Axions can be stimulated to decay to photons by ambient photons of the right frequency or by photons from decay of neighboring axions. If the axion density is high enough the photon intensity can be amplified, which is a type of lasing or an axion maser. Here we review the astrophysical situations where axion lasing can appear and possibly be detected.

We study the back-reaction of fermion fields on the kink solution in one space and one time dimension. We employ a variational procedure to determine an upper limit for the minimum of the total energy. This energy has three contributions: the classical kink energy, the energy of valence fermions and the fermion vacuum polarization energy. The latter arises from the interaction of the kink with the Dirac sea and is required for consistency of the semi-classical expansion for the fermions. Earlier studies only considered the valence part and observed a substantial back-reaction. This was reflected by a sizable distortion of the kink profile. We find that this distortion is strongly mitigated when the Dirac sea is properly accounted for. As a result the back-reaction merely produces a slight squeeze or stretch of the kink profile.

Quantum Gravity is not sufficient to predict the properties of particles (baryonic and non-baryonic) to a great extent. So, we develop General Quantum Gravity (GQG), which is a renormalizable formalization of quantized gravity that emerges from General Relativity through a new scenario of Quantum Mechanics. Inside every observable $(3+1)D$ spacetime in this new scenario of Quantum Mechanics, there must contain an internal hidden $(n+1)D$ spacetime, which immediately yields extra hidden dimensions by a closed continuous mapping, so that the overall spacetime must acquire Supersymmetry. We have also found that Superstrings are inevitably natural and universal but hidden inside every $(3+1)D$ observable spacetime. Superstrings are found eleven-dimensional (rather than lower dimensional) within this quantum spacetime. Consequently, eleven-dimensional Supergravity is necessarily a natural phenomenon within the GQG spacetime. GQG is formalized here in two different aspects. The first one gives an Einstein field equation in a semi-quantum Minkowski spacetime with semi-quantum Lorentzian metric tensor, whereas, the second one yields a purely Quantum Mechanical Einstein field equation in a quantum non-Minkowski spacetime with non-Lorentzian metric tensor. Dark Energy (as well as Dark Matter) appears from GQG quite naturally. We develop here Gravitational Electroweak Dark Energy interactions, where gravity and Dark Energy are allowed to combine with electroweak symmetry. Likewise, in Gravitational Chromodynamic Dark Energy interactions, we combine QCD with gravitational and Dark Energy symmetries. In a Dark Matter gauge symmetry model, we combine Dark matter with all possible gauge symmetries. A Universal Model $SU(7)_{UM}$ combines entire baryonic and non-baryonic particle interactions all together.

The experiment proposed by Bose et al aims to show the non classicality of gravity through entanglement. This paper seeks to establish optimal conditions under which the entanglement would be maximized. The assumptions made by Bose et al to come to the conclusion of quantized gravity would also be discussed along with alternate conclusions that could arise from the experiment.

We propose a new theory beyond the standard model of elementary-particle physics. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. No serious undetermined parameters are assumed. Furthermore, the relations between the forces at the quantum-mechanics level is made clear. Using these relations, we quantize Einstein’s gravitational equation: Beginning with the zero-point energy of the vacuum, and after quantizing Newtonian gravity equation, we combine the energies of a static electromagnetic field and gravity in a quantum spacetime. Applying these results to the Einstein gravity equation, we substitute the energy density derived from the zero-point energy in addition to redefining differentials in a quantized spacetime. This is how we derive the quantized Einstein gravitational equation without assuming the existence of macroscopic masses. For the weak interaction, by considering plane-wave electron and the zero-point energy, we obtain a wavefunction that represents a β collapse. In this process, from a different point of view than Weinberg-Salam theory, we derive the masses of the W and Z bosons and the neutrino, and we calculate the radius and lifetime of the neutron. For the strong interaction, we previously reported an analytical theory for calculating the mass of a proton by providing a specific linear attractive potential obtained from the zero-point energy, which agrees well with the measurements. In the present study, we further calculate the strong interaction between two nucleons, i.e., the mass of the pi-meson. The resulting calculated quantities agree with the measurements, which verifies our proposed theory.

A Berry geometrical phase is identified in a strongly metastable system containing dynamically responsive clathrate hydrate structures within a crystal-fluid material. High energy degeneracy in the associated chemistry produces local stability and false vacuum conditions that lead to non-extensive and non-additive contributions in the fundamental thermodynamic relation. The reciprocating action of a piston expander confirms a net energy gain despite the crystal-fluid material maintaining almost constant density. The property of asymptotic freedom is uncovered in the associated condensed matter and quantum mechanical descriptions providing evidence for scale-invariance that dominates both the macro- and micro-scales of an associated Ginzburg-Landau superconducting phase transition. Application of Ginzburg-Landau theory and the scaling laws reveal a coherence length and a penetration depth for a macro-scale dual superconductor. The coherence length determines non-extensive volume changes whilst its inverse gives the Higgs mass. The penetration depth determines the extent of QCD vacuum suppression whilst its inverse gives the vector boson mass together with its indirect manifestation as non-additive hyperbolic curvature. External pressure perturbations of the low-energy system initiate ‘rolling’ critical responses that see energy and momentum conserved across a synchronized U(2) symmetry group whilst a complex gauge field is also exposed. Simultaneous emergence of the Ginzburg-Landau superconducting phase transition is consistent with gauge-invariant coupling of this scalar field to the Yang-Mills action of QCD. The discovery of an energy gap in the gradient energy term of the system Lagrangian is associated with a critical correlation length revealed in the transition from a gapped to a gapless superconducting state. Together with the emergence and absorption of the Higgs-like scalar field, a mechanism for describing the QCD mass gap arises.

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses; but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created.

The coupled Dirac equations for solar e- and μ-neutrinos are solved in the presence of a small uniform interaction of the e-neutrinos with matter (the Sun). It is shown that the interaction leads to an increase of the amplitude of the neutrinos oscillations and a decrease of the lo- calization probability of the e-neutrinos. However, the strength of this interaction is insufficient to explain the magnitude of the discrepancy between the solar neutrino flux and the neutrino flux measured on the Earth. An alternative interpretation related to a possible superfluid neutrino state is advanced, which may throw some light on the solar neutrino problem.

We review the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. As an example of practical worth, we consider the Drell-Yan process and discuss the gauge invariance of the corresponding hadron tensor. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in SU(3) gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

A new method for multi-shot reconstruction of high-energy photon distributions in the context of studying the interaction between a beam and a plasma in plasma wakefield acceleration (PWFA) experiments is presented. The study investigates the effects of beam perturbations on betatron radiation and analyzes how these perturbations can lead to hosing, a transverse instability that can degrade the quality of the beam. The potential of betatron radiation spectroscopy as a non-invasive diagnostic technique for PWFA experiments is also emphasized.

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD generating functional integral. It obeys the principle of renormalizability of Quantum Field Theory and does not involve new particles like axions.

In this paper we will provide a new equation that explains why there are three generations or families of leptons and quarks, respectively. We will also explain why all those particles have the known mass ratios amongst their three respective generations and flavors. We will also tackle the problem of Yukawa couplings being arbitrary parameters in the Standard Model Higgs mechanism, which is a long standing problem do to their formulaic dependence on the Higgs Vacuum Expectation Value (VEV). We will attempt to solve this problem and provide a strong argument through an equation for Yukawa couplings of all leptons and quarks via a new methodology that depends on the running of the fine-structure constant on the Q scale, quantum numbers and the Weinberg angle (also on the Q scale). We will also make predictions for all three left-chiral neutrino mass eigenstates and we will provide upper limits for the three right-chiral neutrino mass eigenstates

In this article, we give a brief review of the origin of the neutrino mass in some interesting non-linear supersymmetric models with R-symmetry. These models are able to address and solve the most important problems of the particle physics and provide mechanisms for neutrino mass generation and their mixing parameters in agreement with the current experimental data. Their prediction could be experimentally tested in the near future by collider experiments.

