracy and reliability of derived equations, contributing to a richer understanding of classical mechanics and paving the way for further exploration in the field of physics.

The paper suggests that the physical priciple of special relativity's space-time transformation effect is wrong, Uniform linear motion without acceleration does not exist objectively, nor does its same reference frames. Therefore, it is inferred that the space-time transformation effect of special relativity is caused by the acceleration of moving objects, special relativity is only a part of general relativity, not a theoretical system that exists independently from general relativity. The corresponding mathematical demonstration and calculation verification are carried out, and the result proves that the inference of the paper is correct. At the same time, it further explains that the concept of absolute airspace is correct. Special relativity has serious errors in the concept of space, the principle of relativity and the physical principle of space-time transformation effect. Therefore, it is necessary to make a series of revisions to the theory of relativity and to reinterpret some related physical problems.

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

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.

It has been proven that in standard Einstein gravity, exotic matter (i.e. matter violating the point-wise and averaged weak and null energy conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field . Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods of minimizing the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity and in this review paper we first explore f(R) theories and then explore some wormhole solutions in f(R) theories including Lovelock gravity.

Special and general relativity (SR/GR) describe nature “subjectively”, that is, from the perspectives of observers. Despite the Lorentz covariance of SR, the general covariance of GR, and all coordinate-free formulations, the perspective of each observer is egocentric. Even if we consider all egocentric perspectives, we will not craft a “holistic view of nature” (view of nature as a whole and in her own concepts) because there is no absolute time in SR/GR. In Euclidean relativity (ER), there is a relative 4D vector “flow of proper time” and absolute, cosmic time. ER describes nature “objectively”, that is, independently of observers. Each object’s (not only an observer’s) proper space d₁, d₂, d₃ and its proper time τ span an absolute, natural 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are treated the same. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. ER compares to the “advanced heliocentric model”, in which the sun is the center of the solar system, but no star is the center of space. That model provides a holistic view of nature from “beyond” (outside) space. Likewise, ER provides a holistic view of nature from beyond space and time. A master reality ES described by ER is beyond each observer’s reality described by SR/GR. Subjective concepts (space, time, waves, particles) have objective counterparts in the master reality. “Pure distance” is the counterpart of space and time. “Pure energy” is the counterpart of waves and particles. I do not identify the counterparts of forces and fields. ER solves 15 mysteries (time’s arrow, the Hubble constant tension, entanglement) geometrically—without forces and fields.

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e. its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called "quantum potential" in this context is briefly discussed.

Special and general relativity (SR/GR) describe nature “subjectively”, that is, from the perspectives of observers. Despite the Lorentz covariance of SR, the general covariance of GR, and all coordinate-free formulations, the perspective of each observer is egocentric. Even if we consider all egocentric perspectives, we will not craft a “holistic view of nature” (view of nature as a whole and in her own concepts) because there is no absolute time in SR/GR. In Euclidean relativity (ER), there is a relative 4D vector “flow of proper time” and also an absolute cosmic time. ER describes nature “objectively”, that is, independently of all observers. Each object’s (!) proper space d₁, d₂, d₃ and its proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are treated the same. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. The projections are relative. ER compares to the “advanced heliocentric model”, in which the sun is the center of the solar system, but no star is the center of space. This model implies a holistic view of the universe from “beyond” (outside) space. Likewise, ER implies a holistic view of nature from beyond space and time. This makes sense because space and time are subjective concepts. There is a master reality ES (described by ER) beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries (such as time’s arrow, the Hubble constant tension, entanglement). ER also declares five concepts of today’s physics obsolete (such as dark energy, non-locality). The 15 mysteries are solved without any field equations. Physical fields come into play in an observer’s reality only.

Here, using the theory of electrical-quantum modelling of the neutron and proton as a three-phase alternating current electrical generator, we will analyse the proton decay and the inverse neutron decay and determine the following subatomic particles, Dproton, Protoniu, Dneutron and Neutroniumd.

The Schwarzschild metric emerges independent of Einstein's field equations, offering a straightforward derivation solely reliant on Newtonian mechanics and Minkowskian proper acceleration. This approach provides a clear path to understanding the gravitational field around a spherically symmetric mass without the need for the complexities of Einstein's full theory of General Relativity. Transitioning to our exploration of the cosmic Friedmann equations, we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe's dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations—namely, the conservation, Euler, and Poisson equations—with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.

Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends beyond conventional frameworks. In classical mechanics, time is perceived as an absolute, continuously progressing backdrop, largely independent of events. Quantum mechanics treats time as a static parameter that does not influence quantum states but provides a framework for their evolution. In cosmology, time is considered a dimension that emerges from the Big Bang and serves as a measure for the universe's expansion, yet it does not interact with the structural dynamics of the cosmos. Challenging the transformative insights of Einstein’s relativity, which merges time with spatial dimensions under extreme conditions, we advocate for a perspective that views time as a Hyperdimensional and universal constant. This perspective posits that time, despite its unique and intrinsic properties, does not dynamically interact with or alter physical phenomena. Instead, it underpins our understanding of phenomena across different scales—from the minutiae of quantum states to the macroscopic dynamics of cosmology—without direct causation or change. A critical examination of time dilation and relativistic assumptions reveals significant discrepancies in traditional interpretations, particularly in how they are applied across different physical contexts. Our findings challenge the uniform applicability of time dilation, suggesting that observed phenomena often attributed to relativistic effects might better be explained through non-relativistic mechanisms such as phase shifts or changes in wavelength rather than temporal dilation. By synthesizing insights from various scientific domains, we advocate for a unified theory that recognizes time as a fundamental, universal dimension that is conceptual and non-interactive. Our goal is to bridge existing gaps between diverse scientific interpretations and promote a more integrated, profound understanding of time's autonomous and intrinsic nature.

