Popular information can also be found on my website [a]. In the end a description is given of the window of visible matter a new formula, which is independent of the cosmological constant. In addition several examples of institutional evidence is shown to support the DTT-formulations. My opinion is: It is unbelievable how science anno wants holds on to Big Bang. Forget the Big Bang! Some diagrams. Authors: J. The dynamics of reality is well regulated. What is the mechanism that controls dynamics and what rules this mechanism? The models of contemporary physics do not answer these questions.

In the realm of elementary particles the special habits of quaternions appear to play an essential role. In the past physics had a choice between the Maxwell based approach and the quaternionic based approach. That choice has a significant influence on how physics equations look. Einstein selected the Maxwell approach and in this way physics inherits the spacetime view on the universe in which we live. Authors: Valeriy V.

Dvoeglazov Comments: 13 Pages. Prepared for the special issue of the "Adv. Recently, several discussions on the possible observability of 4-vector fields have been published in literature. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskii and Polubarinov, Hayashi, and Kalb and Ramond. Cockett and R.

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Weakly distributive categories. Crans and R. Presentations of omega-categories by directed complexes. Cruttwell and M. A unified framework for generalized multicategories. On closed categories of functors. Duncan and K. Interacting Frobenius algebras are Hopf.

A92 A29 no. The computational power of the W and GHZ states. Danos and L. Proof-nets and the Hilbert space. Dunn and J. Surface proofs for nonsymmetric linear logic extended abstract. Vidal, and J. Three qubits can be entangled in two inequivalent ways. Notes on Banach spaces and Hilbert spaces.

Eckmann and P.

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Group-like structures in general categories I: multiplications and comultiplications. Eilenberg and G. Closed categories. Quantum cryptography based on Bell's theorem - Ekert, Artur K. Algebraic real analysis. Gogioso and F. Infinite-dimensional categorical quantum mechanics. Greenberger, M. Horne, A. Shimony, and A. Proof-nets: the parallel syntax for proof-theory. Lecture Notes in Pure and Applied Mathematics, pages Grandis and L. Cubical sets and their site. Theory Appl. Categ, 11 8 Guiraud and P.

Identities among relations for higher-dimensional rewriting systems. Polygraphs of finite derivation type. Mathematical Structures in Computer Science, pages Stabilizer Codes and Quantum Error Correction. PhD thesis, California Institute of Technology. Higher cospans and weak cubical categories cospans in algebraic topology, i. Categ, 18 12 Directed Algebraic Topology. Cambridge University Press,. A diagrammatic axiomatisation for qubit entanglement. A topological perspective on interacting algebraic theories. Representable multicategories.

From coherent structures to universal properties. Models of multipartite entanglement. Categorical Quantum Models and Logics. Amsterdam University Press. Hinze and D. Equational reasoning with lollipops, forks, cups, caps, snakes, and speedometers. Journal of Logical and Algebraic Methods in Programming. Graphical classification of entangled qutrits. Hyland and J. The category theoretic understanding of universal algebra: Lawvere theories and monads.

Hahn and G. Heunen and J.

Categorical quantum mechanics: an introduction. Joyal and J. Weak units and homotopy 3-types. In Street Festschrift: Categories in algebra, geometry and mathematical physics, pages Coherence for weak units. Documenta Mathematica, The combinatorics of n-categorical pasting. Jeandel, S. Perdrix, and R. Joyal and R. The geometry of tensor calculus, I. Aspects of cubical higher category theory.

Knots and Physics. World Scientific Publishing Co. Introduction to virtual knot theory. Knot Theor. Many-variable functorial calculus. In Coherence in Categories, pages Nature. Pictures of Processes: Automated graph rewriting for monoidal categories and applications to quantum computing. PhD thesis, University of Oxford. Kock, A. Joyal, M. Batanin, and J. Polynomial functors and opetopes. Merry, and M. Pattern graph rewrite systems. Elementary remarks on units in monoidal categories. Cambridge Phil. A monadic approach to polycategories.