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the universal formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors. Expressions for the electric and magnetic fields of a photon during its interaction with an electron.Thus, a unified way to describe bosons and fermions in spinor space is proposed. Each spinor using the same formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field, coordinates and momentum vectors of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.While quantum mechanics treats probability as a real number, quantum field theory deals with probability as a four-dimensional real vector. The place of the probability amplitude, which in quantum mechanics is a complex number, in quantum field theory is taken by a complex spinor.In the same way as in quantum mechanics the processes of propagation and interaction are described at the level of complex probability amplitudes, and the final result is translated into a real probability value, so in quantum field theory all processes should be described in terms of complex spinor space, and the result is translated into the form of a real vector in Minkowski space.The presented approach, at its proper development, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

The question of whether some neutrinos are tachyons remains unresolved although various evidence from cosmic ray and other data exists that the electron neutrino has an effective $m_\nu^2\approx -0.25 eV^2,$ which would require that one or more mass states is also tachyonic. In 2013 the $3+3$ model of the neutrino masses, which includes one tachyonic mass state, was proposed based on supernova SN 1987A neutrino data. Here we update evidence for tachyonic electron neutrinos and the $3+3$ model and discuss one test which could prove conclusive. The update of earlier evidence includes many new elements, including new data which makes the earlier cosmic ray evidence more robust, new results on cosmic ray composition, the ankle of the spectrum, leptonic cosmic ray data, and the statistical significance of finding the three large neutrino masses stipulated in the $3+3$ model. Barring a galactic supernova, which occur only around twice a century, a decisive test of the $3+3$ model could involve observing an extragalactic supernova neutrino burst, that is a cluster of neutrinos in a specific time window well beyond what chance would predict. Even though existing searches for such bursts have yielded only upper limits on the extragalactic supernova frequency within a certain distance, it is shown that the choice of a one-day window for possible neutrino clusters in time might be far more sensitive. A search using a one day time window could be done using existing data, and if a signal is found it would confirm the $3+3$ model. Of course, the absence of any day-long neutrino burst would not disprove the model, since it could mean only that the nearest supernova during the period when detectors were active was simply too far to be detected. Finally, apart from testing the 3 + 3 model, an alternative type of search is suggested using existing hadronic cosmic ray data (from the IceCube Collaboration) that might verify the tachyonic neutrino hypothesis.

In any region of a space, the gravitational field cannot be eliminated. The speed of light in a vacuum has never been observed and cannot be observed with current technology. Till now, only the speed of light in a gravitational field has been observed. It results in that all the observed speed of light are always being varied by the gravity. Here, it is presented that light could be dispersion in a gravitational field analogous to the dispersion of light in the Newtonian prism experiment. The relativistic mass density on the surface of a neutron star is on the level of 10¹⁷kg/m³ while on the surface of the Earth is only 10^-7kg/m³, the effect of the gravitational field acting on the speed of light by a neutron star is much larger than that by the Earth. Therefore, the dispersion of light in strong gravitational field could be generally observed from the image of a star and it should have been observed through the double-image gravitational lensing and the spectroscopic binary system. And, it should affect the observed numbers, spectrogram, size and distance of the celestial objects.

Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the $\lambda\phi^4$ theory in three dimensions and make a comparison between the sharp-cutoff regularization method and other more recent methods. The former gives considerably better results, while the other methods are far from optimal in the perturbative domain. In addition, these methods present theoretical problems that are already manifest in the renormalization of mass.

The aim this text to present the confined covariant quark model (CCQM) and review its applications to the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we review also. The physics principles are in detail exposed for the CCQM, the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering successively three categories of decay processes: leptonic, semileptonic and non-leptonic.

The origin of an anomalous excess of high-energy (about 100 GeV and higher) positrons in cosmic rays is one of the rare problems in this field which is proposed to be solved with dark matter (DM). Attempts to solve this problem are faced with the issue of having to satisfy the data on cosmic positrons and cosmic gamma-radiation, which inevitably accompanies positron production such as FSR (final state radiation), simultaneously. We have been trying to come up with a solution by means of two approaches: making assumptions (*) about the spatial distribution of the dark matter, and (**) about the physics of its interactions. This work is some small final step of a big investigation regarding the search for gamma suppression by employing the second approach and a model with a doubly charged particle decaying into two positrons (X++→e+e+) is suggested as the most prospective one from those considered before.

In this work the author utilizes the quantum geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

Our matter universe is made up of four components of dark energy (DE), dark matters (DMs), leptons and quarks which are created from the decay of the primary black hole through the inflation after big bang. In the three-dimensional quantized space model, the sum (DER) of the dark energy (DE) and radiations (R) is the flat photon space and there are 39 particles of 3 dark matters, 9 leptons and 27 quarks. Generally speaking, the mass ratio of the quarks with the 27 particles is smallest and the mass ratio of the DER photon space with the 1 massless photon is largest. Therefore, the mass ratios of DER, DMs, leptons and quarks are inversely proportional to the particle numbers of DER, DMs, leptons and quarks as the first assumption. This simple rule is called as the universe mass ratio golden rule in Fig. 12. This simple rule is successfully applied to the observed mass ratios of the Planck and WMAP missions. The best particle number combination (1, 3, 9, 27) of the four components (DER, DMs, Leptons, Quarks) to explain the Planck 2018 and WMAP results is the same as the particle number combination (1, 3, 9, 27) of the 3-dimensional quantized space model. The calculated mass ratios of DER, DMs, leptons and quarks are 67.5 %, 22.5 %, 7.5 % and 2.5 %, respectively. And the calculated mass ratios of neutrinos and ordinary matters are 5.0 % and 5.0 %, respectively. The mass ratios of the dark energy (68.47(23) %) and matters (31.53(23) %) obtained from the Planck 2018 results are consistent with the calculated mass ratios of the DER (67.5 %) and matters (32.5 %). The mass ratio of the dark energy (72.1(15) %) obtained from the WMAP 9 year results is explained as the summed mass ratio (72.5 %) of DER (67.5 %) and neutrinos (5.0 %). The universe evolution including the super-massive black holes (SMBHs) is shown in Fig. 4. The accelerated space expansion of our universe requires the addition of the new dark energy. If this new dark energy is added, the mass ratio of the dark energy is a little bit increased. The difference (0.97 %) between the observed value (68.47(23) %) and calculated value (67.5 %) is explained by adding the new dark energy in Figs. 2, 4, 7, 8, 9, 10 and 11. The corrected mass ratios of DER, DMs, leptons and quarks are 68.47 %, 21.8286 %, 7.2762 % and 2.4254 %, respectively. The corrected mass ratios of the neutrinos (called as cosmic background neutrinos) and ordinary matters (OMs) are 4.8508 % and 4.8508 %, respectively. These corrected mass ratios can explain the mass ratios obtained from the WMAP and Planck missions. In other words, the mass ratios calculated from the best particle number combination support the elementary particles, dark matters and dark energy (photon space) proposed by the three-dimensional quantized space model based on the 10-D Euclidean space.

The scalar meson f0(980) has been a long-standing puzzle in light hadron physics. The mass and width of the f0(980) in normal decay processes are estimated to be M=990±20 MeV/c2 and Γ=40−100 MeV, respectively. Theoretically, the internal structure of the f0(980) is proposed to be a conventional quark-antiquark meson, tetraquarks state, KK¯ molecule, or quark-antiquark gluon hybrid. So far, explanations about the nature of f0(980) have been controversial for a long time. Recently, anomalously narrow width f0(980) were observed by the BESIII experiment in five independent isospin-violating decay channels. Based on the experimental data, we performed a simultaneous fit to ππ invariant mass distributions, and the mass and width in isospin-violating decays are determined to be M=990.0±0.4 MeV/c2 and Γ=11.4±1.1 MeV, respectively. In addition, we use the parameterized Flatté formula to simultaneously fit the same ππ invariant mass distributions, the two coupling constants of gfππ and gfKK¯ are measured to be gfππ=0.46±0.03 and gfKK¯=1.24±0.32, respectively. According to the joint confidence regions of gfππ and gfKK¯, we conclude that the experimental data tend to support the KK¯ molecule model and the quark-antiquark (qq¯) model, but tend not to support the tetraquarks (q2q¯2) model and the quark-antiquark gluon (qq¯g) hybrid model.

The neutrino is perhaps the most elusive member of the particle zoo. The questions about its nature, namely: Dirac or Majorana, the value of its mass and the interactions with other particles, the number of its components including sterile species, are long standing ones and still re- main in large extent without conclusive answers. From the side of the nuclear structure and nuclear reactions, both theories and experiments, the need to elucidate these questions have, and still has, prompt crucial developments in the fields of double beta decay, double charge exchange and neutrino induced reactions. The measurements of neutrino flavor os- cillation parameters contribute largely to restrict models with massless neutrinos. From the particle physics side, the possibilities to extent the standard model of electroweak interactions to incorporate a right handed sector of the electroweak lagrangian are directly linked to the adopted neu- trino model. Here, I would like to address another aspect of the problem by asking the question of the neutrino mass mechanism in the cosmological context, and particularly about dark matter.

