A deep relationship is identified between the Coulomb Force and Gravity. A gravitational constant for strong gravity is calculated from the relationship. The equivalence between mass and charge is explored. Implications are given for the expansion of Einstein's Field Equations to include vector gravity.

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.

The electric field is enormously more powerful than the gravitational field. However, in our normal experience there is no electric field, the electric force is missing. How is it that when you get to larger and larger scales the gravitational field is extremely important whereas the electric field becomes less and less important [1]? This paper proposes a model to explain why gravitation dominates at a larger scale.

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. The model is developed using a constructive approach. 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.

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.

I demonstrate that the macrocosmic gravitational interaction between two masses and the microcosmic electrostatic interaction between two charges unify in simple concepts and mathematical laws when electric charge and ordinary mass are interpreted in reciprocal terms. No previous research has ever attempted to unify charge and mass. The difficulty has been lack of an intelligible definition of charge. A three-point paradigm shift solves the problem, giving convincing evidence – for the first time – that positron and negatron are the ultimate elementary particles. That is, matter is pure positive and negative grains of electricity. Paradigm shift #1: Electron is a moving charge; a charge is static electron – ‘one entity two identities’. This implies that ordinary matter contains equal numbers of positive and negative electrons – observed in motion as ‘electrons’ and at rest as ‘charges’. In motion, a positron-negatron pair obeys the laws of electrodynamics and annihilates; at rest, the pair obeys the laws of electrostatics and neutralizes. Paradigm shift #2: Electron mass and electrostatic field are either positive or negative. Opposite masses and fields, rather than indefinable ‘charge’, make opposite electrons physically different. Paradigm shift #3: Electric charge and ordinary mass interconvert. Positive charge (e⁺) and negative charge (e^-) neutralize to neutral charge (2e⁰), which is nature’s quantum of ordinary mass. Conversely, a quantum of ordinary mass splits to opposite charges e.g. in frictional electrification. The insights systematize the search, identification and classification of ‘elementary particles’, ending decades of confusion in the ‘elementary particle zoo’. They identify a new, stable subatomic particle – a third nucleon.

Inflationary model provides a conceptual explanation of the horizon problem, the flatness problem and may also suppress the over abundant magnetic monopoles predicted by Grand Unified Theories. Although various inflationary models have been proposed since 1981, difficulties like fine tuning is not only unsolved but also becomes severer in confrontation with data of Planck Satellite. This paper proposes an alternative model of inflation: the spontaneous symmetry breaking phase transition at early universe is only responsible for the production of magnetic monopoles expected by Grand Unified Theories; it is the subsequent energy release of monopole annihilation that drives the inflation. As a result, the early universe underwent a free expansion with a heat source originating in the annihilation, which expects a smooth, plateau-like potential consistent with the observational data. Beside interpreting a number of long standing inflationary problems, the new scenario predicts a significant increase of entropy during the inflation, and tends to produce large scale structures exceed scale of 300 million light-years correlated with a CMB smoothen and flatten by a simple dynamical mechanism.

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.

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.

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.

It is shown that the relationship between gravity and quantum physics can be described in terms of the symmetry break of space due to elementary constituents, dubbed as “darks”, which constitute a universal energetic background field that extends from the cosmological level down to the nuclear level. It requires (a) the awareness of the polarisable second elementary dipole moment of a recently discovered third Dirac particle type, next to the electron-type and the Majorana-type, and (b) the awareness that Einstein’s Lambda is not a constant of nature, but, instead, a covariant integration constant with a value that depends on the scope of the cosmological system under consideration, such as solar systems and galaxies, eventually showing up as the Cosmological Constant at the level of the universe. The relationship has been made explicit by relating two major gravitational constants quantaties (the gravitational constant and Milgrom’s acceleration constant) with a single nuclear quantity (the rest mass of the pion derived from the Higgs boson value).

A dynamic view is conjectured for not only the universe but also the underlying theories in contrast to the convectional pursuance of single unification theory. As the 4 -d spacetime evolves dimension by dimension via the spontaneous symmetry breaking mechanism, supersymmetric mirror models consistently emerge one by one at different energy scales and scenarios involving different sets of particle species and interactions. Starting from random Planck fluctuations, the time dimension and its arrow are born in the time inflation process as the gravitational strength is weakened under a 1-d model of a “timeron” scalar field. The “ timeron” decay then starts the hot big bang and generates Majorana fermions and U(1) gauge bosons in 2-d spacetime. The next spontaneous symmetry breaking results in two space inflaton fields leading to a double space inflation process and emergence of two decoupled sectors of ordinary and mirror particles. In fully extended 4-d spacetime, the supersymmetric standard model with mirror matter before the electroweak phase transition and the subsequent pseudo-supersymmetric model due to staged quark condensation as previously proposed are justified. A set of principles are postulated under t his new framework. In particular, new understanding of the evolving supersymmetry and Z2 or generalized mirror symmetry is presented.