Combinatorial Algebraic Topology Berlin Heidelberg. Badly incomplete normed linear spaces. Kassel and V. Braid Groups New York. Kapranov and V. Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders list of results. Kissinger and V. Quantomatic: A proof assistant for diagrammatic reasoning. Composing PROPs Algebra and geometry of rewriting. Functorial Semantics of algebraic theories. PhD thesis, Columbia University.

Categories of space and of quantity. In The Space of Mathematics. Higher Operads, Higher Categories. Lamata, J. Salgado, and E. Inductive classification of multipartite entanglement under stochastic local operations and classical communication. Inductive entanglement classification of four qubits under stochastic local operations and classical communication. Lafont, F. A folk model structure on omega-cat. The electric field intensity strength E corresponds to a measure of the phase alignment of Lorentz contracted dipoles forming Faraday field lines.

Magnetic flux lines represent quantized vortex filaments. Vortical motion of Planck masses gives rise to vortical filaments similar to that observed in a Bose-Einstein Condensate BEC zero viscosity superfluid such as 4He when stirred while supercooled. The wave function y describes the shape of the potential field f.

EM potential Am describes the wave function as a function of position and time. Curvature of wavefronts is a result of localized slowing of EM waves in regions of increased dipolar density. Curvature k of arc length s of field wavefronts is equivalent to a gravitational acceleration g in the direction of the normal vector N and proportional to the radius of curvature of the geodesic described by the tangent vector T and binormal vector B of the propagating EM potential wave Ama.

Electrostatic potential energy represents a form of stress resistance to confinement or volumetric compression of charge elements. Space and time are relational properties that depend on the presence of matter and energy. The laws of physics are taken to be invariant, or symmetric, under all changes in reference frames as a result of assumed isotropy. Quantum Vacuum As noted by Tuisku et al [14] the passage of time is associated with energy flow.

The hour glass provides a familiar example. Energy density gradients determine flow of energy and mark the passage of time. Geodesic world-lines describe the energy density gradient. Travelling waves and moving standing waves follow the least action path. In a quantum vacuum composed of Planck particles, energy density gradients correspond to volumetric density gradients, a scalar potential f. The potential energy gradient between a region of high energy density and low energy density drives an energy flow down the steepest gradients along space-time geodesics in accordance with principle of least action.

Only changes in energy density are observable. For a photon at constant frequency, proper time is equal to zero becoming manifest during a change in frequency as a result of a change in potential. EM wave length distance between nodal points correspond to the metric gun. Spacetime curvature is equivalent to a curvature of EM wavefronts. The number of loops corresponds to the Berry geometric phase f. Interactions between particles occur along affine manifold connections defining causal relationships. This binary aspect may ultimately be expressed at the Planck scale in the form of Planck dipoles of positive and negative Planck mass mP.

Following the Big Bang, photon collisions resulted in quark-anti-quark and electron- positron formation. In the radiation dominated era, photon collisions overwhelmed gravitational attraction preventing atomic nuclei formation. Both the radiation and matter densities decreased as the universe expanded with radiation density decreasing faster than that of matter as matter was formed.

The number N of electron masses in the current epoch would be 1. The angular velocity of all matter is derived from the angular velocity of the initial mass pair through successive divisions due to conservation of angular momentum. Quantum Vacuum temperature of the universe cools over time. The hierarchical organization of cosmological structures exhibits a linear relation in a logarithmic plot mass expressed in electron pairs 2me versus radius in units of the electron Compton radius 2RC.

The mathematical archetype of a binary geometry may be visualized as a dyad formed by division of a monad, a point or unit circle symbolizing oneness. The dyad is formed of two polarized monads of opposite curvature and energy suggestive of the Big Bang genesis. The transformation of a dimensionless point into a circle of many points in a circuit generated by rotary motion of a point in space and time represents a metaphor of the transcendental creation.

A conceptual illustration of this process is shown in Fig. In the Sternglass model, all matter consists of electrons and positrons. Evolution of the universe fireworks model in conversion of radiation to matter proceeds in stepwise fashion from a single supermassive electron-positron pair with formation of composite structures as the result of successive pair divisions up to the present epoch with half the mass-energy of the preceding parent electron-positron pair.