Special and general relativity (SR/GR) describe nature “subjectively”, that is, from the perspectives of observers. Despite the Lorentz covariance of SR, the general covariance of GR, and all coordinate-free formulations, the perspective of each observer in SR/GR is egocentric. Even if we put all these perspectives together, we will not craft a “holistic view of nature” (view that is simultaneous for all observers) because there is no absolute time in SR/GR. I show: In Euclidean relativity (ER), there is a relative 4D vector “flow of proper time” and absolute cosmic time. ER describes nature “objectively”, that is, a holistic view of nature is provided. Each object’s (!) proper space d₁, d₂, d₃ and proper time τ span an absolute 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are treated the same. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. These projections are relative. ER compares to an “advanced heliocentric model”, in which the planets revolve around the sun without the sun being the center of the universe. The model requires the imagination of being “beyond” (outside of) the universe. In a similar way, ES is a master reality beyond each observer’s reality. Equipped with this holistic view, ER solves several mysteries (such as time, time’s arrow, the Hubble constant tension, entanglement). ER also declares some concepts of today’s physics obsolete (such as dark energy, non-locality). Since the laws of physics apply to an observer’s reality only, I do not derive any field equations in ES. This finish may be disappointing, but it is fine because none of my solved mysteries requires field equations.

This paper describes an entropy equation that can be used for measuring energy. It originated from measuring economy in AI models, where the assumption would be that any organic system makes use of energy efficiency to form its structures. Looking at clustering and cohesion resulted in the equation E = (mean * variance). It was apparent however, that it was a very generic type of equation and it could be adjusted so that distance represents mean. This new version was applied to the domain of physics and the universe, when the equation can support the idea that work is done through the energy released by the 'change' in entropy. A comparison with Einstein's relativity equation is made and also the audacious suggestion that a black hole has only potential energy inside, which converts to kinetic energy after a Big Bang, for example. From that suggestion, a universal theory about state change can be made.

We explore an idea put forward many years ago by Zeldovich and Novikov concerning the existence of compact objects endowed with arbitrarily small mass. The energy-density of such objects, which we call “Ghost stars”, is negative in some regions of the fluid distribution, producing a vanishing total mass. Thus, the interior is matched on the boundary surface to Minkowski space-time. Some exact analytical solutions are exhibited and their properties are analyzed. Observational data that could confirm or dismiss the existence of this kind of stellar object, is commented.

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.

Special and general relativity (SR/GR) describe nature “subjectively”, that is, from the perspective of just one observer at a time (one group of observers, to be exact). Mathematically, SR/GR are correct. I show: (1) Physically, SR/GR have an issue. Despite the covariance of SR/GR, there is always just one active perspective. Because of this constraint, there is no holistic view of nature. The issue shows itself in unsolved mysteries. Still, the Lorentz factor and gravitational time dilation are correct. This is why the concepts of spacetime in SR/GR work well except for cosmology and quantum mechanics. (2) Euclidean relativity (ER) describes nature “objectively”, that is, from the perspectives of all objects at once. An object’s (!) proper space d₁, d₂, d₃ and proper time τ span 4D Euclidean spacetime (ES), where d₁, d₂, d₃ and d₄ = cτ are treated the same. All energy moves through ES at the speed c. An observer’s reality is created by projecting ES orthogonally to his proper space and to his proper time. In SR, these concepts are considered coordinate space and coordinate time. Neither their reassembly to a non-Euclidean spacetime nor the parameterization in SR/GR provides a holistic view. The scalar τ, in particular, cannot factor in an object’s 4D vector “flow of proper time” τ. The SO(4) symmetry of ES is incompatible with waves. This is fine because waves and particles are subjective concepts. A master reality (described by ER) is beyond each observer’s reality (described by SR/GR). ER solves 15 mysteries at once, such as time’s arrow, the Hubble tension, dark energy, and non-locality.

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

In our investigation of the time evolution of energy states Einstein’s interpretation from more than a century ago is found to have greater internal consistency than that of non-relativistic quantum mechanics. We choose to align more closely with his methods by abandoning the non-relativistic Hamiltonian method, which has been the standard for nearly a century, in favor of a relativistically correct Lagrangian method. Integral equations of motion for the absorption and emission of radiation are derived that underlie and anticipate the differentially motivated Schrödinger equation. This new interpretation applies to a large volume of experimental evidence of both classical and quantum mechanical origin. Among the examples discussed in support are Planck’s law describing black body radiation, matrix mechanics, the function of the simplest quantum mechanical system an electron cyclotron, chaos theory, and evolutionary biology.

The article aims to present an alternative perspective on the relativistic expression of energy. This perspective is based on the virtual use of a Dempster mass spectrometer. In this spectrometer, it is possible to simulate Alfred Bucherer's experiment and conclude, using Lienard's relativistic equation, that the classical expression of energy predicted by Special Relativity is a more complete expression than the one presented by high school and college physics textbooks.

The new observations, including the fastest star, the circular velocity curve of the Milky Way and the fast galaxy bar, should imply that the mass of the center of the Milky Way is almost 10¹¹ times the mass of the Sun.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory