4D Space-time Research Articles

A Creation Model from the Gell-Mann Standard Model to the Creation of Bio Cells: Based on the Assumption of Homogeneous 5D Space-Time Universe

In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to Tc in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition Tc upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schrödinger to most recently Geesink.

X-ray diffraction methods for structural diagnostics of materials: progress and achievements

The development of X-ray diffractometry at the turn of the 21st century is presented. The review covers instrumentation development for structural studies based on the use of both standard continuously radiating X-ray generators and state-of-the-art sources of ultrashort and ultra-bright X-ray pulses. The latter technique enables investigation of the structural dynamics of condensed matter in a 4D space–time continuum with a resolution reaching a tenth of a femtosecond. New engineering approaches to enhancing the sensitivity, accuracy, and efficiency of X-ray diffraction experiments are discussed, including new and promising X-rays sources, reflective collimating and focusing X-ray optical devices, and fast low-noise and radiation-resistant position-sensitive X-ray detectors, as well as a new generation of X-ray diffractometers developed based on these elements. The presentation is focused on modern engineering solutions that enable academic and applied-research laboratories to perform X-ray diffraction studies on-site, which earlier were only feasible using synchrotron radiation sources at international resource sharing centers.

Solar Radiation, Perelman Entropy Mapping, DNA, Viruses etc.

A short note based on the homogeneous 5D space-time topological mappings is extended to cover DNAs of viruses and how the body’s immune system can be enhanced to recognize and remove it.

Dark Future for Dark Matter

The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is based on the Einstein gravitational field equation. However, a thorough scrutiny of the underlying theory calls into question the suitability of the field equation, which states that the Einstein tensor Gμv is a constant multiple of the stress-energy tensor Tμv when they both are evaluated at the same 4D space-time point: Gμv = 8πkTμv, where k is the gravitational constant. Notwithstanding its venerable provenance, this equation is incorrect unless the cosmic pressure is p = 0; but then all that remains of the Einstein equation is the Poisson equation which models the Newtonian gravity field. This shortcoming is not resolved by adding the cosmological constant term to the field equation, Gμv +Λ gμv =8πkTμv, as in the ΛCDM model, because then p = Λ, so the pressure is a universal constant, not a variable. Numerous studies support the concept of a linearly expanding universe in which gravitational forces and accelerations are negligible because the baryonic mass density of the universe is far below its critical density. We show that such a coasting universe model agrees with SNe Ia luminosity vs. redshift distances just as well or even better than the ΛCDM model, and that it does so without having to invoke dark matter or dark energy. Occam’s razor favors a coasting universe over the ΛCDM model.

The Mathematical Origin of Gravitational Singularities

In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.

Anisotropic evolution of D-dimensional FRW spacetime

We examine the time evolution of the D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.

Cosmic acceleration from topological considerations II: fiber bundles

In this work we study an alternative topological model for explaining the observed acceleration of space-time, we answer the question of whether this acceleration could be a consequence of the topology of the universe. For doing that, we propose that the whole universe is composed of a four-dimensional (4D) base space, which represents space-time, endowed with a fiber forming a principal fiber bundle. We analyze this hypothesis for a homogeneous and isotropic 4D space-time and show that the effect of the fiber onto the base space is that the space-time accelerates depending on the group of the fiber, even in an oscillatory way, resembling the behavior of the universe according to recent observations. We conclude that there is the possibility of the accelerating behavior of the universe being due to its whole topology instead of an exotic kind of matter.

Relativistic Wigner Function for Quantum Walks

A relativistic Wigner function for free Discrete Time Quantum Walks (DTQWs) on the square 2D space-time lattice is defined. The transport equation obeyed by the relativistic Wigner function is derived in terms of discrete derivatives and degenerates in the continuum limit into the transport equation obeyed by the Wigner function of 2D Dirac fermions. The first corrections to the continuous equation induced by the discreteness of the lattice are also determined and the similarities with non-quantum relativistic transport in phase space are discussed further.

Fermion mass hierarchy and phenomenology in the 5D Domain Wall Standard Model

We have recently proposed a setup of the “Domain-Wall Standard Model” in 5D spacetime, where all the Standard Model (SM) fields are localized in certain domains of the extra 5th dimension. Utilizing this setup, we attempt to solve the fermion mass hierarchy problem of the SM. The mass hierarchy can be naturally explained by suitably distributing the fermions in different positions along the extra dimension. Due to these different localization points, the effective 4D gauge couplings of Kaluza-Klein (KK) mode gauge bosons to the SM fermions become non-universal. As a result, our model is severely constrained by the Flavor Changing Neutral Current (FCNC) measurements. We find two interesting cases in which our model is phenomenologically viable: (1) the KK-mode of the SM gauge bosons are extremely heavy and unlikely to be produced at the Large Hadron Collider (LHC), while future FCNC measurements can reveal the existence of these heavy modes. (2) the width of the localized SM fermions is very narrow, leading to almost universal 4D KK-mode gauge couplings. In this case, the FCNC constraints can be easily avoided even if a KK gauge boson mass lies at the TeV scale. Such a light KK gauge boson can be searched at the LHC in the near future.

