From Dirac’s Aether to the Dirac Equation

In 1951, Dirac proposed a formalism for a Lorentz invariant Aether with a vacuum state that contains all possible velocity states at each space-time point. Dirac showed no explicit path from the Aether towards the Quantum Mechanics. In this paper, we demonstrate that Dirac’s proposed Aether can be described by a lattice of possible events in space-time built in the local Lorentz frame. The idealised case of single velocity state leads to the famous Dirac equation for a plane wave state and is compatible with quantum statistics. On the lattice, possible space-time events are connected by the Dirac spinors which provide the probability of observing an event. The inertial mass of a particle is shown to be equivalent to the density of possible events on the lattice. Variation of the lattice density of events modifies the metric and provides a space-time curvature leading to the Hilbert action associated with general relativity. In classical limit, the perturbation in the density of possible events of the Aether is proportional to the Newtonian gravitational potential.

On Spinors

For a 2^n-dimensional complex Hermitian vector space S, we prove that any unitary basis of S can be explained as an augmented spinor structure on S. By using this explanation, a SpinC（2n）- action on S is equivalent to an action on a subset of augmented spinor structures. The latter action is a little easy to be understood, and is shown in the last part of this paper. Such kind of understanding could be of use to the discussions of Hermitian manifolds and spin manifolds, especially could help to find connections and elliptical operators.

Twistor Spinors and Quasi-twistor Spinors

The author studies the properties and applications of quasi-Killing spinors and quasi-twistor spinors and obtains some vanishing theorems. In particular, the author classifies all the types of quasi-twistor spinors on closed Riemannian spin manifolds. As a consequence, it is known that on a locally decomposable closed spin manifold with nonzero Ricci curvature, the space of twistor spinors is trivial. Some integrability condition for twistor spinors is also obtained.

Localization of five-dimensional Elko spinors on dS/AdS thick branes

Owing to the special structure of a five-dimensional Elko spinor,its localization on a brane with codimension one becomes completely different from that of a Dirac spinor.By introducing the coupling between the Elko spinor and the scalar field that can generate the brane,we have two types of localization mechanism for the five-dimensional Elko spinor zero mode on a brane.One is the Yukawa-type coupling,and the other is the non-minimal coupling.In this study,we investigate the localization of the Elko zero mode on de Sitter and Anti-de Sitter thick branes with the two localization mechanisms,respectively.The results show that both the mechanisms can achieve localization.The forms of the scalar coupling function in both localization mechanisms have similar properties,and they play a similar role in localization.

Magnetic and Electric Charges in Physics and Technology of Electromagnetic and Magnetoelectric Induction

Experimental and theoretical researches performed by the author (period: 1969-present) showed that magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and immediate sources of all magnetic fields and magnetic manifestations in Nature. Magnetic charges, that constitute together with electrical charges atomic shells got of title: magnetons and antimagnetons (respectively with charges g−and g+ under fundamental condition: g = e). Furthermore, in addition to participating in structures of atomic shells, the magnetic charges exist in potential and even in real zones conduction of solids. The magnetic and electric spinor particles in atoms and substance exist in form such of the spinor associations as the magnetic and electric bispinors. Under influence of external magnetic field in conductor being implemented polarization of magnetic bispinors with formation of magnetic dipoles. Internal fields magnetic dipoles is directed against an external magnetic field and is a simple explanation of such a physical manifestation as diamagnetism. During the rotation of these dipoles in the conductor are formed of the vortex magnetic dipole fields, which and create an electromotive force, i.e. are responsible for the electromagnetic induction. Author proposed new magneto-electric technology called the magnetoelectric induction, as the result of which the permanent current of magnetic charges is created. However, such currents may be implemented solely in the superconductors. In the article presented the main reasons which more hundred year old hinder recognition and technical use of the real magnetic charges and their currents what considerably slow down the global scientific and technological progress.