The Alena Tensor is a recently discovered class of stress-energy tensors that, as previous publications have shown, has extremely useful properties. In curved spacetime, this tensor reproduces Einstein Field Equations and in flat Minkowski spacetime, it describes a physical system with fields that can be widely configured. The use of the discussed tensor significantly simplifies Quantum Field Theory equations and provides canonical, generalized four-momentum with vanishing four-divergence that satisfies Klein-Gordon equation. This article discusses the possible applications of Alena Tensor in Quantum Field Theory and unification theories against the background of existing research directions. The advantages, disadvantages and potential limitations of the approach discussed are also considered.

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

It is shown that gravity and quantum physics can be unified upon the basis of a quark description in terms of a gravitational Dirac particle. It requires the awareness of a second elementary dipole moment (isospin) next to the angular moment (spin) of Dirac particles and the awareness of an (unbroken) omnipresent energetic cosmological background field. The unification has been made explicit by an expression that relates the two major gravitational constants of nature (the gravitational constant and Milgrom’s acceleration constant) with the two major nuclear constants of nature (the weak interaction boson and the Higgs boson).

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

Generalisation from the local 4-dimensional spacetime form for a proper time interval provides an alternative basis for a unified theory contrasting with the more familiar approach of appending extra dimensions of space. In both cases the main goal is to derive a structure of matter that accounts for empirical observations from the properties of the additional components. Previous work has focussed upon the direct and significant connections that this new approach makes with the Standard Model of particle physics while also providing a link with dark matter models. In this paper we elaborate on how a further sector of generalised proper time, incorporating the key component of negative pressure, can account for the apparent dark energy fuelling the accelerating large-scale expansion of the universe. Through comparison with existing dark energy models we elucidate the elementary composition of this sector, its potential relation to an effective cosmological constant term, and the nature of possible interaction with the visible and dark matter sectors.