The present day universe exhibits a dyadic structure of opposites. Nothingness as the absence of something is equivalent to a summation of opposites. Expansion of the universe may result from gravitational dipole attraction and repulsion of positive and negative Planck masses producing a net dipole translation — a quantum gravitational effect.

The phase transition of the Planck vacuum proceeds from an initial spinless, unperturbed, coherent, low entropy state in imaginary time to the present chaotic, frustrated, defect-filled, high spin state with spin wave excitations of Planck dipoles in real time. Physical observables, i.

Non-spin vacuum states of Planck dipoles with net zero mass represent unobservable states corresponding to dark energy. A Planck mass, in common with a black hole, is characterized by size, mass, charge and spin.

## Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions

Spatio-temporal wave decoherence provides an explanation for increasing entropy and quantum entanglement. Spatial coherence refers to in-phase alignment of adjacent waves across the wave front. Monochromatic wavetrains correspond to infinite coherence length. Quantum Vacuum expansion of the universe. The simultaneous creation of positive and negative energy appears consistent with conservation of energy in such a process. Curiously, there seems to have been only one Big Bang rather than a fireworks succession of randomly dispersed Big Bangs in time and space reminiscent perhaps of a highly improbable rogue wave occurrence on an otherwise coherent sea of wavefunctions inducing one-time symmetry- breaking when all hell broke loose.

Also, to be explained is why the Big Bang did not immediately self-extinguish. The vacuum at the Planck scale has been described as a quantum foam of bubble and void-like structures in constant motion resulting in zero-point energy. Did this quantum foam of positive and negative curvature arise as a result of the Big Bang similar to bubble formation during uncorking of a bottle of champagne or was it pre-existing?

Bubbles and voids may be described as positive and negative Planck masses with geometry of inscribed and circumscribed N-polygons with frequency characteristics resembling positive and negative mass. In the creation of the universe from a singularity event, how does Planck mass arise? What is the nature of the singularity? Given the dyadic nature of the known universe, we might guess that the singularity corresponds to a superimposed source and sink. As these are mutually incompatible states, we might suppose that the singularity represents an alternating source and sink of, say, spherical waves resonantly diverging from and converging toward a point.

The radius of convergence equals the distance to the nearest pole. Viewed on a Riemann sphere, a doublet may be represented a stereo projection of poles of a unit sphere on to the complex plane. The lines of constant and real parts may be interpreted as a representation of an example of transformation of imaginary mass into real mass. The gravitational constant G represents the strength of mass coupling.

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Phase transformation corresponds to conversion of counter-propagating massless travelling waves into closed-loop standing waves with real rest mass. Magnetic field lines in a Planck vacuum are interpreted as quantized superfluid vortical filaments of spinning Planck dipoles forming closed loops or string-like linear defects terminating in monopole-like point defects or boojums at the boundary. Elementary particles represent spin wave excitations of Planck dipoles. Photons represent travelling wave excitations of Planck dipoles.

Electrons and positrons represent the simplest possible resonant, standing wave, closed-loop, topologically bound spin wave structures formed of Planck dipoles in a Planck vacuum. The interior of bubbles in the Planck vacuum in the model described resembles in some respects the stasis fields of science fiction. The bubble interior is invulnerable to anything externally and reflects incident radiation. The high frequency domain walls form, in effect, an impenetrable barrier to matter and radiation and act as point scattering centers for electromagnetic waves.

On collision, the Planck bubbles elastically scatter off each other and become immobile in the interior of black holes. But it is evident that this [Planck] length must be the key to some essential structure. But all that is music for the future and prior to that it is still necessary to do a lot of mathematics. Pauli The more the universe seems comprehensible, the more it seems pointless. Ehrenfest It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices.

One could go on to 4 by 4 matrices, and the problem is then easily solvable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to the correct values for the spin and magnetic moment.

This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron. Dirac What we observe as material bodies and forces, are nothing but shapes and variations in the structure of space. Quantum Vacuum Quantum vacuum decoherence Fig. Vacuum expansion dark energy associated with Big Bang may be attributed to phase shift of Planck dipoles from coherent, low entropy, spinless state of a Planck vacuum to expanding state with spin wave structures physical observables.