In particle physics, spin is an intrinsic form of angular momentum carried by the elementary particles. It is believed that spin is a solely quantum-mechanical phenomenon, which does not have a counterpart in classical mechanics. We have derived the simplest equations of spin and magnetic moment of a charged elementary particle. These formulas enable us to understand the physical nature of the spin and the structure of elementary particles. It is shown that the electron and muon are in the shape of a thin ring with a circular cross section (torus), and the proton is in the form of a ring with a non-circular cross section (toroid). The connection between the photon’s spin of and the propagation of electromagnetic waves is considered.

As a first step a unification of the gravitational with the electromagnetic interaction within a classical framework is proposed. It is based on a V₅-geometry, with x₅ = q/m. The sole source term is mechanical stress energy, positioned along x₅. The trajectories of test-bodies are placed in V₄ (x₅ = const)-slices. The resulting field equation couples a geometric G-tensor to mechanical stress energy, its momentum with respect to V₅ and the change of this momentum with proper time τ. The following step proceeds to the quantization of space-time to enable the formalization of elementary particles und strong interaction. This is complimented by the inclusion of spin and the weak force, leading finally to a grand total equation, the stationary version of which corresponds to Schroedinger´s equation, the instationary version to the Einstein equation of General Relativity.

When discussing the gauge symmetries of any theory, the Henneaux-Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux-Teitelboim transformations and the resulting gauge group in the general case, and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving a system of singular Wiener-Hopf integral equations, which is further solved by the Wiener-Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues.

Starting from an overview of neutrino problems and a simplified survey of Fermi’s neutrino theory, it is shown why neutrinos are left-handed and why they seem to show an oscillatory behaviour between their flavours. After addressing the question how to assess the naked mass of the true elementary particles, it is hypothesized that the elementary constituents of the nuclear background energy and the cosmological background energy are the same. This allows to derive the magnitude of the quark’s “naked” mass from the polarization of the vacuum.

We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, charge-less, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, , are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.

Large inconsistencies in the outcome of precise measurements of Newtonian gravitational ‘constant’ were identified throughout more than three hundred experiments conducted up to date. This paper illustrates the dependency of the Newtonian gravitational parameter on the curvature of the background and the associated field strength of vacuum energy. Additionally, the derived interaction field equations show that boundary interactions and spin-spin correlations of vacuum and conventional energy densities contribute to the emergence of mass. Experimental conditions are recommended to achieve consistent outcomes of the parameter precision measurements, which can directly falsify or provide confirmations to the presented field equations.

Our knowledge of electricity is based on two parallel lines of research: one focusing on ‘charge’, the other on ‘electron’. The distinction is blurred. The difficulty is that the fundamental nature of elementary charge is unknown. Here I present evidence that charge is a resting electron and electron is a moving charge – one physical entity two behavioural identities. That is, charge is nonrelativistic electron and electron is relativistic charge. Charges obey the laws of static electricity (electrostatics); electrons obey the laws of moving electricity (electrodynamics). Whether positive or negative, a charge is ejected from the atom at tremendous speed, losing the characteristics of ‘a charge’ and gaining those of ‘an electron’. I conclude that an atom, hence nature in general, contains an equal number of positive and negative electrons, recognised at rest as opposite charges. This solves the mystery of the electron-positron numerical asymmetry. It means that static positions and negatrons (charges) play equivalent roles as subatomic building blocks of matter, revealing a new atomic structure.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces of nature in a unified manner. Thus, each force must furnish a system of units with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is Dirac's fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties imposed by the vacuum itself, thus they must be present in all systems of units. The upgraded Planck system with fundamental units $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide's $K=2/3$ enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of only $K$.

To sustain and advance the development of our laboratory, it is imperative for the laboratory 1 personnel to consistently deliver high-quality products and services that meet customer expectations. 2 The progress of productivity and the pace of technological advancements result in constant evolution 3 of measurement procedures, analytical techniques, and overall work methods. Our research within 4 the Neutron Activation Analysis (NAA) laboratory is aimed at contributing to the establishment of 5 quality assurance that complies with the ISO 17025 standard. As such, the laboratory implements 6 quality-oriented approaches to foster a culture of continuous improvement in its detector operations 7 and enhance customer satisfaction.

A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.

Dirac’s equation depicts electron mass as either positive or negative. Taken as correct description of nature, the equation identifies electron mass as ‘electrically active’ and therefore fundamentally different from the ordinary, ‘electrically passive’ mass. Following this cue, I demonstrate that electron mass (m_e) is the natural elementary mass: positive (m_e⁺) and negative (m_e^–) elementary masses neutralise to an elementary unit of the electrically passive mass (2m_e⁰). Further, I show that electron mass (m_e^± ) and the electrostatic field (e_f^±) surrounding it compose an elementary charge (e^±), thereby relating charge to mass. Two plain principles underlie these findings. 1) Electric charge and gravitational mass have a common root: positive (e⁺) and negative (e^–) charges coexist as neutral charge (2e⁰), which is the quantum of gravitational mass. 2) Charge is a static (nonrelativistic) ‘atom of electricity’ and obeys the laws of electrostatics; electron is the same ‘atom of electricity’ at ultrahigh (relativistic) speed and obeys the laws of electrodynamics. That is, charges are electricity at rest; electrons are electricity in motion – ‘same physical entities two behavioural identities.’ A decisive proof that this paradigm shift correctly portrays is that it verifiably unifies Newton’s law of gravity and Coulomb’s law of electrostatics to: 8G/m_pm_e = K/e²; where G and K are the respective constants, m_p the proton mass, m_e the electron mass, and e the elementary charge. Ultimately, the insights simplify matter to pure ‘atoms’ of positive and negative electricity.

In the extended scalar sector of the SMASH (Standard Model - Axion - Seesaw - Higgs portal inflation) framework, we conduct a phenomenological investigation of the observable effects. In a suitable region of the SMASH scalar parameter spaces, we solve the vacuum metastability problem and discuss the one-loop correction to the triple Higgs coupling, $\lambda_{HHH}$. The $\lambda_{HHH}$ and SM Higgs quartic coupling $\lambda_H$ corrections are found to be proportional to the threshold correction. A large $\lambda_{HHH}$ correction ($\gtrsim 5 \%$) implies vacuum instability in the model and thus limits the general class of theories that use threshold correction. We performed a full two-loop renormalization group analysis of the SMASH model. The SMASH framework has also been used to estimate the evolution of lepton asymmetry in the universe.

In an historic perspective on the development of the Standard Model of particle physics it is shown how mathematically driven axioms have masked the merits of a physically comprehensible structural view. It is concluded that the difference between the two approaches can be traced back to two major issues. Whereas in the Standard Model the quark is a Dirac particle with a single real dipole moment, the quark in the structural model, in confinement with other quarks, is a Dirac particle with two real dipole moments. The second issue is the view that empty space does not exist, but that space is filled with a polarisable energetic fluid. It is shown how recognition of these two issues pave a road to reconcile particle physics with gravity, in which the quark can be seen as a magnetic electron and in which the gluon, as the strong force carrier, can be seen as a massive photon.

The negative energy solutions of the Klein-Gordon and Dirac equations have been used to define the antiparticle with the positive energy from the Feynman - Stueckelberg interpretation in the standard model based on the 4-D Minkowski space with the relative time. The negative energy solutions of the Klein-Gordon and Dirac equations are used to define the antiparticles with the negative energy in the present 3-D quantized space model. Note that all the present results are based on the 4-D Euclidean space with the absolute time (t) and relative time (t_l). Then the particle with the positive energy and antiparticle with the negative energy have the 4-D P₄ = TCP = T_cP symmetry. The continuity equations are derived from the Klein-Gordon, Dirac and Schrodinger equations. The Klein-Gordon and Schrodinger equations with the potential barriers are solved. The Klein paradox is explained by using the pair production of the electron with the positive energy and positron with the negative energy under the P₄ = _TcP symmetry, The effective velocity ( c_eff=√2 " c " ) and effective energy ("Etl =" √2 E ) along the relative time axis (ctl) give the relative time momentum of "p_tl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. This indicates that the photons with the energy of E have the constant photon velocity of c and the constant photon momentum of "ptl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. For the negative energy particles, the space momentum directions are opposite to the particle velocity directions because the energy is negative. And the matter collapse to the photons at the very high particle velocity is discussed from the length expansion. It is, for the first time, proposed that the gamma ray burst is originated from the matter collapse to the photons near the black hole. Also, the wave function collapse is explained from the length expansion. The wave function collapse takes place when the measurement makes the particle velocity to be zero. It is concluded that the negative energy solutions of the Klein-Gordon and Dirac equations support the existence of the partner antimatter universe with the negative energy and negative time direction. Our matter universe has the positive energy and the positive time direction.