To solve a series of major problems, such as the singularity before the Big Bang, the inflation of the early universe and the accelerating expansion of the present universe, this series of studies start with super gravity, dark energy and dark matter, go beyond the surface of a lot of observation data, and systematically reveal the arche-internal mechanism of all things, to establish the arche-unity of physics, and give a natural and reasonable explanation. At present, there are at least three basic pathways that are leading our research field to repulsion against gravitation, quantum repulsion against quantum gravitation and high-dimensional superrepulsion against high-dimensional supergravity, that is, the research on the accelerating expansion mechanism of the current universe, the research on the dynamic mechanism of the early cosmic inflation, and the research on the rebound mechanism near the singularity before the Big Bang. In this series of studies, the arche problem of everything is always placed under the extreme environmental conditions of the initial universe, the starting point of scientific logic is closely combined with the starting point of the universe history, the pseudo vacuum energy considered by the inflationary universe model, the Higgs field predicted by the standard physical model and the dark energy speculated by the observational cosmology are reduced to the positive energy system with strong negative pressure, and they are reduced to the repulsion (all the resistance to gravity) that forms a conjugate relation with gravity. In our opinion, dark energy and dark matter are essentially at the level of quantum gravity and quantum repulsion. Therefore, we not only consider the conventional quantum effect and non commutative quantum effect, but also further consider the arche-conjugate effect and the cluster resonance-at-cofrenquence effect. For noncommutative space-time, we put forth the ultimate supersymmetry, the arche-conjugation and the cluster resonance-at-cofrenquence. A relatively complete natural mechanism forms such an important inference: the closer they get to Planck scale, the stronger the conventional quantum effect, non commutative quantum effect, arche-conjugate effect and co-frequency resonance effect are. In the high-dimensional space-time (the 11 dimensional hyperspace compactly reduced to M 4 × N r ), corresponding to the introduction of supergravity with the supersymmetry between the graviton and the gravitino, we put forth the superrepulsion with the supersymmetry between the repulsion and the repulsitino, and establish the arche-conjugate relationship between the high-dimensional supergravity and the high-dimensional superrepulsion. Therefrom, we propose a basic inference that can be promoted to the principle of hyperholography of high-dimensional universe (or multiuniverse): in a parallel universe formed by mutual coupling and holographic correspondence between the P universe dominated by negative pressure (high-dimensional superrepulsion and quantum repulsion of accumulating positive energy, mainly composed of dark energy) and the N universe dominated by positive pressure (high-dimensional supergravity and quantum gravity of accumulating negative energy, mainly composed of dark matter), there is a correspondence between the small-scale physics (ultraviolet cutoff) of the P universe and the large-scale physics (infrared cutoff) of the N universe, while there is a correspondence between the large-scale physics (ultraviolet cutoff) of the P universe and the small-scale physics (infrared cutoff) of the N universe. In the new research paradigms set in this series, the arche-conjugation between the high-dimensional supergravity and the high-dimensional super repulsion, as well as between the quantum gravity and the quantum repulsion, is higher than the supersymmetry, so it becomes the core concept of the new theory. The arhce-unity of physics is a super unity that transcends the grand unification of four basic interaction, which is formed between high-dimensional supergravity (related to dark matter) and high-dimensional superrepulsion (related to dark energy), between quantum gravity (related to dark matter) and quantum repulsion (related to dark energy). From the basic component point of view, before or after the big bang, the gravitons and repulsons are coupled together, the negative energy contraction dominated by the positive pressure and the positive energy expansion dominated by the negative pressure work alternately, forming the arche-conjugate pulsaton of neither the point particle nor the linear superstring. Under the big unified framework of quantum gravitational field and quantum repulsive field, this series of work comprehensively expands the general relativity and loop quantum ring gravitation theory, sets up the quantum repulsive field equation corresponding to the quantum gravitational field equation, and then establishes the quantum hedge-unified field equation describing the interaction of quantum gravitational field and quantum repulsive field; On this basis, the quantum repulsive universe equation corresponding to the quantum gravitational universe equation is established, thus a set of new equations describing the expansive universe with quantum hedge-unified field are established. On the one hand, scalar disturbance is considered as the exhibition of repulsive effect, on the other hand, tensor disturbance is considered as the exhibition of gravitational effect. In the initial stage of the big ripping, due to the mutual restraint of quantum repulsion and quantum gravity, the scalar and tensor perturbations are not obvious. However, at the end of the big ripping, the scalar and tensor perturbations are very significant, and there is a large power spectral exponential run. Between particle physics and cosmology, we improve and expand the path integral of quantum gravity, create the path integral of quantum hedge-unified field, and set up the basic equation of quantum cosmic-synergetic dynamics, and then establish the basic equation of quantum-cosmic paradigm dynamics. Thus we put up the operator distribution function and its dynamic equation of the quantum arche- pulsaton, and finally use the Wigner-Ville distribution as a non-linear time-frequency distribution to establish the Wigner joint-distribution of quantum-conjuagted pulsation function, so as to analyze the arche of all things with three evolutionary forms: quantum chaotic-pulsaton, quantum quasi-spherical pulsaton and quantum spherical-pulsaton. In this series of work, the mechanism to avoid the singularity of the universe is put forward fundamentally, and the dark energy and dark matter are explained through new mechanisms and effects at the level of quantum gravity. Between particle physics and cosmology, we improve and expand the path integral of quantum gravity, establish the path integral of quantum hedge-unified field, thus establish the basic equation of quantum cosmic-synergy dynamics, and then establish the basic equation of quantum cosmic-paradigm dynamics. Thus the covariant gravitational mass and the covariant inertial mass formed by the ultra-synergy between particles and the universe are presented, and the equivalence hypothesis on the covariant non-inertial system which can be elevated to the basic principle, is presented. Based on this hypothesis, a systematic calculation and analysis of binary stars composed of neutron stars and black holes are made. The master equation, variance and Fokker-Planck equation for the birth-death and migration of a large number of particles are established between binary stars composed of neutron stars and black holes.

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.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their interpretation by giving charge density and mass density, and the four-velocity that describes their motion geometric definitions. These geometric definitions are reminiscent of General Relativity’s interpretation of mass in terms of the scalar curvature R and hint at the emergence of gravity. The gravitational theory that does emerge is shown to be equivalent to Einstein’s General Relativity augmented by an energy-momentum tensor term that mimics the properties of dark matter and/or dark energy. In summary, the proposed geometrization of the Maxwell tensor puts both electromagnetic and gravitational phenomena on an equal footing with both being tied to the curvature of space-time. Using specific solutions to the proposed theory, the unification brought to electromagnetic and gravitational phenomena, as well as the relationship of those solutions to the corresponding solutions of the classical Maxwell and Einstein field equations are compared.