Light and matter represent travelling and standing waves, respectively, composed of Planck mass dipoles. Quantum Vacuum Formation of a polarizable vacuum Fig. Stereographic projection of poles of a pair of Riemann spheres onto the complex plane. Pole rotation about the vertical axis increases the magnitude of the convergence radius. Vacuum instability from a flat, featureless void may result in formation of regions of positive and negative curvature forming bubble-like regions corresponding to inscribed and circumscribed N-sided polygons which naturally converge to fixed radii described by the Kepler-Bouwkamp constant and its inverse.

The nodal patterns correspond to spectral energy densities of positive and negative mass. A vacuum of such dipoles constitutes a polarizable medium. The pattern of constant real and imaginary lines resembles that of electric and magnetic fields as well as lines constant curvature and torsion.

The Riemann sphere is analogous to a 3D Smith chart of impedance. A monopole singularity resembles the electromagnetic dominant mode field pattern of a coaxial AC transmission line viewed end on. Similarly, a dipole singularity resembles the dominant mode field pattern of a parallel wire transmission line. A pulsating singularity may be represented as a wave guide array with sequenced end switching of an AC generator source and load sink or oscillating transformer.

As such, the Big Bang may represent a runaway resonant feedback oscillation. A non-pulsating singularity corresponds to a bimodal degenerate transition from a flat vacuum instability as in a single fold catastrophe manifold expansion from a point with sudden change in curvature into a pairing of opposite curvatures.

As defined by Jefimenko[16,17] an electric field Ek generated by motion of time-variable currents results in an induced electrokinetic force Fk on nearby electrical charges. The induced current caused by the electrokinetic field is opposite to the inducing current when the current is increasing positive time derivative and in the same direction when the current is decreasing negative time derivative. Jefimenko notes that Faraday induction is not an electromagnetic phenomena — induced currents are not caused by changing magnetic fields, but by an electrokinetic field created by changing electric currents.

The vector potential A represents an interaction of moving charges while the scalar potential f represents interaction between static charges. The vector potential is described as the principal observable in quantum mechanics and is featured prominently in the Aharonov-Bohm effect, super-conductivity, etc. The electro- magnetic 4-vector potential Am components are illustrated in Fig. A notional sketch of a quantized vacuum composed of Planck particles is depicted in Fig. In the Planck aether hypothesis advanced by Winterberg[7], the Aharonov-Bohm effect involving a wave function phase shift in the absence of an E and B field external to a region enclosing a magnetic field may be understood as a result of a net differential in kinetic energy of counter-rotating potential vortices of positive and negative Planck masses which are treated as the source charges that produce the electromagnetic field.

Only physical quantities remain invariant under gauge transformations. Gauge transformations allow changes to the scalar f potential and vector potential A without changing the field equations or the E and B field components. During initial charging of the capacitor, current flows radially outward from the connecting lead to the periphery of the conductor plate as voltage is applied.

In a capacitor, current leads voltage and reverses direction with voltage reversal. The phase difference between current and voltage depends on the relative amount of resistance, inductance and reactance in a circuit. The flow of electrons is accompanied by an associated electrodynamic potential momentum A which is in opposition to the direction of current.

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Spacetime is a manifestation of a physical field. Geometric representation of components of the electromagnetic vector potential Am: scalar potential f and vector potential A. Force, then, is…Only a Vector. Photon velocity is proportional to the mean free path. The local energy density departures from the local zero-point energy level represent electrical stresses plus or minus electrical potential.

Wave speed is controlled by tension, the strength of attraction between neighboring weights such as a system of weights connected by springs , speed is proportional to square root of tension, e. The ratio of effective mass to photon energy-momentum depends on how much it is slowed down in regions of increased energy density.

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The photon, in the model considered, constitutes a propagating torsional wave disturbance of a collection of Planck dipoles composed of positive and negative mass with quantized angular momentum. The rotation of the Planck masses provides the observed photon angular momentum with mass cancellation providing net zero rest mass. A photon represented as a kink or topological soliton Planck dipole spin density wave is illustrated in Figs.

