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arXiv2014

Entropy, heat, and Gödel incompleteness

Irreversible phenomena, such as the production of entropy and heat, arise from fundamental reversible dynamics because the forward dynamics is too complex, in the sense that it becomes impossible to provide the necessary information to keep track of the dynamics. On a heuristic level, this is well captured by coarse graining. We suggest that on a fundamental level the impossibility to provide the necessary information might be related to the incompleteness results of Gödel. This would hold interesting implications for both, mathematics and physics.

physics.gen-ph↗

arXiv2014

Liquid Phase 3D Printing for Quickly Manufacturing Metal Objects with Low Melting Point Alloy Ink

Conventional 3D printings are generally time-consuming and printable metal inks are rather limited. From an alternative way, we proposed a liquid phase 3D printing for quickly making metal objects. Through introducing metal alloys whose melting point is slightly above room temperature as printing inks, several representative structures spanning from one, two and three dimension to more complex patterns were demonstrated to be quickly fabricated. Compared with the air cooling in a conventional 3D printing, the liquid-phase-manufacturing offers a much higher cooling rate and thus significantly improves the speed in fabricating metal objects. This unique strategy also efficiently prevents the liquid metal inks from air oxidation which is hard to avoid otherwise in an ordinary 3D printing. Several key physical factors (like properties of the cooling fluid, injection speed and needle diameter, types and properties of the printing ink, etc.) were disclosed which would evidently affect the printing quality. In addition, a basic route to make future liquid phase 3D printer incorporated with both syringe pump and needle arrays was also suggested. The liquid phase 3D printing method, which owns potential values not available in a conventional modality, opens an efficient way for quickly making metal objects in the coming time.

physics.gen-ph↗

arXiv2014

Quantum like modelling of the non-separability of voters' preferences in the U.S. political system

Divided Government is nowadays a common feature of the U.S. political system. The voters can cast partisan ballots for two political powers the executive (Presidential elections) and the legislative (the Congress election). Some recent studies have shown that many voters tend to shape their preferences for the political parties by choosing different parties in these two election contests. This type of behavior referred to by Smith et al. (1999) as "ticket splitting" shows irrationality of behavior (such as preference reversal) from the perspective of traditional decision making theories (Von Neumann and Morgenstern (1953), Savage, (1954)). It has been shown by i.e. Zorn and Smith (2011) and also Khrennikova et al. (2014) that these types of "non-separable" preferences are context dependent and can be well accommodated in a quantum like framework. In this paper we use data from Smith et al. (1999) to show first of all probabilistic violation of classical (Kolmogorovian) framework. We proceed with the depiction of our observables (the Congress and the Presidential contexts) with the aid of the quantum probability formula that incorporates the "contextuality" of the decision making process through the interference term. Statistical data induces an interference term of large magnitude a so called hyperbolic interference. We perform with help of our transition probabilities a state reconstruction of the voters state vectors to test for the applicability of the generalized Born rule. This state can be mathematically represented in the generalized Hilbert space based on hyper-complex numbers.

physics.gen-ph↗

arXiv2014

On Laplace-Runge-Lenz Vector as Symmetry Breaking order parameter in Kepler Orbit and Goldstone Boson

We introduce a type of symmetry breaking and associated order parameter in connection with Laplace-Runge-Lenz vector of Kepler orbit through an extended spatial dimension and Ensemble view. By implementation of a small extra spatial dimension and embedded infinitesimal toral manifold, it has been shown that emerging of LRL vector under SO(4)symmetry is in analogy with a variety of explicit and spontaneous symmetry breaking situations and related Goldstone bosons such as phonons and spin waves. A theorem introduced to generalize this concept of breaking symmetry. The diffeomorphism of circular orbit(geodesic)to elliptic one proved to be equivalent with a covariant derivative and related parallel displacement in this extended four dimensional spatial space.Respect to ensemble definition this diffeomorphism breaks the O(2) symmetry of initial orbit and Hamiltonian to Z2 resulting in broken generators in quotient space and associated Goldstone boson as perturbing Hamiltonian term leading to a perpetual circular motion on 2-torus comparable to the perpetual motion idea in Time Crystal of Wilczek. This leads to an introduction of gravitational gauge potential under the symmetry of Cartan sub algebra of su(2).

physics.gen-ph↗

arXiv2014

Breakup of SUSY Quantum Mechanics in the Limit-Circle Region of the Reflective Kratzer Oscillator