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics – a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for defining elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8 \times E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with left-right symmetry) whose geometry (evolving in Connes time) relates to the four known fundamental forces, while predicting two new forces, $SU(3)_{grav}$ and $U(1)_{grav}$. This latter interaction is possibly the theoretical origin of MOND. Coupling constants of the standard model result from left-right symmetry breaking, and their values are theoretically determined by the characteristic equation of the exceptional Jordan algebra of the octonions. The quantum-to-classical transition, precipitated by the entanglement of a critical number of fermions, is responsible for the emergence of classical spacetime, and also for the familiar formulation of quantum theory on a spacetime background.

In 1982, MIT physicist Frank Wilczek predicted and named ANYONS, quasiparticles (particle-like formations) that are confined to 2 dimensions and were discovered in 2020. The name might come from Prof. Wilczek's lighthearted comment "anything goes". This article's main goal is to show that anyons could be another name for 1) virtual particles, 2) Mobius strips, and 3) figure-8 Klein bottles. Along the way, we'll see the picture painted by the article confirm that Einstein's dream of gravitational-electromagnetic unity fits in with anyons being Mobius strips. The topological hypothesis offers an explanation of dark matter and dark energy. We'll also have encounters with intergalactic travel and imaginary computers. They really could exist but are imaginary in the sense that they use imaginary time (as well as space-time warping).

With reference to our 4G model of final unification, strong coupling constant and strong interaction charge of magnitude $e_s\cong 2.95e$, it is possible to understand the nuclear stability range with a simple power law of the form, $A_s\cong \left(Z+2.95\right)^{1.2\pm0.015}$

Analytical modeling has symmetries and aesthetic-mathematical characteristics that distinguish it from numerical computation. Nanoscience plays an extremely important role in unification efforts that also include holistic aspects of reality. In this paper I present new discovered results about the complete analytical quantum relativistic form of the mean square deviation of position false related to a lately appeared Drude-Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function false gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating processes in Nature. Examples of application and suggestions supplement the paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on the vacuum energy.

Bayesian formulations of learning imply that whenever the evidence for a correlation between events in an animal’s habitat is sufficient, the correlation is learned. This implies that regularities can be learnt rapidly, from small numbers of learning examples. This speed of learning gives maximum possible fitness, and no faster learning is possible. There is evidence in many domains that animals and people can learn at nearly Bayesian optimal speeds. These domains include associative conditioning, and the more complex domains of navigation and language. There are computational models of learning which learn at near-Bayesian speeds in complex domains, and which can scale well – to learn thousands of pieces of knowledge (i.e., relations and associations). These are not neural net models. They can be defined in computational terms, as algorithms and data structures at David Marr’s [1] Level Two. Their key data structures are composite feature structures, which are graphs of multiple linked nodes. This leads to the hypothesis that animal learning results not from deep neural nets (which typically require thousands of training exam-ples), but from neural implementations of the Level Two models of fast learning; and that neu-rons provide the facilities needed to implement those models at Marr’s Level Three. The required facilities include feature structures, dynamic binding, one-shot memory for many feature struc-tures, pattern-based associative retrieval, unification and generalization of feature structures. These may be supported by multiplexing of data and metadata in the same neural fibres.

Within the scope of observed materialistic physical systems, without addressing the roots of H-Bar and big G, it is impossible to construct a workable model of final unification. With reference to our earlier proposed three large atomic gravitational constants, it is possible to reform and compactify the 10 dimensional String theory to 3+1 dimensions

By considering three virtual gravitational constants assumed to be associated with gravitational, electromagnetic and strong interactions, Fermi’s weak coupling constant can be shown to be a natural manifestation of microscopic quantum gravity. As our approach is heuristic and completely different from the current methods of estimating the Newtonian gravitational constant, with reference to the call of ‘Ideas lab 2016’ organized by NSF, we appeal for inclusion of this theoretical work as a project under unification scheme.

The phenomenon of dissipative self-organization is studied on the example of time-crystal networks. Particular attention was given to transient processes, attractor topologies, phase transitions, and asymptotic stability. New concepts were introduced, including topological phases, spinorial states, and bond flavors. Concepts such as ground states, chemical potentials, elastic forces, temperature, and statistical distributions were endowed with a new meaning associated with asymptotic stability. Phenomena usually attributed exclusively to quantum physics have been shown to occur in this essentially classical environment. They coexist with, and in some cases, such as charge quantization, are related to the phenomenon of time dilation. The approach was applied to model vacuum self-organization. We have shown that under the ac-tion of competing forces, such as gravity and antigravity, a cascade of phase transitions can transform an unorganized vacuum into phases in which interactions, fields and waves resemble electromagnetic, weak, and strong, and their elements can be used as building blocks for prototype particles. In addition, some interrelation field parameters and probabilities of particle transmutations were calculated, which are not predicted by the standard model. The results are consistent with the experiment. The presented material and methodology may be of interest for studying self-organization in different environments.