As shown, light waves represent a soliton spin density wave disturbance in a polarized vacuum of variable index of refraction KPV r,w,M. Electric field intensity E corresponds to alignment of Planck dipoles while the magnetic field intensity H corresponds to a differential rotation of dipoles.

The photon magnetic field B represents an alignment of the spin angular momentum vectors of spinning Planck dipoles. The electric field E of the photon represents an instantaneous, periodic in-phase alignment of Planck dipoles. The shape of KdV solitary waves are extraordinarily stable against small distortions and, like solitons, photons may remain unchanged after collision.

Position and momentum fluctuations in spacetime consist of elastic deformations due to curvation and plastic deformations due to torsion. Waves from moving sources: Adagio, Andante, Allegro moderato. Electromagnetic 4-Potential Fig. Electromagnetic 4-Potential Soliton kink spin wave Fig.

Soliton kink spin density wave in a Planck vacuum formed by synchronous alignment of Planck mass dipoles. In the presence of curvature and torsion, a loop closure failure defect in the Planck mass trajectory arises corresponding to a tetrad rotation and translation in tangent space which yields an uncertainty in position and momentum on the order of the Planck scale. An effective mass results from a change in curvature or torsion. Waves we cannot have lest they be waves in something. Electromagnetic 4-Potential Soliton twisted ribbon model Fig.

Soliton twisted ribbon model of spin aligned Planck dipoles. A spinning Planck mass dipole constitutes a mass current generating a magnetic vector potential A. Rotation of the spin plane about the wave propagation axis creates topological charge. A pair of coupled rotational solitons exhibit confinement properties of two quarks interconnected by a string.

The finite time of propagation was thought by field theorists to be sufficient evidence that a field exists in places where there was no matter. The existence of [electromagnetic] waves showed that the propagation of electric and magnetic effects take time, as claimed in the field theory.

When they are first proposed they often have the same quality of unexpectedness, and perhaps wrongheadedness, as say, cubism, abstract art, or atonal music. Waddington A style of reasoning makes it possible to reason towards a certain kind of propositions, but does not itself determine their true value. Hacking Ignorance is like a delicate exotic fruit; touch it and the bloom is gone.

The electric permeability e0 and the magnetic permeability m0 corresponds to a superfluid density and compressibility, respectively. Using G-1 as the appropriate coupling factor, the discrepancy is reduced by orders of magnitude. As explanation for the vacuum energy density mismatch between calculated and observed values, Winterberg[7] hypothesizes that the vacuum must contain a large negative mass cancelling the large positive mass of the zero-point energy.

In the Winterberg model, electric charge is associated with a net imbalance of spin direction of vortical flow. In the Winterberg Planck aether hypothesis, the physical vacuum is ultimately composed of spinning Planck scale mass dipoles of positive and negative energy. Mass may be viewed a result of increased energy density due to increased dipole volumetric density. Gravitationally bound collections of Planck dipoles of positive and negative mass, such as the neutrino or postulated spinor rotons, with net zero particle mass but with positive mass energy of the gravitational field, may account for a portion of dark matter consisting of non- baryonic matter and cold, diffuse baryonic matter.

In accordance with the Jefimenko gravitational model, an accumulation of mass results in a polarization of the vacuum with matter consisting of a concentration of positive energy and an outwardly displaced gravitational field of negative energy. One half of the gravitational binding energy lost during mass accretion is converted to heat while the remainder is radiated away.

http://kick-cocoa.info/components/xysohuxe/ful-come-spiare-il.php Hence, the total energy of the consolidated mass is less that the mass total of the individual masses prior to contraction. Classical action of torsion involves contact interaction between spins. Effective mass mi is associated with a change in torsion t due to increased energy density. Soliton Confinement Unlike light rays composed of multiple photons, individual photons do not undergo dispersion in a vacuum, but remain confined within a constant radius during propagation in the manner of a soliton wave.