The super-weak interaction includes three simple extensions of the standard model: gauge extension, fermionic extension, and scalar extension. All of these extensions are strongly influenced by their complex phenomenology. They can explain a number of unresolved questions in particle physics and cosmology, including the genesis of dark matter, cosmic inflation, asymmetry of matter and antimatter, neutrino masses, and vacuum stability, if combined into a single structure. This is an extension of the gauge group of the standard model $G_{\rm SM}$ by $G_{\rm SM}\otimes U(1)_Z$ without any anomalies. We investigate the implications of the development of a general Majorana mass renormalization group for neutrinos with masses in the range of 0.03 $eV$ and 0.1 $eV$, which fall within the recently published range as well as the range to be explored in future planned experiments.

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system with an electromagnetic field, leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress-energy tensor expresses relativistic Cauchy's momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

We propose a phenomenological theory of spin behavior in a magnetic field, which explains from the point of view of classical physics the two-valued result of the Stern-Gerlach experiment. The behavior of the spin and intrinsic magnetic moment of an electron wave of an atom in an external magnetic field is considered. We show that in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector. Within the framework of classical electrodynamics, the calculation of the motion of an atomic beam in an inhomogeneous magnetic field is carried out, which reproduces the results of the Stern-Gerlach experiment.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

The absolute time and relative time are defined in terms of the 4-D Euclidean space. Our universe is the 3-D x₁x₂x₃ quantized photon space which follows the absolute time simultaneity when the universe moves along the absolute time axis of ct. The length expansion of Dx = gDx₀ is derived under the condition of the absolute time (ct) simultaneity. From the similarity between this length expansion of Dx = gDx₀ and the energy increasing of E = gE₀, it is assumed that the energy is proportional to the particle size of Dx. The extension of this assumption to the 4-D Euclidean space gives the new definition that the particle energy (E) is the 4-D volume. Then, the particle mass energy is defined as E= mc² = cDtDV = gE₀. The masses of the elementary particles are originated from the 4-D warped volume of the photon space because the particle is the warped photon space with the velocity of v < c. Therefore, the Higgs boson concept in the standard model (SM) is not needed in the present 3-D quantized space model (TQSM). The scalar boson with the spin of zero, photon with the spin of 1 and graviton with the spin of 2 are the two-boson states. Therefore, the observed Higgs boson is reinterpreted as the two-boson state of the scalar boson with the spin of zero. The cosmic muon observation and twin paradox are explained by using the absolute time and relative time. The relative time is the observed time in the twin paradox and cosmic muon observation. In the twin paradox, a person who travels the long distance is more aged than a person on the earth in terms of the relative time ages because of the space and time conversion effect (STCE effect) of the moving space distance (x). But twins are in the same ages in terms of the absolute time without STCE effect. The fast-moving cosmic muon has the expanded half-life from the time expansion of the relative time. Also, the quantum entanglement and Pauli exclusion principle are explained. The quantum base of the photon space line connects two entangled particles. Two particles and quantum base system is fluctuated along the absolute time axis by the time clicking when one particle is measured. Another particle is instantly selected by the time clicking. This is called as the quantum entanglement. The photons which are the flat photon space with the constant speed of c along the space axis and absolute time axis have the 4-D photon velocity of c_eff = 2^0.5 c. Total 10-D Euclidean space including three 3-D quantized spaces and one absolute time axis is required for the electric charges (EC), lepton charges (CC) and color charges (CC) of the elementary particles. The 3-D photon space is very stiff along the absolute time (ct) axis and very soft along the space axes. The Coulomb force through the photons (2EM waves) of the space fluctuations is much stronger than the Gravitational force through the gravitons (G waves) of the time fluctuations between two electrons.

Natural systems of units $\{U_i\}$ need to be overhauled to include the dimensionless coupling constants $\{\upalpha_{U_i}\}$ of the natural forces. Otherwise, they cannot quantify all forces in a unified manner. Thus, each force must furnish a system with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{ G, \upalpha_G \}$, thus it cannot account for gravitation. The cosmological system discounts $\{ \slashed{h}, \upalpha_\slashed{h} \}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, $\upalpha_G$ is the gravitational coupling constant and $\upalpha_\slashed{h}$ is the fine-structure constant. The speed of light $c$ and the impedance of free space $Z_0$ are resistive properties of the vacuum, thus they must be present in all systems of units. The upgraded Planck system $${\rm UPS} \,:=\,\{ c, Z_0, G, \upalpha_G, \slashed{h}, \upalpha_\slashed{h}, \,\dots\,\!\},$$ describes all physical scales in the universe---it is nature's system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics, and some of which have been designated as mere coincidences. Based on the UPS results, that relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed/measured physical properties are coincidental in this universe.

The well-known coupling between the magnetic and electric fields in electromagnetic radiation is revisited in light of the recent introduction of a microscopic theory for the Ørsted magnetic field induction. I argue that, if the Ørsted magnetic field induction does indeed have a microscopic origin rather than the continuum solution offered by the Maxwell-Ampere equation, the "electromagnetic wave"' propagating in vacuum will not have a magnetic component.

Measured values of the electron mass and Compton wavelength produce a value of Planck's constant with a relative standard uncertainty of 3 x 10^-10. This is only slightly larger than the 1.3 x 10^-10 relative standard uncertainty in measurements performed using the Kibble balance. Compton scattering represents an alternative pathway to improving the value of Planck's constant in the future. Natural units of length, mass, and time offer new pathways to improving the values of physical constants. While extensive values of the Planck units lie beyond the reach of present-day instrumentation, certain product and quotient pairs of Planck units such as the speed of light can be measured with relatively high precision. Better measurements of certain unit pairs will improve the value of the gravitational constant.

In this study, we describe quark confinement in terms of linear interaction potentials and solve the problem of the net spin of a proton. The three quarks in a proton are assumed to revolve around a common center, and their masses are determined assuming they are Dirac particles. On the basis of these assumptions, the magnetic moment of a proton can be derived. Moreover, the rotation of the quarks is considered, in which an electrical current induces a magnetic field. Thus, the scalar product of the magnetic moment and field describes the linear interaction potential between the quarks, and the mass of the proton can be obtained. The proton mass predicted by this physical model is consistent with experimental values, and no numerical or fitting calculations are required. Furthermore, using the newly derived spins and angular momentum of the three quarks, we derived the net spin of a proton. Additionally, we predicted the mass of a pi-meson from the same model, which agrees with the experimental values.

“Non-Locality is most naturally incorporated into a theory in which there is a special frame of reference. One possible candidate for this special frame of reference is the one in which the Cosmic Microwave Background (CMB) is isotropic. However, other than the fact that a realistic interpretation of quantum mechanics requires a preferred frame and the CMB provides us with one, there is no readily apparent reason why the two should be linked” (L. Hardy). Starting from this remark we first argue that, given the present view of the vacuum, the basic tenets of Quantum Field Theory cannot guarantee that Einstein Special Relativity, with no preferred frame, is the physically realized version of relativity. Then, to try to understand the nature of the hypothetical preferred Σ−frame, we consider the so called ether-drift experiments, those precise optical measurements that try to detect in laboratory a small angular dependence of the two-way velocity of light and then to correlate this angular dependence with the direct CMB observations with satellites in space. By considering all experiments performed so far, from Michelson-Morley to the present experiments with optical resonators, and analyzing the small observed residuals in a modern theoretical framework, the long sought Σ− frame tight to the CMB naturally emerges. Finally, if quantum non-locality reflects some effect propagating at vastly superluminal speed vQI→∞, its ultimate origin could be hidden somewhere in the infinite speed cs→∞ of vacuum density fluctuations.

