Theory of strong interactions. I. Kinematics

This paper is the first of a series devoted to strong interaction theory. As a general introduction to the series, we give a critical survey of theories and models presently in force.In a previous paper, we studied the kinematics of a single unstable hadron, the state of which was described as an incoherent superposition of states with different masses. To such a state there corresponds a function on the Poincaré group, called a characteristic function. Here we take up these old results anew, we work them out, and we go more thoroughly into their physical foundations. Then we describe the kinematics of several particles.The theory of strong interactions must take into account two opposed features of unstable hadrons: their identity and their difference with stable hadrons. The identity implies that an unstable hadron is in a certain state, described by a density operator; the difference is that this state has a mass spectrum, whose width cannot be neglected.We make the further assumption that the state is an incoherent superposition of components with different masses. This assumption is compared to the statistics experiment of Baton and Laurens, in which the components with different masses have been effectively separated.We define the characteristic function of such a state, and we point out its analogy with a usual characteristic function in probability theory. The physical meaning of characteristic functions is studied on the example of a spin, then in the general case.Then we study the characteristic function of several hadrons, and we define two notions: the global particle and the inclusive characteristic function.     

Special Theory of Relativity in Electrodynamics

A method of teaching of one of the divisions of electrodynamics devoted to relativity theory is suggested. The presentation is based on the four-dimensional formalism, which allows a number of fundamental physical phenomena to be considered from a unified position. The content is in full conformity with the approved standard programs for students and postgraduates of radio physical and radio technical specialities of universities. The methods can be useful to the teachers, scientific workers, and engineers concerned with other directions and specialities.     

Chronostructures of Special Relativity Theory

The class of all theoretically admissiblegeometric structures describing relative rates at whichmoving clocks work (the so called chronostructures) isconsidered. The transformations of space-timecoordinates of events implied by the choice of thechronostructure are determined. It is shown that thechronostructure is invariant with respect to thetransformations which it determines if, and only if, itis correlated with the Lorentz chronostructure. Thischronostructure is the simplest one in the class ofinvariant chronostructures.     

An Introduction to Influence Theory: Kinematics and Dynamics

Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their empirically determined relationships, from a more primitive model. It is postulated that there exist things, which are call particles, that influence one another in a discrete and directed fashion resulting in a partially ordered set of influence events. The problem of consistent quantification of the influence events is considered. Observers are modeled as particle chains (observer chains) as if an observer were able to track a particle and quantify the influence events that the particle experiences. From these quantified influence events, consistent quantification of the universe of events based on the observer chains is studied. Herein, the kinematics and dynamics of particles from the perspective of influence theory are both reviewed and further developed.     

Kinematics in matrix gravity

We develop the kinematics in Matrix Gravity, which is a modified theory of gravity obtained by a non-commutative deformation of General Relativity. In this model the usual interpretation of gravity as Riemannian geometry is replaced by a new kind of geometry, which is equivalent to a collection of Finsler geometries with several Finsler metrics depending both on the position and on the velocity. As a result the Riemannian geodesic flow is replaced by a collection of Finsler flows. This naturally leads to a model in which a particle is described by several mass parameters. If these mass parameters are different then the equivalence principle is violated. In the non-relativistic limit this also leads to corrections to the Newton’s gravitational potential. We find the first and second order corrections to the usual Riemannian geodesic flow and evaluate the anomalous nongeodesic acceleration in a particular case of static spherically symmetric background.     

Kinematics of the Earth continental drift

The drift of regions in northeast Eurasia was studied using the precise satellite geodesy method (Global Positioning System (GPS)). Observational data were analyzed invoking the International Database. Despite the rather short observations (～6 years), the drift directions of the basic Eurasia and Northern America regions were detected and the drift velocities were estimated. The results of the study are discussed in general terms of the deformation and fracture of solids.     

Kinematics of the most efficient cilium

In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although cilia have a remarkably conserved internal molecular structure, experimental observations report very diverse kinematics. To address this diversity, we determine numerically the kinematics and energetics of the most efficient cilium. Specifically, we compute the time-periodic deformation of a wall-bound elastic filament leading to transport of a surrounding fluid at minimum energetic cost, where the cost is taken to be the positive work done by all internal molecular motors. The optimal kinematics are found to strongly depend on the cilium bending rigidity through a single dimensionless number, the Sperm number, and closely resemble the two-stroke ciliary beating pattern observed experimentally.     

The Vacuum as Ether in the Last Century

In this paper we review the evolution of the concept of vacuum according to different theories formulated in the last century, like Quantum Mechanics, Quantum Electrodynamics, Quantum Chromodynamics in Particle Physics and Cosmology. In all these theories a metastable vacuum state is considered which transforms from one state to another according to the energy taken into consideration. It is a fluid made up by matter and radiation present in the whole Universe, which may be identified with a modern definition of ether     

Dispersion in the Ether: Light over the Water

This is an account of measurements of the velocity of light by James Young (1811-1883) and George Forbes (1849-1936) around 1880 based upon an improved version of Fizeau's toothed-wheel method. They presented evidence for a dispersive effect resulting in a difference in the velocity of 1.8% across the visible spectrum. This conflicted with Albert A. Michelson's measurements and prompted discussions by Lord Rayleigh, Arthur Schuster, Léon Gouy, J. Willard Gibbs, and Paul Ehrenfest that led to the conclusion that not the phase velocity but the group velocity was being measured, and that there was no theoretical foundation for Young and Forbes's result.     

