Mathematical Physics

Generalizations of Notions of Differential Geometry

Authors: Johan Noldus
Comments: 20 Pages.

The notions of Torion and Riemann curvature are generalized towards general path metric spaces.
Category: Mathematical Physics

Possible Transition from Order Into Chaos and Vice Versa

Authors: Udo E. Steinemann
Comments: 28 Pages. (Note by viXra Admin: Article file size should be <10MB and no author photo should ber used))

The specific model-case of the quadratic-iterator is an illuminating way of understanding the chaotic-behaviour. It is agreed that for the special-cases of iteration of transformations there are common characteristics of chaos: Sensitive dependence on initial conditions, mixing and dense, periodic points. Therefore discussion starts with an important metaphor in chaos-theory, kneading of dough, by 2 different uniform-processes performed iteratively each of them in unit-iterval: [1] Stretch the dough, fold it over in the middle and stretch it again (as often as required), and [2] stretch the dough, cut it in the middle, paste the 2 halfs together and stretch it again (as often as required). This processes guarantee that a pocket of spice inserted into the dough will be mixed thoroughly throughout the mass. Both kneading-processes were found to be compatible in view of their chaotic-characteristics. In a further step of discussion, equivalence could be shown between the 2 uniform kneading-processes and the non-uniform kneading of the quadratic-iterator y = au2022x(1-x), where a = 4 were chosen, via simple coordinate-transformations of the unit-interval. Chaotic characteristics of all 3 iteration-transformations could also be proven as being equivalent to each other. Thus, further investigations were based now on quadratic-iterator. The range from states of order up to the complete chaotic dynamics of the quadratic-iterator can be divided into 3 distinct parts: [1] regime 1 ≤ a < (s∞ = FEIGENBAUM-point) were oscillations of the iterator will experience period-doublings, [2] an area s∞ < a < 4 which can be looked as mirror-image of regime [1], and [3] the chaos-area for a = 4. Boarder between regime [1] and [2] is a CANTOR-set. The mirror-image-area of the quadratic-iterator’s final-state-diagram is characterized by a complicated band-structure and therefore different orbit-dynamics can be expected for (a < s∞) ⇄ (s∞ < a). In other words, transitions from order to chaos and vice-versa may occur but with respect to orbit-dynamics they happen differently every time.
Category: Mathematical Physics

5-Bit Classification in Crystal Classes and Genetic Code

Authors: Giuliano Bettini
Comments: 15 Pages.

I show that 5 bits, or better properties, should be enough to classify the 32 crystal classes of 7 crystal systems, and nothing more. From a rigorous point of view, each of the 32 bit sequences (from 00000 to 11111) must unambiguously identify a class, and each class must unambiguously identify a bit sequence. In this article, which aims to be very simple, easy, and understandable, I emonstrate the thesis by connecting the various bits to properties already present and known in crystallography. I use the same approach to show how even in the genetic code 5 properties or entities or bits are used to create complex structures. I start from the 64 codons table (nucleotide triplets U C A G in RNA, with T substituting U in DNA) that I then examine in a sub-version with 32 codons, still able to codify all 20 amino acids that contribute to the formation of proteins. Considering 32 codons to show symmetries can make sense in an evolutionary process of modifying the genetic code, starting from an ancestral code. I show in this way that there are analogies between the symmetries of the crystal classes and the genetic code. The basic idea is that Nature, having identified a "motif" that works, uses it in several fields.
Category: Mathematical Physics

Is Time a Fundamental Category?

Authors: P. A. M. Moellers
Comments: 25 Pages. This work is prepared from an Informatics background awaiting comments from physics.

Is Time a fundamental category and, if so, on the smallest thinkable scales? Maybe not. To test this conjecture this paper proposes a simple discrete model, the Klick Model. It bases Time on the correlation of two other categories, abstract definitions of motion and state implementation - an Informatics based approach to a problem in physics.

The original motivation to develop the model was to understand the biological/atomic ageing of the twins of the so-called Twin-Paradox, seen as a benchmark combining time and space of smallest and largest scales. Without loss of generality, let us assume that the twins can be represented by two isolated (free) abstract particles in steady motion.

A model is only a model. It has to make falsifiable predictions for the real world. Therefore, I will show that for the Twin-Paradox it leads to the known result from Special Relativity Theory. For smallest scales the task is much more difficult. Only a qualitative test based on structural similarities can be offered here, defining a discrete logic for ground states, excited states and their correlations in the framework of the model, trying to map the abstract model to Einstein’s discrete interpretation of Planck’s law of radiation.

To understand the rational of the proposed model it is helpful not to expect a concept of space and time on smallest scales, particularly on the question whether they can be assumed continuous or discrete, although the model leans to a discrete structure.

The assessment based on the proposed model: The underlying relation for time relying on motion and state implementation is (likely) discrete, suggesting age as more fundamental than time. Regarding Hermann Weyl’s Tile Argument, I think that Pythagorean Law prevails, not through geometry or a metric, but as a preserving law between the above categories. Geometry, needed to define time on our scales, might only evolve on larger scales and dependent on the (dynamic) content of space.