Wavelets and convolution quadrature for the efficient solution of a 2D space-time BIE for the wave equation

We consider a wave propagation problem in 2D, reformulated in terms of a Boundary Integral Equation (BIE) in the space-time domain. For its solution, we propose a numerical scheme based on a convolution quadrature formula by Lubich for the discretization in time, and on a Galerkin method in space. It is known that the main advantage of Lubich’s formulas is the use of the FFT algorithm to retrieve discrete time integral operators with a computational complexity of order RlogR,R being twice the total number of time steps performed. Since the discretization in space leads in general to a quadratic complexity, the global computational complexity is of order M2RlogR and the working storage required is M2R/2, where M is the number of grid points on the domain boundary.To reduce the complexity in space, we consider here approximant functions of wavelet type. By virtue of the properties of wavelet bases, the discrete integral operators have a rapid decay to zero with respect to time, and the overwhelming majority of the associated matrix entries assume negligible values. Based on an a priori estimate of the decaying behaviour in time of the matrix entries, we devise a time downsampling strategy that allows to compute only those elements which are significant with respect to a prescribed tolerance. Such an approach allows to retrieve the temporal history of each entry e (corresponding to a fixed couple of wavelet basis functions), via a Fast Fourier Transform, with computational complexity of order R¯elogR¯e. The parameter R¯e depends on the two basis functions, and it satisfies R¯e≪R for a relevant percentage of matrix entries, percentage which increases significantly as time and/or space discretization are refined. Globally, the numerical tests show that the computational complexity and memory storage of the overall procedure are linear in space and time for small velocities of the wave propagation, and even sub-linear for high velocities.

Pixelated Dark Energy

AbstractWe study the phenomenology of a recent string construction with a quantum mechanically stable dark energy. A mild supersymmetry protects the vacuum energy but also allows TeV scale superpartner masses. The construction is holographic in the sense that the 4D spacetime is generated from “spacetime pixels” originating from five‐branes wrapped over metastable five‐cycles of the compactification. The cosmological constant scales as in the pixel number. An instability in the construction leads to cosmic expansion. This also causes more five‐branes to wind up in the geometry, leading to a slowly decreasing cosmological constant which we interpret as an epoch of inflation followed by (pre‐)heating when a rare event occurs in which the number of pixels increases by an order one fraction. The sudden appearance of radiation triggers an exponential increase in the number of pixels. Dark energy has a time varying equation of state with , which is compatible with current bounds, and could be constrained further by future data releases. The pixelated nature of the Universe also implies a large‐l cutoff on the angular power spectrum of cosmological observables with . We also use this pixel description to study the thermodynamics of de Sitter space, finding rough agreement with effective field theory considerations.

Counting the number of Killing vectors in a 3D spacetime

We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the values of differential invariants arising from the compatibility conditions of the Killing equation. As illustrating examples, we classify the Lifshitz and pp-wave spacetimes into a hierarchy based on their level of symmetry. A complete classification of spacetimes admitting 4 Killing vectors is also presented.

Studies on the SJ vacuum in de Sitter spacetime

In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O(4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = mc cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.

Topology of a 4D universe for every 3-manifold

A 4D universe is a 4-dimensional boundary-less connected oriented manifold with every closed 3-manifold (i.e., a 3-dimensional closed connected oriented manifold) embedded. A 4D punctured universe is a 4-dimensional boundary-less connected oriented manifold with the punctured manifold of every closed 3-manifold embedded. Every 4D universe and every 4D punctured universe are open 4-dimensional manifolds. If a closed 3-manifold is considered as a 3D universe, then every 4D spacetime is embedded in every 4D universe and hence every 4D universe is a classifying space for every spacetime. In this paper, it is observed that a full 4D universe is produced by collision modifications between 3-sphere fibers in the 4D spherical shell (i.e., the 3-sphere bundle over the real line) embedded properly in any 5-dimensional open manifold. As a previous result, it was shown that any 4D universe and 4D punctured universe must have infinity on some homological indexes. It is shown in this paper that the second rational homology groups of every 4D universe and every 4D punctured universe are always infinitely generated.

General field theory and weak Euler-Lagrange equation for classical particle-field systems in plasma physics

A general field theory for classical particle-field systems is developed. Compared to the standard classical field theory, the distinguishing feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is developed on the 4D space-time, which plays a pivotal role in establishing the connections between symmetries and local conservation laws in space-time. Specifically, the nonvanishing Euler derivative in the weak Euler-Lagrange equation generates a new current in the conservation laws. Several examples from plasma physics are studied as special cases of the general field theory. In particular, the relations between the rotational symmetry and angular momentum conservation for the Klimontovich-Poisson system and the Klimontovich-Darwin system are established.