A 9.4 T/400 MHz superconducting magnet with a warm bore of 60 mm is being designed. The 400 MHz NMR magnet is composed of 9 coaxial coils to generate a central field of 9.4 T. The magnetic field homogeneity is better than 4 ppm for 50 mm diameter spherical volume (DSV) and better than 1 ppb for 5 mm DSV. Three types of NbTi strands were used to reduce the cost of the superconducting materials. A preload with 80 MPa was exerted on the superconducting coils and over-banding with stainless steel was adopted to release the stress from the electromagnetic forces. The magnet will be operated in persistent mode with superconducting joints to reduce the field decay. The pulse tube cryocooler with a cooling capacity of 1 W at 4.2 K can be used to reduce the liquid helium evaporation and vibration during operation. The magnet will be equipped with Bi2223/AgAu HTS current leads to reduce the heat losses. In this paper, the design of the 9.4 T NMR superconducting coils, electromagnetic field calculations, and stress analysis of the superconducting coils were presented.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

This paper first explains the theory of the origin of force from a new perspective, explaining that the origin of all forces is caused by the "missing of energy in the time dimension" (non-conservation in a certain period of time), and constructs a unified theory of force on this basis. Then, through the unified theory of force, the following phenomena are reinterpreted: (1) The common origin of the inverse square law of gravitation and electromagnetic force; (2) The origin of the repulsive force of electrons and protons at small distances; (3) The mystery of the rotation curve of galaxies and the new explanation of "dark matter"; (4) explain the origin of the magnetic field; (5) Predict that moving magnets have the same radiation effect as charged particles (electron magnetic moments also have radiation effects); (6) Reinterpret Maxwell's displacement current; (7) Reinterpret synchrotron radiation and bremsstrahlung; (8) Explain that the strong and weak forces are short-range forces; (9) Predict the true structure of black holes and the origin of gravitational waves;(10) Possible explanation for the origin of the speed of light.

The description of stellar interiors remains as a big challenge for the nuclear astrophysics community. The consolidated knowledge is restricted to density regions around the saturation of hadronic matter $\rho _{0} = 2.8\times 10^{14} {\rm\ g\ cm^{-3}}$, regimes where our nuclear models are successfully applied. As one moves towards higher densities and extreme conditions up to five to twenty times $\rho_{0}$, little can be said about the microphysics of such obejects. Here, we employ an MCMC strategy in order to access the variability of polytropic three-pircewised models for neutron star equation of states. With a fixed description of the hadronic matter we explore a variety of models for the high density regimes leading to stellar masses up to 2.5 $M_{\odot}$. In addition, we also discuss the use of a Bayesian power regression model with heteroscedastic error. The set of EoS from LIGO was used as inputs and treated as data set for testing case.

The Multi-Level Model (=MLM) was suggested by A. Levichev as a description of quarks and gluons. The review recalls MLM-terminology while MLM-findings (for quarks and leptons) are compared to the theoretical and experimental data as accepted by the Standard Model (=SM). MLM is based on Segal’s compact space-time U(2) and on the sequence of embeddings: U(2) into U(3), U(2) into U(4), etc. These groups were called the levels (of matter): U(2) - the 0th (that is, our mundane world), U(3) - the 1st, U(4) - the 2nd, etc. Such a convention matches the SM-quarks' generations list. Each SM-quark is viewed either as a sunken proton, or as a captured proton. The MLM-proton is elementary and indestructible (hence no need for confinement). For MLM-quarks, in terms of the notion of a ruling group, flavor and color are defined mathematically. The number of colors (and of flavors) is level-dependent. For levels U(3) through U(6) the correspondence with the SM-quarks is established. Three new quarks and two new leptons are predicted. The SM-puzzle of quark and lepton generations is solved. Using the Han-Nambu scheme, the notion of the quark’s electric charge is expressed in terms of color charges. The original part of the review suggests studying the proton’s properties (like mass, shape and inner pressure) on the ba-sis of its wave function.

We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.

This short reading is an extraction from our previous work (Nyambuya 2020), the purpose of which is to make clear that it is very much possible to use Weyl (1918)'s idea of a conformal metric to achieve tensorial affinities. We are of the strong view that this is very important as it is predominantly assumed that this not possible. We want to dispel this myth once and for al-time.

The time symmetry of T_c = CT is redefined based on the 4-D Euclidean space. The time inversion symmetry of T_c = CT changes the signs of the charge (q) and absolute time (ct) of the particle. The P symmetry changes the signs of the space momenta and handedness of the particle. The T_c symmetry changes the signs of the time momentum (P_t=E/c) and charges. The handedness are classified as the left-handedness and right-handedness on the 3-D space. The charges (|q| = cDt) and energies (E= cDtDV) of the particles are originated from the upward warping (q>0) and downward warping (q<0) of the particles along the time axis. The evolution of our matter universe with P_t > 0 since the big bang can be interpreted based on the CTP symmetry with the partner antimatter universe with p_t < 0. The photon space is called as the vacuum space. Then the E and M waves are the space fluctuations, and the gravitational G wave is the time fluctuations. And the E, M and G fields are newly explained. The zero E and M fields of the photon space indicates that the photon space and gamma ray are the 2EM waves. The rest mass energy of the particle is the 4-D space volume of the warped photon space. In the present work, the quantum wave function is considered as the 4-D vector with the space wave function and time axis wave function in the 4-D Euclidean space. The warped photon space corresponds to the squared wave function which is the probability density. It is concluded that, in the quantum mechanics, the imaginary number concept is introduced in the quantum wave functions instead of the time axis component of the 4-D wave function vector. The left-handed neutrino puzzle is explained from the handedness partner relation with the right-handed dark matters. Finally, the modified Lorentz transformations derived in the 4-D Euclidean space are compared with the Lorentz transformations of the special and general relativity theories in the 4-D Minkowski space.

The spin magnetic moments and spin g factors (g_s = -2) of electron, muon and tau are explained based on the electric charges (EC) and lepton charges (LC) in terms of the three-dimensional quantized space model. The spin g factors of electron, muon and tau are g_s = -2 which is the sum of the EC g factor (g_EC = -1) and the LC g factor (g_LC = -1). The spin g factor (g_s = -2) of the electron is predicted by the Dirac’s equation. The orbit g factors of electron, muon and tau are g_L = g_EC = -1 from the EC g factor (g_EC = -1) without the contribution of the LC g factor (g_LC = -1). The spin g factors of the elementary fermions are calculated from the equation of g_s = g_EC + g_LC + g_CC where g_EC = EC/|EC|, g_LC = LC/|LC| and g_CC = CC/|CC|. For example, the spin g factors of the neutrinos and dark matters are g_s = -1. The spin g factors of the u and d quarks are g_s = 0 and g_s = -2, respectively. The g factor problem of neutrinos with the non-zero LC charges are solved by the LC Coulomb force of F_c(LC) ≈0. It is, for the first time, proposed that the binary motion (fluctuations) of the m_EC and m_LC masses for the electron, muon and tau leptons make the anomalous g factor. This binary motion could be originated from the virtual particle processes including the photons. Also, the weak force (beta) decay is closely related to the binary motion of the m_EC and m_LC for the electron, muon and tau leptons.

A geometric Planck-scale model of quantum electrodynamics is tested against observations. Based on Dirac’s proposal to describe spin 1/2 particles as tethered objects, elementary fermions are conjectured to be fluctuating rational tangles with unobservable tethers. As Battey-Pratt and Racey showed, when such tangles propagate, they obey the free Dirac equation. Classifying rational tangles yields the observed spectrum of elementary fermions. Classifying deformations of tangle cores yields exactly three types of gauge interactions. They exchange three types of elementary gauge bosons and have the symmetry groups U(1), broken SU(2) and SU(3). The possible rational tangles for fermions, Higgs and gauge bosons allow only the observed Feynman diagrams. The complete Lagrangian of the standard model arises, including the Lagrangian of quantum electrodynamics. Over 50 tests of the tangle model are deduced. They include details on the perturbation expansion of the g-factor and the existence of limit values for electric and magnetic fields. Measurements agree with most tests, though this could change in the future. Some tests are genuine predictions that still need to be checked. In particular, the geometry of the process occurring at QED interaction vertices suggests an ab-initio estimate for the fine structure constant. In addition, the average geometric shapes of the elementary particle tangles suggest ab-initio lower and upper limits for the mass values of the electron and the other leptons.