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

An attempt is made to model the atomic nucleus as a combination of bound and free or unbound nucleons. Due to strong interaction, bound nucleons help in increasing nuclear binding energy and due to electroweak interaction, free or unbound nucleons help in decreasing nuclear binding energy. In this context, with reference to proposed 4G model of final unification and strong interaction, recently we have developed a unified nuclear binding energy scheme with four simple terms, one energy coefficient of 10.1 MeV and two small numbers 0.0016 and 0.0019. In this paper, by eliminating the number 0.0019, we try to fine tune the estimation procedure of number of free or unbound nucleons pertaining to the second term with an energy coefficient of 11.9 MeV. It seems that, some kind of electroweak interaction is playing a strange role in maintaining free or unbound nucleons within the nucleus. It is possible to say that, strong interaction plays a vital role in increasing nuclear binding energy and electroweak interaction plays a vital role in reducing nuclear binding energy. Interesting observation is that, Z can be considered as a characteristic representation of range of number of bound isotopes of Z. For medium, heavy and super heavy atoms, beginning and ending mass numbers pertaining to bound states can be understood with 2Z+0.004Z^2 and 3Z+0.004Z^2 respectively. With further study, neutron drip lines can be understood. Based on this kind of data fitting procedure and by considering the mass ratio of pions and electroweak bosons, existence of our 4G model of electroweak fermion of rest energy 584.725 GeV can be confirmed confidently.

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

A number of experiments suggest that the elementary particles are non-local entities. A dissipative self-organization, that treats particles as open systems may provide a better understanding of the underlying phenomena than conservative models. The proposed toy model is such an attempt. We found that self-gravitation (although accompanied by self-diffusion) may not only be compatible with the quantum phenomena but is perhaps the major reason for the existence of quantum fields. According to the proposed model, fields/particles (resemble those of the Standard Model) emerge from a dynamic self-organized medium (which we associate with vacuum dust) from competition between self-gravitation and self-diffusion. These forces produce turbulence in the form of vortices (which we call vacuum cells) that serve as the building blocks for fields and particles. Field/particle features and symmetries are based on their internal (intracellular) dynamics and vortex synchronization (intercellular dynamics). This model allows for rough estimations of relative field coupling strengths, the quantity of charges and flavors, the probabilities of quark transmutations, the dimensionality and the topologies of phase spaces, and other Standard Model parameters that came not from the theory but rather determined by experiment.

We would like to suggest that, by considering three virtual gravitational constants assumed to be associated with gravitational, electromagnetic and strong interactions along with a strongly interacting virtual nuclear elementary charge, a workable model of final unification can be developed. In a verifiable approach, Newtonian gravitational constant and Fermi’s weak coupling constant can be interrelated via nuclear and electromagnetic gravitational constants.

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.

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 (mass), charges and absolute time are newly defined based on the 4-D Euclidean space. The photons and gravitons are understood as the 2-D space fluctuations along the space axes and 1-D time fluctuations along the time axis, respectively. This indicates that the electromagnetic (EM) and gravitational (G) waves can be unified into the so called gravityelectromagnetic (GEM) wave which has both space and time fluctuations. The photon with zero force fields is the 2EM wave because an EM wave corresponds to a charged fermion. The dark matter bosons, weak force bosons, strong force bosons are the 1-D time fluctuations which can be expressed by the G waves. This indicates that all five forces are unified by the GEM wave. It is called as the super unification theory in the present work. And the force carrying bosons and mesons are, for the first time, proposed as the possible candidates of the magnetic monopoles like the fermions and baryons are the electric monopoles. The signs of the magnetic charges quantized as q_m=cq are newly defined. 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.

In our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, e_n=2.95e and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. The aim of this paper is associated with understanding the mystery of quantum of magnetic flux, Planck’s quantum radiation constant and Reduced Planck’s constant. Proceeding further, quark charges, strong coupling constant, nuclear stability, nuclear binding energy, medium and heavy atomic X-ray levels and celestial magnetic moments can be understood in a unified approach. It may also be noted that, by considering integral nature of elementary particle masses, it seems possible to understand the discreteness of angular momentum. Considering our proposed e_n=2.95e=3e as a characteristic nuclear charge, it seems possible to understand the integral nature of quarks electromagnetic charge. With this idea, neutron, proton and pions decay can be understood very easily. In all the cases, up quark of charge (±2e) seems to play a crucial role with the internal transformation of down quark of charge (±e) and external observable elementary basic elementary particles. It needs further study at fundamental level.

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

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