3D Behavior Recognition Based on Multi-Modal Deep Space-Time Learning

This paper proposes a dual-stream 3D space-time convolutional neural network action recognition framework. The original depth map sequence data is set as the input in order to study the global space-time characteristics of each action category. The high correlation within the human action itself is considered in the time domain, and then the deep motion map sequence is introduced as the input to another stream of the 3D space-time convolutional network. Furthermore, the corresponding 3D skeleton sequence data is set as the third input of the whole recognition framework. Although the skeleton sequence data has the advantage of including 3D information, it is also confronted with the problems of the existence of rate change, temporal mismatch and noise. Thus, specially designed space-time features are applied to cope with these problems. The proposed methods allow the whole recognition system to fully exploit and utilize the discriminatory space-time features from different perspectives, and ultimately improve the classification accuracy of the system. Experimental results on different public 3D data sets illustrate the effectiveness of the proposed method.

Holographic duality for 3d spin-3 gravity coupled to scalar field

The 3d spin-3 gravity theory is holographically dual to a 2d W3-extended CFT. In a large-c limit the symmetry algebra of the CFT reduces to SU(1,2)×SU(1,2). On ground of symmetry the dual bulk space–time will be given by an 8d group manifold SU(1,2). Hence we need to introduce five extra coordinates in addition to three ordinary ones. The 3d space–time is a 3d hyper-surface Σ embedded at constant values of the extra variables. Operators in the CFT at the boundary of Σ are expressed in terms of W descendants of the operators at the boundary of Σ0, where the extra variables vanish. In this paper it is shown that AdS/CFT correspondence for a scalar field coupled to 3d spin-3 gravity is realized in this auxiliary 8d space. A bulk-to-boundary propagator of a scalar field is found and a generating functional of boundary two-point functions of scalar W-descendant operators is obtained by using the classical action for the scalar field. Classically, the scalar field must satisfy both Klein–Gordon equation and a third-order differential equation, which are related to the quadratic and cubic Casimir operators of su(1,2). It is found that the coefficient function of the derivatives of the scalar field in the latter equation is the spin-3 gauge field, when restricted to the hypersurface. An action integral in the 8d auxiliary space for the 3d spin-3 gravity coupled to a scalar field is presented. In general, this 8d auxiliary space is a deformation of the manifold SU(1,2). An 8d local frame is introduced and the equations of motion for the 8d connections Aμ, A‾μ are solved. By restricting those solutions onto Σ, flat connections in 3d SL(3,R)×SL(3,R) Chern–Simons theory are obtained and new 3d black hole solutions with and without spin-3 charge are found by this method.

Self-gravitating gaseous spheres in 5D framework

One of the suitable theoretical ideas for the polytrope in the Kaluza–Klein cosmology is discussed. Assuming a 5-dimensional (5D) spacetime model described by the Kaluza–Klein theory of gravity, we implement the energy density and pressure of the polytrope which is a self-gravitating gaseous sphere and still very useful as a crude approximation for more realistic stellar models. Next, we obtain the best-fit values of auxiliary parameters given in the model according to recent observational dataset. Finally, we study some cosmological features and the thermodynamical stability of the model.

Time-dependent characteristics of secondary electron emission

The recent development of the time-resolving capability for scanning electron microscopy (SEM) enables it to be a real 4D space-time imaging technique, which is extremely suitable for investigating the ultrafast dynamic processes concerned with secondary electron emission (SEE). This paper attempts to investigate the dynamic SEE process with the aid of a Monte Carlo method; the understanding of the mechanism will surely benefit the construction and application of various kinds of time-resolved SEMs. Our simulation modeling is based on the use of the Mott cross section and a dielectric function approach for the respective description of the electron elastic and inelastic scattering. One secondary electron is assumed to be produced in an inelastic scattering event, and the owned kinetic energy enables it to transport and produce other secondary electrons, forming the cascade production process. From the simulation, not only the time delay of SEE from the incidence instant of primary electrons but also the time dependences of the involved physical quantities, including the energy-, depth-, direction-, emission site-, and production site-distributions can be theoretically derived. The calculations provide useful knowledge on the time dependence of SEE from the theoretical perspective for the applications to the available time-resolved SEMs.

Gapped gravitinos, isospin $\frac{\mathbf{1}}{2}$ particles, and $\mathcal{N}=2$ partial breaking

Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin $\frac{1}{2}$ and $\frac{3}{2}$ fermions. We apply this approach to study partial breaking in 4D $\mathcal{N}=2$ gauged supergravity in rigid limit and we describe the fermionic gapless mode in terms of chiral anomaly. We study as well the homologue of the usual spin-orbit coupling $\vec{L}.\vec{S}$, that opens the vanishing band gap for free $s=\frac{1}{2}$ fermions; and show that is precisely given by the central extension of the $\mathcal{N}=2$ supercurrent algebra in 4D spacetime. We also give comments on the rigid limit of Andrianopoli et al obtained in [28] and propose an interpretation of energy bands in terms of a chiral gapless isospin $\frac{1}{2}$-particle (iso-particle). Other features, such as discrete T- symmetry in FI coupling space, effect of quantum fluctuations and the link with Nielson-Ninomiya theorem, are also studied.