It is shown that the four fundamental physical forces, i.e. weak interaction, strong interaction, electromagnetism and gravity, all have their origin in the quark as the single true elementary particle.This requires conceiving the quark as a Dirac particle in a pseudo-tachyon mode, which possesses two real dipole moments: the common one associated with its angular momentum and a second one that is polarisable in a scalar field. This Dirac particle carries a regular charge magnetic monopole without Dirac’s string, theorized by Comay. The boson carrier of its field of energy is the gluon showing an exponential decay of its spatial range because of the influence of an omni-present energetic background field, known as the Higgs field, in this article interpreted as the Lambda in Einstein’s Field Equation.

Using two metal insulated metal waveguides (MIM) and five resonator (a quadrilateral cavity and three rings with different dimensions), we design a plasmonic refractive index sensor. Using the time domain finite difference method, we examine and analyze the sensor performance (numerical analysis) and using the transmission line model method, we theoretically examine the performance of the sensor By summarizing these two methods and calculating the sensitivity coefficient S, quality coefficient Q and figure of merit (FOM), a plasmonic sensor with good performance is obtained. Using the supermods of the resonators, we will achieve a stable wavelength spectrum and a suitable and stable sensitivity coefficient spectrum. Challenges and changes that occur in different modes of this sensor will lead to a balanced and relatively good structure. This designed sensor can be useful in the development of integrated optical circuits.

A structure-based view on mesons is given, based upon the concept of an archetype quark, described as a pointlike source producing an energy flux, the spatial description of which is derived from Dirac’s second dipole moment. This enables to conceive the archetype meson (pion) as a structure that behaves as a one-body anharmonic quantum mechanical oscillator. All mesons appear being excitations of the archetype, thereby allowing a calculation of the mass spectrum without the use of empirical parameters for the masses of the quark flavors. This includes a physically comprehensible analysis of the spin-spin interaction between quarks. It also provides a solution for the eta-etaprime puzzle. Next to this, it is shown that quite some particles that are presently regarded as elementary, have a common root and can be traced back to a few archetypes only.

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

A half-harmonic oscillator, which gets its name because the coordinate is strictly positive, has been quantized and determined that it was a physically correct quantization. This positive result was found using affine quantization (AQ). The main purpose of this paper is to compare results of this new quantization procedure with those of canonical quantization (CQ). Using Ashtekar-like classical variables and CQ, we quantize the same toy model. While these two quantizations lead to different results, they both would reduce to the same classical Hamiltonian if $\hbar\rightarrow0$. Since these two quantizations have differing results, only one of the quantizations can be physically correct. Two brief sections illustrate how AQ can correctly help quantum gravity and the quantization of most field theory problems.

It is discovered that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*10¹⁶~5.87*10¹⁸kgm^-3 which can be larger than the mass density of the neutron star (~10¹⁷kgm^-3). And, the total relativistic mass of the gravitational field of the Sun is ~10⁷ times the mass of the Sun. For different stars, the relativistic mass of the gravitational field is larger as the mass density of the star is larger. In the Milky Way, the total relativistic mass of the gravitational fields is much larger than the total mass of the stars, planets and gas. And, the relativistic mass density of the observed strongest magnetic field is 2.17*10⁸kgm^-3. This discovery should be a new frame to understand the fundamental problem of physics.

The present study was aimed at revealing the influence of the mechanical stress induced by water molecules adsorption on the composition of crystalline phases in the ZrO2–3mol%Y2O3-nanoparticles. Three basic methods have been used to determine the phase transition: neutron diffraction, Raman microspectroscopic scanning, and X-ray diffraction. The fact of phase-structural β → α transformation and the simultaneous presence of two polymorphic structural modifications (β is the phase of the tetragonal syngony and α of monoclinic syngony in nanosized particles (9nm)) under normal physical conditions was established by these methods. Satisfactory consistency was achieved between the results obtained using different techniques.

It is extremely fascinating and astonishing that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*10¹⁶~5.87*10¹⁸kgm^-3 which can be larger than the mass density of the neutron star (~10¹⁷kgm^-3).Therefore, it is the author’s first intuitional imagining that this field could directly convert into mass. In so strong a gravitational field, electron and proton could be produced directly from graviton–photon collision. The gravitational field exists in everywhere in our universe. No vacuum that the region of a space is “empty” does exist. A particle is clearly always being acted on by the gravitational field. The quantum vacuum fluctuation and vacuum polarization need be re-understood with the interaction between photon and gravitational field. Therefore, the gravitational field is naturally one of the foundations of modern physics.

All fundamental Planck scale symmetries are restored on a global level when a new charge is postulated in a finite, closed, Euclidean discrete space. Gravity emerges as a residual effect of the electromagnetic force in this scenario, resulting in a deterministic toy universe driven by a single input parameter. Randomness is identified using a Chaintin argument. Aleph0 definite value is tied to the size of the universe. This is not an interpretation of Quantum Mechanics, but a deeper attempt to describe nature.

Unification based upon the generalisation of proper time is proposed as a comprehensive framework to account for the fundamental structure of matter, in a manner contrasting with the more familiar approach based on extra dimensions of space. The elementary properties of matter to be incorporated include the Standard Model of particle physics together with a source for the dark sector and a coherent formalism for quantum gravity. We elaborate upon the manner in which all such material phenomena and empirical properties as distributed in an extended 4-dimensional spacetime can be encompassed within, and derived from, the continuous flow of time alone via a generalised arithmetic form for infinitesimal intervals of proper time. This approach will also be compared and contrasted with the basic structure of causal set theory as a means of demonstrating how it is possible to construct a full physical theory essentially from elements of time alone, as explicitly developed from the most elementary level. The conception of time as utilised and elucidated in this theory, with emphasis upon the causal continuum properties and as the basis for unification, will be clarified.

Space-time evolution of our universe is explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (E = cDtDV), charges and energy density (|q| = r = cDt) and absolute time (ct) are newly defined based on the 4-D Euclidean space. The photon flat space with the constant energy density of r = cDt_q is proposed as the dark energy (DE). The dark energy is separated into the n DE and photon DE which create the new photon spaces with the constant energy density of r = cDt_q. The v DE is from the n pair production by the CPT symmetry and the photon DE is from the photon space pair production by the T symmetry. The vacuum energy crisis and Hubble’s constant puzzle are explained by the photon space with the n DE and photon DE. The big bang and inflation of the primary black hole is connected to the accelerated space expansion and big collapse of the photon space through the universe evolution. The big bang from the nothing is the pair production of the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry. Our universe is the matter universe with the negative charges of electric charge (EC), lepton charge (LC) and color charge (CC). This first universe is made of dark matter -, lepton -, and quark - primary black holes with the huge negative charges which cause the Coulomb repulsive forces much bigger than the gravitational forces. The huge Coulomb forces induce the inflation of the primary black holes, that decay to the super-massive black holes and particles.

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

The recent Planck Legacy release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. In addition, the spacetime curvature of the entire galaxy differs from one galaxy to another due to their diverse energy densities. This study considers both the implied positive curvature of the early Universe and the curvature across the entire galaxy as the curvature of ‘the background or the 4D bulk’ and distinguishes it from the localized curvature that is induced in the bulk by the presence of comparably smaller celestial objects that are regarded as ‘relativistic 4D branes’. Branes in different galaxies experience different bulk curvatures, thus their background or bulk curvature should be taken into consideration along with their energy densities when finding their induced curvatures. To account for the interaction between the bulk and branes, this paper presents extended field equations in terms of brane-world modified gravity consisting of conformal Einstein field equations with a boundary term, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic branes over the conformal space-time of the 4D bulk is presented.

We create a model universe by equipping a topological surface (system) with compact dimensions insulated by an information blocking horizon. The insulated compact WF can produce entanglement independent of distance. Interaction between the system and the WF changes the curvature of the first and the quantum state (frequency) of the second in an interconnected relationship. Thus, the field curvature measures the evolution of the particle WF as time. Positive field curvature creates pressure, whereas negative field curvature generates a vacuum, satisfying the Borsuk-Ulam Theorem and the Page and Wootters mechanism of static time. The accumulation of pressure or vacuum generates poles with contrasting dimensionalities, two-dimensional black hole horizons (time infinite), and four-dimensional cosmic voids (time zero). The orthogonality of the field and the compact WF give rise to global self-regulation that fine-tunes the cosmic parameters and can promote fractal topology. The four-dimensional vacuum in cosmic voids can produce an accelerating expansion without dark energy. When gravity effects are eliminated, we find a new, so far unexplored, order-increasing side of entropy. The verifiable and elegant hypothesis satisfies Mach's principle.