The paper studies violation of conventional rules of SUSY quantum mechanics for the centrifugal potential V(r) within the limit-circle (LC) range. A special attention is given to transformation properties of the Titchmarsh-Weyl m-function under Darboux deformations of the reflective Kratzer oscillator: centrifugal Kepler-Coulomb (KC) potential plus a Taylor series in r. Since our analysis is based on Fulton's representation of a regular-at-infinity solution [Math. Nachr. 281, 1418 (2008)] as a superposition of two Frobenius solutions at the origin, we refer to the appropriate expressions as the Titchmarsh-Weyl-Fulton (TWF) functions. Explicit transformation relations are derived for partner TWF functions associated with SUSY pairs of centrifugal potentials. It is shown that these relations have a completely different form for Darboux transformations (DTs) keeping the potential within the LC range. As an illustration, we use regular nodeless Frobenius solutions to construct SUSY partners of the radial r- and c-Gauss-reference (GRef) potentials solvable via hypergeometric and confluent hypergeometric functions, respectively. We explicitly demonstrate existence of non-isospectral partners of both radial potentials in the LC region and obtain their discrete energy spectra using the derived closed-form expressions for the TWF functions. The general transformation relations for the TWF function have been verified taking advantage of form-invariance of the radial GRef potentials under double-step DTs with the so-called 'basic' seed solutions (SSs). Similarly we directly ratify that TWF functions for three shape-invariant reflective potentials on the half-line -- hyperbolic Poschl-Teller (h-PT), Eckart/Manning-Rosen (E/MR), and centrifugal KC potentials - do retain their form under basic DTs.

physics.gen-ph↗

arXiv2014

An Electroweak-like Theory from Four Fermion Interactions

An electroweak-like theory of a broken chiral symmetry that is constructed by the collective modes of fermion pairs from four fermion interactions of one lepton generation is presented. The products of Dirac spinors lead to the separation of the two chiral fermions to couple respectively with two different kinds of polarization states. Because of a broken vacuum, a fermion and an anti-fermion out of the four pair up to form vector bosons, which behave like gauge bosons, such as $W^\pm$, $Z$ and $γ$ in a group structure of $SU(2)_L\times U(1)_Y$. The pairing of spinors only allows left-handed fermions to interact with charged bosons to secure the gauge invariance, while, as desired, $Z$-like bosons mediate different weak forces for two chiral fermions and $γ$-like bosons interact freely with fermions.

physics.gen-ph↗

arXiv2014

Physical metric and the nature of gravity

A physical metric is defined as one which gives a measurable speed of light throughout the whole space time continuum. It will be shown that a metric which satisfies the condition that speed of light on the spherical direction is that in a vacuum gives a correct result. All the metric functions thus obtained are positive definite and exhibits a repulsive force at short distances. The horizon in the sense of vanishing of the speed of light still exists in the radial direction. It is located at 2.60 times of the Schwarzschild radius. This radius corresponds to the size of a black hole, as well as the photon sphere radius. The metric can be used to calculate general relativistic predictions in higher order for any process.

physics.gen-ph↗

arXiv2014

Induced energy polarization of the vacuum and the resulting cosmology

The theory of an induced energy polarized vacuum provides an alternative to the standard cosmological model. The theory has previously been shown to lead to the Baryonic Tully-Fisher Relationship [1], to agree with the observed rotation curve of the Galaxy [2], to readily produce the observed features in the rotational curves of other spiral galaxies [3], and to agree with observations of the Coma cluster [4]. All without the need for any free parameters. The theory of an induced energy polarized vacuum is now applied to superclusters. From a model of the distribution of superclusters, the overall density parameter of universe as given by the theory of an induced energy polarized vacuum is Omega = 0.94 plus/minus 0.23. This is consistent with a geometrically flat universe. In addition, by treating the superclusters as unbound systems, the theory leads to an accelerating expansion of the universe in line with observations and without requiring the need for dark energy.

physics.gen-ph↗

arXiv2014

The Hafele-Keating experiment, velocity and length interval transformations and resolution of the Ehrenfest paradox

A relativistic analysis based on the paths, in a non-rotating frame comoving with the centroid of the Earth, of clocks carried by aircraft circumnavigating the Earth in different directions, as in the Hafele-Keating experiment, predicts time differences between airborne and Earth-bound clocks at variance with the results of the experiment. The latter imply new relativistic velocity transformations differing from the conventional ones. These transformations demonstrate in turn the invariance of length intervals on the surface of the rotating Earth and so resolve the Ehrenfest paradox for this case.

physics.gen-ph↗

arXiv2014

The 'Sears paradox'

We resolve a paradox in special relativity proposed by F. W. Sears for the action of forces on a rigid body. In the paradox, a moving rigid rod is struck at different times by impulsive forces, but continues to move with unchanged velocity, with the forces having no effect. Our conclusion is that the usual laws of mechanics can be applied to a rigid body only in its rest system

physics.gen-ph↗

arXiv2014

Modern elementary particle physics

The purpose of these lectures is to describe the state of affairs in modern particle physics to young physicists who do not specialize in this subject.