“Electrical” and “Magnetic” Worlds in Universe

Magnetic spinor particles (magnetic charges), which are the direct sources of all magnetic fields and magnetic manifestations in Nature, were experimentally discovered by the author in the structures of atoms and substance. The main reasons that the real magnetic charges were “buried alive” in modern theoretical concepts are the Physics their of confinement in the structures of substance, which is cardinally different from the confinement of electrons, as well as electromagnetic concept of Maxwell, in which magnetic field was erroneously deprived of its own source, i.е. of magnetic pole or magnetic charge. Magnetic and electric charges form atomic shells, which are electromagnetic, and not electronic, as is commonly assumed in the existing physical theory. Namely, the magnetic and electric charges in the joint physical processes form all the varieties of the physical mass, i.е. atoms, nucleons, substance and others. The main feature of physical mass is its ability to radiate gravitational field, which in reality is of the vortex electromagnetic field. The immediate sources of gravitational field are joint orbital currents of electric and magnetic charges in compositions of atomic shells. In 2008 the author for the first time introduced the concepts of “electric” and “magnetic” worlds. So, in the “magnetic” world the processes of condensing all elementary varieties of physical mass: atoms, nucleons and others are initiated not by electric charges as in our “electric” world, but by means of magnetic charges. Electric and magnetic charges in the compositions of physical mass, in differently charged worlds are changing their functional roles and, for example, detect electrons in the “magnetic” world also difficult as the magnetic charges in our of “electric” world. According to conceptions of the author and in our Universe existence of both “electric” so and “magnetic” masses, including charged differently of biological masses is quite possible. It is impossible to exclude and the existence of otherwise “charged” living organisms and even “electrical” and “magnetic” anthropoid beings. The latter allows to assume perhaps the existence of the differently “charged” civilizations and in our Universe.

Real Magnetic Charges in the Substance, Ferrogravitation and Technical Levitation

Experimental and theoretical investigations by author of the present article (period: 1968-2013) have shown that the magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and are immediate sources of all magnetic fields in Nature. Joint orbital currents of electric and magnetic charges within atomic shells are the natural sources of gravitational field which is a vortex electromagnetic field. The vector character of the elementary gravitational field is similar to the vortex magnetic field that allows entering in the submission of such fundamental states of the gravitational field, as a paragravitation and ferrogravitation. Physical masses (atoms, nucleons, substance, etc.), which emit ferrogravitational field are repelled off from sources paragravitational field, for example, from Earth. It is a manifestation of the effect of levitation, which was discovered by the author of this article. Technical forces levitation, that induced by technical ferrogravitational fields, could be used in transport, lifting and space technology, power engineering and many other areas of human activity. The main reasons that real magnetic charges are “buried alive” in modern theoretical notions are as physics their of confinement in the structures of atoms and substance which are radically different from the confinement of electrons so and fallacious electromagnetic concept Maxwell in which the magnetic field is by mistake deprived of its own source of the magnetic pole or of the magnetic charge.

Real Magnetic Poles (Magnetic Charges) in the Physics of Magnetism, Gravitation and Levitation

Experiments executed by author of the present article (period 1968-1992) showed that the magnetic spinorial particles (magnetic charges) are real structural components of atoms and substance and are immediate sources of all magnetic fields in Nature. Joint orbital currents of electric and magnetic charges within atomic shells are the natural sources of gravitational field which is a vortical electromagnetic field. The vector nature of the gravitational field, in essence, is analogous to the vortical magnetic field that allows entering in the physical representations of such States of the gravitational field as paragravitation and ferrogravitation. Physical masses (atoms, substance, etc.), which emit ferrogravitational field, are repelled by sources paragravitational field, for example, from Earth. It is a manifestation of the effect of levitation, which was discovered by the author of this article. The forces of the technical levitation, which are formed by technical ferrogravitational fields, can be used in transport, lifting and space technology, energy and many other areas of human activity. The main reason that the real magnetic charges were “buried alive” in modern theoretical physics is the conditions of their confinement in the structures of atoms and substance, which is radically different from the confinement of electrons. Very negative role is played here by erroneous electromagnetic concept Maxwell, in which the magnetic field was officially deprived of their own source: magnetic pole or magnetic charge.