The relative force strengths of the Coulomb forces, gravitational forces, dark matter forces, weak forces and strong forces are compared for the dark matters, leptons, quarks, and normal matters (p and n baryons) in terms of the 3-D quantized space model. The quark confinement and asymptotic freedom are explained by the CC merging to the A(CC=-5)₃ state. The proton with the (EC,LC,CC) charge configuration of p(1,0,-5) is p(1,0) + A(CC=-5)₃. The A(CC=-5)₃ state has the 99.6% of the proton mass. The three quarks in p(1,0,-5) are asymptotically free in the EC and LC space of p(1,0) and are strongly confined in the CC space of A(CC=-5)₃. This means that the lepton beams in the deep inelastic scattering interact with three quarks in p(1,0) by the EC interaction and weak interaction. Then, the observed spin is the partial spin of p(1,0) which is 32.6 % of the total spin (1/2) of the proton. The A(CC=-5)₃ state has the 67.4 % of the proton spin. This explains the proton spin crisis. The EC charge distribution of the proton is the same to the EC charge distribution of p(1,0) which indicates that three quarks in p(1,0) are mostly near the proton surface. From the EC charge distribution of neutron, the 2 lepton system (called as the koron) of the koron is, for the first time, reported in the present work.

Space-time evolution is briefly explained by using the 3-dimensional quantized space model (TQSM) based on the 4-dimensional (4-D) Euclidean space. The energy (E=cDtDV), charges (|q|= cDt) and absolute time (ct) are newly defined based on the 4-D Euclidean space. The big bang is understood by the space-time evolution of the 4-D Euclidean space but not by the sudden 4-D Minkowski space-time creation. The big bang process created the matter universe with the positive energy and the partner anti-matter universe with the negative energy from the CPT symmetry. Our universe is the matter universe with the negative charges of electric charge (EC), lepton charge (LC) and color charge (CC). This first universe is made of three dark matter -, lepton -, and quark - primary black holes with the huge negative charges which cause the Coulomb repulsive forces much bigger than the gravitational forces. The huge Coulomb forces induce the inflation of the primary black holes, that decay to the super-massive black holes. The dark matter super-massive black holes surrounded by the normal matters and dark matters make the galaxies and galaxy clusters. The spiral arms of galaxies are closely related to the decay of the 3-D charged normal matter black holes to the 1-D charged normal matter black holes. The elementary leptons and quarks are created by the decay of the normal matter charged black holes, that is caused by the Coulomb forces much stronger than the gravitational forces. The Coulomb forces are very weak with the very small Coulomb constants (k₁(EC) = k_dd(EC) ) for the dark matters and very strong with the very big Coulomb constants (k₂(EC) = k_nn(EC)) for the normal matters because of the non-communication of the photons between the dark matters and normal matters. The photons are charge dependent and mass independent. But the dark matters and normal matters have the similar and very weak gravitational forces because of the communication of the gravitons between the dark matters and normal matters. The gravitons are charge independent and mass dependent. Note that the three kinds of charges (EC, LC and CC) and one kind of mass (m) exist in our matter universe. The dark matters, leptons and quarks have the charge configurations of (EC), (EC,LC) and (EC,LC,CC), respectively. Partial masses of elementary fermions are calculated, and the proton spin crisis is explained. The charged black holes are not the singularities.

In this article, we show theoretically and experimentally the formation of spin-waves band gaps in a magnonic crystal that was implemented by the deposition of periodic micro-structured strips of magnetite nanoparticles. A theoretical model describing the spectra of the transmitted spin-waves bandgaps is proposed. This is achieved using a simple model based on microwave transmission line theory and considering the presence of micro-structured strips of magnetite nanoparticles on the surface. Such magnonic crystal of equally spaced micro-structured strips of magnetite nanoparticles on the surface of an yttrium iron garnet thin film has been implemented and measured. The periodic micro-structured nanoparticles are deposited on the surface of such yttrium iron garnet single-crystal film grown on a gallium-gadolinium garnet substrate via dip-coating technique. Propagation of magnetostatic surface spin-waves is studied and it is shown that the presence of such periodic structure leads to the formation of spin-wave band gaps in the transmission characteristics. The spin-wave detection has been carried out using a pair of microwave antennas and a vector network analyzer. The results show that the periodic structure formed by the magnetite strips modifies the spectra of the transmitted spin waves producing band gaps.

Many models with structures of matter associated with a structure of extra spatial dimensions have been proposed in recent decades. On employing a further generalisation from the local 4-dimensional spacetime form to a general form for proper time, we describe how matter fields resembling the Standard Model of particle physics can be accommodated far more directly than with a higher-dimensional spacetime theory. The successful identification of key features of visible matter in this non-spatial sector of extra dimensions in turn motivates seeking a candidate for dark matter residing in the original extra spatial dimension sector, and provides a close guide for the explicit form this invisible matter might take. We describe how such Standard Model and dark matter sectors in different extra-dimensional branches of generalised proper time are gravitationally connected through their common root in the local 4-dimensional spacetime and consider further possible mutual interactions and implications in comparison with existing dark matter models. A yet further possible branch of generalised proper time can be connected with dark energy models, hence in principle accounting for all three major components of cosmological structure within this framework.

We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

Appling the controlling relative permittivity and permeability in the equations for the gravitational-magnetic-electric field interaction, a very large variation of the gravitational acceleration of the Earth by electric/magnetic field could be arrived at. This conclusion may be supported by some of the experiments for the gravitational effect of superconductivity.

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

As the Universe is dominated by of baryons, there must have been a process in early Universe creating such a asymmetry via baryon number violation. However, until recently all the confirmed experimental data indicate that lepton and baryon number are conserved in agreement with Standard Model of quarks and leptons. This paper proposes an alternative path of baryogenesis. Once the over abundant magnetic monopoles predicted by grand unification emerged at universe temperature of $10^{16}$ GeV, then their annihilation should first give rise to photons driving the expansion of the early universe. As the universe temperature dropped to the desert scale of around 10 EeV, departure from thermal equilibrium occurred. Thus the annihilation produced photons give rise to electron-positron pairs, which collide with remnant magnetic monopoles and antimonopoles. The resultant unstable intermediate X and antiX particle become asymmetric, and thereby leading to baryon asymmetry. The excess of antimonopoles corresponding to ten times of mass comparing with that of baryons provides a natural candidate for dark matter. The physics of such a desert regime baryogenesis can be simply characterized by three parameters. The collision predicts a ratio of particle and anti-particle equivalent to that of ultra-high-energy neutrino to their anti-particle, which can be tested by future observations, e.g., the constructing IceCube-Gen2.

Microscopes based on dielectric mesoscale particles, using the effect of a photonic jet or terajet in the terahertz range, are a promising tool for overcoming the diffraction limit. However, the image they generate has limited contrast, which limits the application of this method. In this letter, we demonstrate that it is possible to increase the contrast of an image based on dielectric mesoscale particles that provide the formation of photonic hooks. In this case, the illumination of the object is carried out by an oblique incidence of subwavelength terajet, which significantly (more than 2 times) increases the contrast of the image.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

This paper consists of two parts. In part I some new relations for a field theory with time intervals are derived. One concept of field theory evaluated is complementarity, another is field operators both defined within a time interval description. Part II includes specific results and commentary. Discussed are time interval dependent wave propagation surfaces for star source emission waves and derived is a metric propagation surface area requirement. The results allow to consider one same field that like gravitation within General Relativity applies to both non zero and zero mass. The associated field energy is space time dependent for non zero mass, and is related to a space time dependent metric tensor for zero mass wave particles. Defined is internal energy transfer where wave particle numbers increase linearly and mass and momentum diminish, decrease inversely with the distance from the wave emission source. The commentary are applications related to cosmological overall volume and temperature dependence.

Many experiments and collected data support general relativity as it explains spacetime as a smooth Riemannian manifold. However, general relativity does not explain the chaotic nature of spacetime on the quantum level, where determinism is almost impossible. This is one of the major problems in physics yet it requires a deeper theory to solve this incompatibility. In this research, a derivation made from Newton’s law of gravitation to better explain the behavior of spacetime in the quantum world with the assumption that spacetime is quantized with energy wave-particles and these wave-particles accumulate to form massive wave like particles (hence the standard model of particle physics). In the end, the derivation and the assumption together clearly illustrate general relativity and quantum theory.