Kinematics of new transformations

By constructing a composite mapping of Voigt and Lorentz transformations some new non relativistic transformations of conformal type are obtained where the laws of Maxwell’s electromagnetic theory are found to be invariant. This new scheme is consistent with some of the well established experimental facts.     

Method of Length Measurement Symmetrical about the Laboratory and Moving Reference Systems in the Special Theory of Relativity

With the use of symmetry it is demonstrated that for equal moduli of non-simultaneity of fixing the ends of the measurable length in both reference systems, the coordinate difference is equal to the length itself. The identity of scales of both reference systems is proved. A method of calculating the coordinate difference for non-simultaneities that differ from those in the symmetrical measurement scheme is described. The method is based on the use of experimental non-simultaneities and obviates the need for the application of the Lorentz transformation of coordinates. It is demonstrated quantitatively that there are no false discontinuities in a closed flow when an increase in the particle flow density is proved for a stationary observer and that the observable sizes of a rotating disk remain unchanged.     

Kinematics for the scattering of spacelike momentum

The kinematics of elastic and inelastic tachyon-bradyon and tachyon-tachyon scattering 22 is examined. To get kinematic limits finite, the initial and final momenta of a tachyon are subjected to the restrictionpp<0. This is sufficient in tachyon-bradyon scattering; in tachyon-tachyon scattering additional covariant restrictions exist, though these follow from the problem. In an alternative approach, where there is interaction the particle energies must be positive relative to the rest frame of the total momentum, which additional condition is shown to lead to a simplification of the kinematic results.     

Kinematics of deformable media

We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations. The analytical solutions allow us to study the dependence of the kinematical quantities on initial conditions. In particular, we are able to identify regions of the space of initial conditions that lead to a singularity in finite time. Some generic features of the deformations are also discussed in detail. We conclude by indicating the feasibility and utility of a similar exercise for fluid and geodesic flows in a flat and curved spacetimes.     

Kinematics of Yang-Mills solitons

In SU(2) Yang-Mills theory, theN-monopole configuration space is a bundle with fibers isomorphic to U(1)×...×U(1), and state vectors for which each monopole has chargen e/2 are homogeneous of degreen with respect to each U(1). Translations and rotations are defined for individual monopoles in theN-monopole space. The commutator of two translations is found to be a U(1) transformation that agrees for large monopole separation with the analogous phase change accompanying the translation of a charged point particle in an external magnetic field. The theory developed here is applied in a companion paper to prove a spin-statistics theorem for monopoles in SU(2) Yang-Mills theory.     

Non-Linear Kinematics of Line-Structures

In a preceding paper [3] we have formulated a geometrical theory of structural defects for a very large classe of materials e. g. ordinary crystals, line structured materials as polymers and others. The application to a special kind of material requires a physical interpretation of the geometrical terms for this material. Referring to the papers of ANTHONY [1, 2], we give here a generalization of the geometrical theory of line structures, that is comprising a general internal motion of the material including the motion of defects. In order to do this the theory is to be formulated within anholonimic coordinates, here defined by the Frenets triads of the structural lines, being generally in motion. The geometrical terms for the current of the dislocation of the line structure, the current of the torsion of the lines (without defects) as well as the current of line disclination are explained.     

Spherulitic Growth of Poly (Ether Ether Ketone) Crystallized at High Pressure

High-pressure crystallized poly (ether ether ketone) (PEEK) samples were prepared with a piston-cylinder apparatus by varying temperature, pressure, crystallization time, and molecular weight, and were investigated using wide-angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC), and scanning electron microscopy (SEM). The applied etching experiments showed that the chemical resistance of the polymer was significantly improved through the high-pressure treatment. The results also revealed that PEEK spherulites with folded-chain lamellae as substructures and with different characteristics were formed at high pressure. Crystalline elliptical micro-spheres consisting of flake-like lamellae with rugged surfaces were observed on the etched samples with SEM, which may diversify niche applications in functional fillers, carriers, adsorbents, etc. Morphological observations suggested that such micro-spheres might possibly have evolved from a novel dendritic crystal. Furthermore, a granular substructure of the lamellae was observed in these single-phase polymer systems with rigid molecular backbones, which further confirmed the model developed by Strobl for polymer crystallization.     

Reduction of Relativistic Three-Body Kinematics

The Klein—Gordon system describing three scalar particles without interaction is cast into a new form by transformation of the momenta. Two redundant degrees of freedom are eliminated; we are left with a covariant equation for a reduced wave function with three-dimensional arguments. This new formulation of the mass-shell constraints is equivalent to the original KG system in a sector characterized by positivity of the energies and, if the mass differences are not too large, by a moderately relativistic regime. Introducing mutual interactions provides a model which is (at least for three equal masses) tractable and admits a reasonable nonrelativistic limit.