Dirac’s “Holes” Are the True Antielectrons and Real Particles of Antimatter

Experimental and theoretical studies performed by the author showed that electric and magnetic spinor particles as spinors, i.e. particles of Matter so and Antispinors, particles of Antimatter, are structural components of atoms and substance. Together with electric spinors, for example, electrons in the structures of atoms and substances in same quantities, there are real electric anti-spinors, i.e. the true antielectrons, which are not to be confused with electronic vacancies or positrons. Atomic-shaped electromagnetic structures, consisting of electric and magnetic spinor particles, such as nucleons and atoms, represent a Physical Mass. A characteristic property of all varieties of Physical Mass is the ability to emit a gravitational field which is a vortex electromagnetic field. Sources of the gravitational field are joint orbital currents of electric and magnetic charges in the compositions of atomic or nucleon shells. The main reason that the real antielectrons turned out in the Physical sciences under the guise of Dirac’s “holes” or vacancies of electrons, is the Physics of the confinement of these particles in atoms and a substance that is fundamentally different from the confinement of electrons. So, namely Physics confinement of the magnetic spinor particles and electric antispinors in atoms is the main “culprit” creating a fallacious concept of purely electronic atomic shells. The main contributions to the formation of the above-mentioned misconceptions did as J. C. Maxwell with its primitive-surface electromagnetic concept so and P. Dirac, with his erroneous theory of electronic vacancies or “holes”.

The World Physical Triad: Matter, Antimatter and “Dark Energy” in the Processes of Climatic Changes on the Earth

The opening and many years of research of magnetic spinor particles (real magnetic charges) in atoms and substance have enabled the author to formulate the conception of the Physical Triad, according which the real World consists of three fundamental phases: Matter, Antimatter and Energo-phase (Energo-medium). Particles of Matter are called spinors and particles of Antimatter are called antispinors. Energo-medium is a gasiform phase of high density that fills by himself all the infinite space of the real World. It consists of spinless and massless particles-energions. Spinor fields can be both flows energions (fields of Matter), so and anti-flow energions (fields of Antimatter). Atomic-shaped structures consisting of electric and magnetic spinor particles represent a Physical Mass (atoms, nucleons, etc.). The main characteristic of all varieties of Mass is its ability radiate gravitational field, which is a vortex electromagnetic field. All spinor particles are massless so as individually generate a gravitational field they can’t. All primary forces in the real World are implemented by means of Energo-medium, i.e. contact pressure its particles—energions. The spinor fields, including the gravitational field, myself the real of the power significance, have not. They are only intermediaries, inducing in Energo-medium its active (power) education, which is called “Dark Energy”. “Dark Energy” can be both positive, so and negative. Namely, a positive “Dark Energy”, which is associated with the technical activity of man, is responsible for stable climatic changes on Earth. Greenhouse gases are not the main “culprit” of climatic changes on our planet. However, these gases are the simplest indicator of the overall level of irreversible physical processes that stimulate the growth of the positive “Dark Energy” and are responsible for the negative thermal scenario on Earth.

Electromagnetic Shells of Atoms and the Periodic System of Elements

Experimental and theoretical researches performed by the author (period: 1969-present) showed that the magnetic spinor particles (magnetic charges) are real structural components of atoms and substance and are immediate sources of all mag-netic fields and magnetic manifestations in Nature. Magnetic charges, which constitute together with electrical charges the atomic shells, got of the Author’s title: magnetons and antimagnetons (respectively, with magnetic charges g− and g+, under fundamental condition: g = e). Besides, together with electrons and magnetic charges in the structures of atomic shells, in the same quantities as the electrons, exist real electric antispinors, i.e. the true antielectrons. In the structures of the atomic shells on each electron fitted still three a real spinor particles: two magnetic (magneton and antimagneton) and one electric, i.e. true antielectron with a charge of e+. The spinor particles in atomic shells exist in the form of the two spinor associations: the electromagnetic dibispinors or S-Gravitons and magnetic bispinors (spinorial magnetic dipoles). Magnetic bispinors, which inhabited on the 3d and 4f-shells are the sources of the atomic magnetic fields and are responsible at all magnetic manifestations of the so-called magnetic atoms (iron, nickel, cobalt and others). In composition of S-Graviton is two related bispinor (electric and magnetic). S-Gravitons make up bulk of the charged density of atomic shells and are direct sources of the atomic gravitational field.If to replace all electrons on known of the atomic levels and sub-levels on S-Gravitons, can get an idea about the real electromagnetic device atomic shells most of the elements making up the Periodic Table. In article shows features the structural organization real (electromagnetic) shells of atoms that make up the periodic system of elements, as well as is considered the possibility of adaptation of the well-known quantum numbers, the Pauli’s principle and Hund’s rule, in relation to the atomic electromagnetic device. The main reasons for the fact that the real magnetic charges, as well as the true antielectrons, were “buried alive” in the modern theories are as physics confinement them in atoms and substance, which is cardinally different from the confinement, for example, electrons, so and vicious electromagnetic concept of Maxwell. In the framework of this concept really existing in atoms and substance the magnetic charges, have been mistakenly substituted on acts of the mechanical displacement of electrical charges.