An analysis is presented of the possible existence of a second anomalous dipole moment of Dirac’s particle next to the one associated with the angular momentum. It includes a discussion why, in spite of his own derivation, Dirac has doubted about its relevancy. It is shown why since then it has been overlooked and why it has vanished from leading textbooks. A critical survey is given on the reasons of its reject, including the failure of attempts to measure and the perceived violations of time reversal symmetry and charge-parity symmetry. It is emphasized that the anomalous electric dipole moment of the pointlike electron (AEDM) is fundamentally different from the quantum field type electric dipole moment of an electron (eEDM) as defined in the standard model of particle physics. The analysis has resulted into the identification of a third type Dirac particle, next to the electron type and the Majorana particle. It is shown that, unlike as in the case of the electron type, its second anomalous dipole moment is real valued and is therefore subject to polarization in a vector field. Examples are given that it may have a possible impact in the nuclear domain and in the gravitational domain.

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the group $F_4$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for up, charm and top quark. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ symmetry. We motivate from our Lagrangian as to why the eigenvalues computed in this work could bear a relation with mass ratios of quarks and leptons. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

Astrophysical accretion processes near the black hole candidates, such as active galactic nuclei (AGN), X-ray binary (XRB), and other astrophysical sources, are associated with high-energetic emission of radiation of relativistic particles and outflows (winds and/or jets). It is widely believed that the magnetic field plays a very important role to explain such high energetic processes in the vicinity of those astrophysical sources. In the present research note, we propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamical motion of charged particles in the vicinity of a weakly magnetized black hole. We show that in the presence of the magnetic field, the radius of the innermost stable circular orbits (ISCO) for a charged particle is located close to the black hole’s horizon. The fundamental frequencies, such as Keplerian and epicyclic frequencies of the charged particle are split into two parts due to the magnetic field, as an analog of the Zeeman effect. The orbital velocity of the charged particle measured by a local observer has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiating charged accelerating relativistic particle orbiting around the magnetized black hole.

In this paper, a relativistic scalar particle under Lorentz symmetry breaking effects in the presence of a scalar potential is investigated. We introduce the scalar potential by modifying the mass via transformation M → M+S(r) in the wave equation and analyze the behaviour of a scalar particle. We see that the analytical solution to the KleinGordon equation can be achieved, and the energy eigenvalues and the wave function depends on the Lorentz symmetry breaking parameters as well as potential

In this article, the general solution of the tachyonic Klein-Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex \omega-plane. In particular, it is proved that under given boundary conditions this solution does not contain any superluminal components. On the basis of this result, we infer that all possible spacelike wave equations describe the dynamics of subluminal particles endowed with imaginary mass. This result is validated for the Chodos equation, used to describe the hypothetical superluminal behaviour of neutrino. In this specific framework, it is proved that the wave packet propagates in spacetime with subluminal group velocities and that for enough small energies it behaves as a localized wave.

A grand unification of electroweak and strong forces is presented based on a new idea called Unified Charged Vectors. Using this new concept, it is shown that: The electroweak and strong forces can be unified into a single electro-weak-strong force. The various charges and coupling constants of fermions (like the electroweak mixing angle) can be predicted, rather than presupposed. The Lagrangian symmetries can be predicted rather than presupposed. The standard model Lagrangian can be cast into a simple unified form.

Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.

We prove that it is necessary to introduce the non-zero gluon masses into the fundamental Lagrangian of Quantum Chromodynamics in order to describe the mass-gap in the reaction of electron-positron annihilation into hadrons. A new restriction on the gluon masses is obtained. The renormalized theory with non-zero Lagrangian gluon masses is constructed.

The magnetic polarization tensor has a promising capability of determining the geometry and material properties of metallic samples. In this paper, a novel computation method is proposed to estimate the magnetic polarization tensors for the metallic samples using the boundary element method. In this method, the metallic sample is placed in a uniformly distributed magnetic field. Based on assumptions that the excitation frequency and/or the conductivity of the sample is very high, the metallic sample is regarded as a perfect electrical conductor (PEC). Therefore, the scattered field at a certain distance can be simulated. By utilising the boundary element method, the magnetic polarization tensor can be derived from the simulated scattered field. The theoretical calculation is presented and simulations and experiments have been carried out to validate the proposed method. The results from the simulation are matched with the analytical solution for the case of sphere samples. Moreover, there is a good agreement between the simulation results and the experimental results for the copper cylindrical samples.

The apparent shape of the black hole shadow provides a full description of the spin, the inclination angle and the charge of a Kerr black hole, without any astrophysical process or underlying theory in the astrophysical process.

The origins of the stellar mass neutron black holes and supermassive dark matter black holes without the singularities are reported based on the 4-D Euclidean space. The neutron black holes with the mass of m_BH = 5 – 15 m_sun are made by the 6-quark merged states (N_6q) of two neutrons with the mass (m(N_6q) = 10 m(n)) of 9.4 GeV/c² that gives the black hole mass gap of m_BH = 3 – 5 m_sun. Also, the supermassive black holes with the mass of m_SMBH = 10⁶ – 10¹¹ msun are made by the merged 3-D states (J(B1B2B3)₃ particles) of the dark matters. The supermassive black hole at the center of the Milky way galaxy has the mass of mSMBH = 4.1 10⁶ m_sun that is consistent with m_SMBH = 2.08 - 6.23 10⁶ m_sun calculated from the 3-D states (J(B1B2B3)₃ particles) of the dark matters with the mass of m(J) = 1.95 10¹⁵ eV/c². In other words, this supports the existence of the B1, B2 and B3 dark matters with the proposed masses. The first dark matter black hole (primary black hole) was created at the big bang. This first dark matter black hole decayed to the supermassive dark matter black holes through the secondary dark matter black holes that are explained by the merged states of the J(B1B2B3)₃ particles. The universe evolution is closely connected to the decaying process of the dark matter black holes since the big bang. The dark matter cloud states are proposed at the intermediate mass black hole range of m_IMBH = 10² – 10⁵ msun. This can explain why the dark matter black holes are not observed at the intermediate mass black hole range of m_IMBH = 10² – 10⁵ m_sun.

We consider the Dirac electron as a nonperturbative particle-like solution consistent with its own Kerr-Newman (KN) gravitational and electromagnetic field. We develop the earlier models of the KN electron regularized by Israel and López, and consider the non-perturbative electron model as a bag model formed by Higgs mechanism of symmetry breaking. The López regularization determines the unique shape of the electron in the form of a thin disk with a Compton radius reduced by 4π. In our model this disk is coupled with a closed circular string which is placed on the border of the disk and creates the caused by gravitation frame-dragging string tension produced by the vector potential of the Wilson loop. Using remarkable features of the Kerr-Schild coordinate system, which linearizes the Dirac equation, we obtain solutions of the Dirac equation consistent with the KN gravitational and electromagnetic field, and show that this solution takes the form of a massless relativistic string. Parallelism of this model with quantum representations in Heisenberg and Schrodinger pictures explains remarkable properties of the stringy electron model in the relativistic scattering processes.

The evolution of integrable classical systems leads to conserved quantities and vanishing Poisson brackets. In contrast, such invariants do not exist in the dynamics of non-integrable systems, which include (but are not limited to) deterministic models with long-term chaotic behavior. The object of this review is to briefly survey the mathematical background of nonintegrability and its role in the physics unfolding well-above the Standard Model (SM) scale.

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

Origins of the time, mass, electric charges and magnetic monopoles are explained. The energies, electric charges and magnetic charges of the particles are defined as E = cDtDV and |q| = cDt = E/DV, and |q_m| = c²Dt, respectively, for the 3-D quantized spaces warped along the time axis direction of ct in the 4-D Euclidean space. The energy (or mass) and charges (or electric charges and magnetic charges) are the vectors along the time axis of ct in the 4-D Euclidean space. This new concept is closely connected to the wave function of the quantum mechanics. The electric charges, magnetic charges and energies have the property of the space direction independence. Magnetic monopoles (charges) are the force carrying bosons with the inside electric field time loop. Electric monopoles are the elementary fermions. Photon space fluctuations are explained with the quantized magnetic charges.