The mechanism for soliton confinement is hypothesized to be the result of an abrupt change in permittivity at the amplitude envelope periphery at the speed of light radius creating an optical waveguide. A radial variation in Planck dipole density gives rise to a cylindrical well in the index of refraction KPV of the vacuum which acts as a waveguide and provides topological confinement. The Korteweg de Vries KdV equation in soliton theory has been shown to arise in Fermi-Pasta-Ulam nonlinear lattice vibrations as the spacing approaches zero.

In a quasi-lattice of a polarizable vacuum composed of Planck dipoles, each Planck mass acts as a harmonic oscillator with coupled harmonic oscillators forming a helical wave and are reflected from the index of refraction boundary similar to an a dielectric resonator or optical ring resonator. Assuming a Kerr electro-optic effect due to the alignment of Planck dipoles in an electric field, the refractive index of a polarizable vacuum in analogy to material dielectrics in- creases with increasing frequency and square of the electric field intensity. For a circularly polarized photon, the complex wave field may be expected to give rise to torque orthogonal to the direction of propagation.

A notional diagram of cylindrical waveguide resulting in topological confinement is illustrated in Fig. At the cylindrical boundary, the E-field has both radial and tangential components. Outside the boundary, the Planck dipoles become depolarized with random E-field direction. For a focused beam of photons, even in a vacuum, the axial velocity is reduced below c due to the inclination of the wave vector k with respect to the axial direction. Soliton Confinement Fig. Soliton spin wave confinement in an optical waveguide composed of oriented polarized Planck dipoles.

That he [Einstein] may sometimes have missed the target…as, for example, in his hypothesis of light quantity, cannot really be held against him. Electromagnetic Field Dimensions The photon has no electric charge, yet is characterized by an electric field component. Electric charge q is conventionally taken as a fundamental property and represented as a separate dimension [Q] in the S.

MKS system of units. However, although related to topological charge, its exact nature has remained a mystery. Electromagnetic Field Dimensions Conservation of momentum in electrodynamics is realized as both moving charges and attendant electromagnetic fields carry momentum, i. In a collection of point charges, mechanical momentum of particles may be interchanged with the electrodynamic momentum of fields.

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As Mead[21] has shown, the inertia of a collection of interacting charges varies with the square of the number of charges. Hence, the momentum of an electric current in a conducting wire exhibits considerably more momentum than isolated electric charges.

At velocities small compared to the velocity of light, inertial mass is essentially constant. The minus sign is a convention signifying the force is attractive. Charge arises from this precession; mass arises as a result of wave interference. Electrostatic potential energy corresponds to a volumetric compression of dipole charge elements. A summary table of mechanical equivalents of electromagnetic quantities is illustrated in Table For reference, also shown are Planck scale units.

For simplicity, the conversion formulas show only the rotation angle topological charge in radians associated with electric charge Q. The corresponding conversions based on Eqn are tabulated in a subsequent section for various electromagnetic parameters illustrating the derived dimensions and MKS SI units conversion into mechanical equivalents. Units conversion may also be expressed in terms of the electron Compton wavelength lC.

Space-time reference frames in uniform relative motion known as inertial frames exhibit physical equivalence. Inertial frames are in constant relative motion with respect to each other and are related by Lorentz transformations. A change in position is a translation; a change in orientation is a rotation; and a change in velocity is a boost. The set of rotations and boosts are known as Lorentz transformations. Electromagnetic Field Dimensions corresponding to Lorentz transformations.

The set of all Lorentz transformations in Minkowski spacetime is named the Lorentz group denoted as Lie group O 1,3. Lorentz transformations and rotations may each be represented as 4 x 4 matrices. Under Lorentz transformations, the form of physical laws remain unchanged in accordance with the general principle of covariance. By its very nature the Aether is a vibrating medium.

A new aspect of the universe is striving to reveal itself. But no fact is so simple that it is not harder to believe than to doubt at the first presentation. I do not apologize, for I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Lynden Bell The life contest is primarily a competition for available energy. Nature treats life as though it were the most valueless thing in the world.

It is the task of fundamental physics to understand these facts. Dick Man can know the nature of things. But without it we go nowhere.