The proposed model is Informatics based, driven by interest and not by competence in physics. Nevertheless, I will use terms from physics based on the approach of Denotational Semantics, keeping the gap between Syntax and Semantics as close as possible by relating abstract model properties to supposed properties of the real world.

Keywords: Discrete Space, Discrete Time, Twin Paradox, Hermann Weyl’s Tile Argument, Einstein’s Theories, Sub-Quantum Assumption, Einstein Coefficients

On Linkage Between Incompressible Integers as Distance and 1/r Potential

Authors: Dara O. Shayda
Comments: 14 Pages.

The main result: assuming distances are numericized as incompressible integers, given two objects, one stationary and the other moving, the rate of change of the measure of their distantial randomness is that of the potential form 1/r. This form is known as the Newtonian potential. If the incompressible assumption dropped then the potential form vanishes as well (conjecture). The supplementary results by Whittaker: for any force varying as the inverse square of the distance, the potential of such a force satisfies both Laplace's equation and the wave equation, and can be analyzed into simple plane waves propagating with constant velocity. The sum of these waves, however, does not vary with time, i.e. standing waves. Therefore, the 1/r potential can be defined as summation of waves. Thus the linkage between the incompressible integers and particular standing waves in physics.
Category: Mathematical Physics

The Electromagnetic Duality in a Quaternionic Vacuum

Authors: Thierry L. A. Periat
Comments: 6 Pages.

The electromagnetic duality in vacuum is an intriguing property characterizing Maxwell’s equations. It was the starting point of numerous developments. One of the most important topic related to that property certainly is the discussion due to Dirac concerning magnetic mono-poles. This exploration proposes representations of the duality with elements in M(4, H) involving the three generators of the imaginary part of H, the non-commutative set of quaternions.
Category: Mathematical Physics

Exact Formulas of the Age of the Universe and of the Gravitational Constant Dependent on Physical Constants

Authors: Andreas Ball
Comments: 7 Pages.

The british Physicist Paul Dirac (1902 - 1984) founded the Large Number Hypothesis[1], which handles with strange relations using numbers in order of magnitude 1,0E+40. Also the german Physicist, Mathematician and Philosopher Hermann Weyl (1885 - 1955) was occupied with relations of High Order Numbers. In this report Formulas are presented, which give the Age of the Universe and the Gravitational Constant within their Tolerance Range both in dependence on Physical Constants.
Category: Mathematical Physics

The Observable Universe in the Central Universe

Authors: Zhengxi Wang
Comments: 11 Pages.

The entire universe is a rotating disk, similar to the Milky Way, with a "galactic disk," a "core," and "spiral arms." The observable universe rotates around the center of the universe and play centrifugal motion, galaxies move away from each other and spread outward and around the periphery. With the Earth as a reference point, galaxies are in recession, and the recession velocity is proportional to their distance from the Earth. The recession velocities of galaxies differ in different directions, the velocities in the horizontal are greater than those in the longitudinal directions, the longitudinal directions are greater than those in the vertical direction. The universe has a zone for the development and growth of stars and galaxies, where stars and galaxies reach maturity. The continuous energy eruptions provide abundant materials for the rapid growth of stars. During this period, they revolve around the center in circular motions or in low-speed centrifugal motions. Galaxies are not moving away from each other, or are moving away from each other at a low speed. Mature galaxies had already come into existence before they accelerated to the Hubble velocity. The universe diffusion outward, the direction point to Ophiuchus, Scutum, Sagittarius and so on. According to the derivation based on the energy density formula, we are 10^27 meters away from the center of the universe. Additionally, the observable universe might be elliptical in shape.
Category: Mathematical Physics

Symmetric Theory: Omnipresent Planck Medium

Authors: Giuseppe Azzarello
Comments: 18 Pages. In Italian

In this article we continue the development of Symmetric Theory. What we will show is the coupling between the universe and the Planck medium, understood as the medium that formalizes the characteristics of the zero-point field. We will show how the phenomena of the infinitely large of the universe and the infinitely small of the atom harmonize in relation to the medium Planck. We will show how the Hawking radiation, Unhru effect, Casimir effect, Entropic force,Stefan-Boltzmann constant, Wien's displacement law, are all phenomena referring to the Planck medium. We will show that the electron in the first energy level of the hydrogen atom can never fall into the atomic nucleus because it is supported from Planck energy, through the phenomenon of resonance. What emerges is a new meaning of fine structure constant, in the sense of coupling constant between the electron and the Planck medium. Finally he comes indicated a path that could resolve the wave-particle duality.
Category: Mathematical Physics

Yield Stages of Viscoplastic Fluids in Tubes of Elliptical, Rectangular, Triangular and Annular Cross Sections

Authors: Taha Sochi
Comments: 20 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we visualize the stages of yield in the process of flow of viscoplastic fluids through tubes of elliptical, rectangular, triangular and annular cross sections. The purpose of this qualitative investigation is to provide an initial idea about the expected yield development in the process of flow of yield-stress fluids through tubes of some of the most common non-circular (and non-simply-connected) cross sectional geometries.
Category: Mathematical Physics