physics.gen-ph↗

arXiv2014

On the material origin of the cosmological constant

We consider a possible connection between matter and cosmological constant $Λ$ via the Newtonian cosmic potential of the matter within the expanding particle horizon. Consistent with GR, an increasing potential may drive the metric expansion of space. Cosmic recession of mass must, in turn, affect the potential in an opposite sense. Independent of this, several considerations point at $-\tfrac{1}{2}c^{2}$ as the representation of the background potential in the various GR metrics. This suggests that the cosmic potential, while subject to the expansion of space, always yields a constant background potential $-\tfrac{1}{2}c^{2}$. Analysis of this 'redshift' of the cosmic potential yields for perfect fluids the exact same solutions of the scale factor as the standard Friedmann equations, including an accelerating de Sitter universe. Though counter intuitive at first sight, gravity may drive cosmic acceleration.

physics.gen-ph↗

arXiv2014

Many worlds interpretation for double slit experiment

As is well known, the double slit experiment contains every key concepts of quantum mechanics such as phase effect, probability wave, quantum interference, quantum superposition. In this article, I will clarify the meaning of quantum superposition in terms of phase effect between states. After applying standard quantum theory, it leads to serious questions about the unitary process of an isolated system. It implies that non collapsing interpretations including many worlds may not be justified. This also could explain that there is no such boundary between classical and quantum domains.

physics.gen-ph↗

arXiv2014

Matrices de commutation tensorielle: de l'équation de Dirac vers une application en physique des particules

We construct two sets of representations of the Dirac equation. They transform themselves from one to another in multiplying by the tensor commutation matrix (TCM) $2\otimes 2$. The Gauss matrix can lead us to the Cholesky decomposition. The TCMs can be used in order to obtain different transforms of some matrix equations to linear matrix equations of the form $AX=B$. A TCM $n\otimes n$ is expressed in terms of the $n\otimes n$-Gell-Mann matrices. In order to generalize this expression to which of TCMs $n\otimes p$, we introduced what we call rectangle Gell-Mann matrices. The electric charge operator (ECO) for eight leptons and quarks of the Standard Model (SM) of a same generation proposed by Zenczykowski is expressed in terms of the TCM $2\otimes 2$. An ECO including all the fermions of the SM is constructed in terms of TCM $4\otimes 4$. Then the eigenvalues of a TCM take sense.

physics.gen-ph↗

arXiv2014

To Photon Concept and to Physics of Quantum Absorption Process

The status of the photon in the modern physics was analysed. Within the frames of the Standard Model of particle physics the photon is considered to be the genuine elementary particle, being to be the messenger of the electromagnetic interaction to which are subject charged particles. In contrast, the experts in quantum electodynamics (in particular, in quantum optics) insist, that the description of an photon to be the particle is impossible. The given viewpoint was carefully analysed and its falseness was proved. The expression for a photon wave function is presented. So, the status of the photon in quantum electodynamics was restored. The physics of a quantum absorption process is analysed. It is argued in accordance with Dirac guess, that the photon revival takes place by its absorption. Being to be a soliton, it seems to be keeping safe after an energy absorption in a pinned state, possessing the only by spin. It is shown, that the time of the transfer of absorbing systems in an excited state is finite and moreover, that it can govern the stationary signal registered. The given result is significant for the all stationary spectroscopy, in which at present the transfer of absorbing systems in an excited state is considered to be instantaneous.

physics.gen-ph↗

arXiv2014

The standard model and the constituents of leptons and quarks

A complete set of postulates of the standard model of the electroweak interaction and mass generation is formulated and confirmed deriving the Lagrangian for the standard model. A massive fermion is formed by a right-handed and a left-handed elementary massless fermion, exchanging a scalar doublet. The elementary massless fermions forming leptons belong to an approximate SU(3) octet. The charges are quantised due to this symmetry.

physics.gen-ph↗

arXiv2014

A vectorial form of the Schrödinger equation

We rewrite the time dependent Schrödinger equation by using only three dimensional vector algebra and by avoiding to introduce any complex numbers. We show that this equation leads to the same conclusions than the "complex version" concerning the hydrogen atom and the harmonic oscillator. We show also that this equation can be written as a Maxwell-Ampère equation.

physics.gen-ph↗

arXiv2014

Proper time and length in Schwarzschild geometry

We study proper time ($τ$) intervals for observers at rest in the universe ($U$) and anti-universe ($\bar{U}$) sectors of the Kruskal-Schwarzschild eternal spacetime of mass $M$, and proper lengths ($ρ$) in the black hole (BH) and white hole (WH) sectors. The fact that in asymptotically flat regions, coordinate time $t$ at infinity is proper time, leads to a past directed Kruskal time $T$ in $\bar{U}$. In the BH and WH sectors maximal proper lengths coincide with maximal proper time intervals, $πM$, in these regions, i.e. with the proper time of radial free falling (ejection) to (from) the singularity starting (ending) from (at) rest at the horizon.

physics.gen-ph↗