Clifford代数的spinor表示空间

讨论了Clifford代数的结构 ,证明Clifford代数的pinor或spinor空间都可以表示为其子空间 ,且都可以由一个元素生成 .选取不可约表示空间的基 ,具体建立了Clifford代数与矩阵代数之间的同构 .

APPLICATION OF SPINOR METHOD TO THE DYNAMIC ANALYSIS OF ROBOT

A method known as spinor method is applied to the study of dynamic model of robot.It merges velocity and angular velocity.Force and moments into an organic whole by their internal relation, and mates Newton-Euler method more concise and efficient.A reference system is formed with respect to the mass center of the arms of robot, which simplifies the calculation of inertial lensor and mass center acceleration.And further reduces work load in calculation, and thus ensures a fast real-timecalculation.

Clifford代数的Spinor表示空间

讨论了Clifford代数的结构 ,证明Clifford代数的Pinor或Spinor空间都可以表示为它们的子空间 ,且都可以由一个元素生成 选取不可约表示空间的基 。

Neutrino Masses and See-Saw Mechanism

A neutrino is a subatomic particle that is very similar to an electron, but has no electrical charge and a very small mass. Neutrinos are one of the most abundant particles in the universe. Because they have very little interaction with matter, however, they are incredibly difficult to detect. We present a study of the physics of neutrinos using the Dirac lagrangian. Based on Lorentz invariance we introduce the notion of Majorana spinor. Then we derive the mass terms for both Dirac and Majorana neutrinos. We further discuss the general framework of the See-Saw mechanism considering a simplification of the problem.

Quantum Entanglement on Cosmological Scale

It has been indicated that relational logic may serve as the common foundation of quantum mechanics and string theory. A relation may be represented by a spinor and the Cartan-Penrose connection of spinor to geometry, allows to abstract geometry as the outcome of entangled relations-spinors. Our approach goes in parallel with Wheeler’s pregeometry, where pregeometry, the stage preceding geometry, is based on a calculus of relations-propositions. With a single spinor related to the null cone of Minkowski space-time, we search for the geometry when we couple a left-handed spinor and a right-handed spinor. We find that a Majorana-type coupling gives rise to the ordinary entanglement, while a Diractype coupling generates an extra dimension with two branes coexisting in the extra dimension. One brane hosts lefthanded particles (our brane), while the other brane hosts right-handed particles. A distinct phenomenology accompanies our proposal. The left-right symmetry is achieved with having two “mirror” branes and the neutrino appears as the ideal mediator between the branes. We may revisit also the dark matter, dark energy issues, with everything on the other brane and in the bulk appearing “dark” to us. During the brane collision all points are causally connected, making less pressing the inflationary scenario. Our scheme brings closer logic—quantum theory—cosmology, while space-time, rather than an abstract and an a priori construction, appears as the outcome of a quantum logical act.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

Target Detection in Three-Dimension Sensor Networks Based on Clifford Algebra

The three-dimensional sensor networks are supposed to be deployed for many applications. So it is signifi-cant to do research on the problems of coverage and target detection in three-dimensional sensor networks. In this paper, we introduced Clifford algebra in 3D Euclidean space, developed the coverage model of 3D sensor networks based on Clifford algebra, and proposed a method for detecting target moving. With Clif-ford Spinor, calculating the target moving formulation is easier than traditional methods in sensor node’s coverage area.

Cosmological Constant and Energy Density of Random Electromagnetic Field

It is shown that the non-equilibrium electrically neutral and relativistically invariant vacuum-like state with the negative energy density and positive pressure may exist at the non-zero temperature in the system of spinor particles, antiparticles, and random electromagnetic field generated by particle-particle, particle-antiparticle, and antiparticle-antiparticle transitions. At the temperature of the order of 10 -5 K, the energy density of its state corresponds to the dark energy density in absolute magnitude. The cosmological constant for such material medium turns out to be negative.

PLANNING MOTION TRACE OF ROBOT BY SPINOR METHOD

The spinors applied to describe position and attitude of robot are studied. In dual spaces, the terminal trace of robot is planned through the mapping point, of attitude spinors. As a handy method directly perceived through the sense, the spinor method directly converges tracking error in the planning. It promotes the dynamic accuracy of trace operation. It is also suitable to the exerciser with redundant freedom.