Quantum Physics

We present an asymmetric step-barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert  W-function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection in transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or variable variation regions, the reflection coefficient is smaller because of the lesser steepness of the potential on the incidence side. Presenting the derivation of the Lambert potential we show that this is a four-parametric sub-potential of a more general five-parametric one also solvable in terms of the confluent hypergeometric functions. The latter potential, however, is a conditionally integrable one. Finally, we show that there exists one more potential the solution for which is written in terms of the derivative of a bi-confluent Heun function.

We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq.15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix M. If M is normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and when M is circulant the strength of interaction can be related to the power spectrum of white noise. We extend this by calculating the expected force (Eq. 41) for real stochastic processes with zero-mean and independent intervals. To quantify the dominance of the c.c. attraction, we calculate the variance of other forces. We apply the results to the Hatano-Nelson model and provide other numerical illustrations. It is our hope that the simple dynamical perspective herein might help better understanding of the aggregation and low density of the eigenvalues of real random matrices on and near the real line respectively.

This paper starts from the idea that physical reality implements a network of a small number of mathematical structures. Only in that way can be explained that observations of physical reality fit so well with mathematical methods.
The mathematical structures do not contain mechanisms that ensure coherence. Thus apart from the network of mathematical structures a model of physical reality must contain mechanisms that manage coherence such that dynamical chaos is prevented.
Reducing complexity appears to be the general strategy. The structures appear in chains that start with a foundation. The strategy asks that especially in the lower levels, the subsequent members of the chain emerge with inescapable self-evidence from the previous member. The chains are interrelated and in this way they enforce mutual restrictions.
As a consequence the lowest levels of a corresponding mathematical model of physical reality are rather simple and can easily be comprehended by skilled mathematicians.
In order to explain the claimed setup of physical reality, the paper investigates the foundation of the major chain. That foundation is a skeleton relational structure and it was already discovered and introduced in 1936.
The paper does not touch more than the first development levels. The base model that is reached in this way puts already very strong restrictions to more extensive models.
Some of the features of the base model are investigated and compared with results of contemporary physics.

As far as I can tell length, as an abstraction or as a physical abstraction, has not been discussed extensively. There's displacement, position, change in position etc and others  but length has meaning in our world where it has a number attached to it 134 centimeters. I just waded in here because I wanted to have some fun.

Theory of The Special Information's Effect on Matter: (in short)
A kvantumesemények titka: az információ: A Speciális Információ hatása az anyagra.

Mi történik a kétréses kísérletben méréskor/megfigyeléskor?
Amikor tudatunk a mérés elvégzésére fókuszál, igen rövid ideig megfordul az időnyíl. Ez Planck időn belül visszaáll, tehát nem sérti a termodinamika 2. törvényét.
Ebben a tört pillanatban entrópia-fluktuáció: negatív entrópia jön létre: információs vákuum keletkezik

Summary article. The Dirac equation electron is modeled as a helically circulating charged photon, with the longitudinal component of the charged photon's velocity equal to the velocity of the electron. The electron's relativistic energy-momentum equation is satisfied by the circulating charged photon. The relativistic momentum of the electron equals the longitudinal component of the momentum of the helically-circulating charged photon, while the relativistic energy of the electron equals the energy of the circulating charged photon. The circulating charged photon has a relativistically invariant transverse momentum that generates the z-component of the spin  of a slowly-moving electron. The charged photon model of the electron is found to generate the relativistic de Broglie wavelength of the electron. This result strongly reinforces the hypothesis that the electron is a circulating charged photon. Wave-particle duality may be better understood due to the charged photon model--electrons have wavelike properties because they are charged photons. New applications in photonics and electronics may evolve from this new hypothesis about the electron.

The Dirac equation electron is modeled as a helically circulating charged photon, with the longitudinal component of the charged photon's velocity equal to the velocity of the electron. The electron's relativistic energy-momentum equation is satisfied by the circulating charged photon. The relativistic momentum of the electron equals the longitudinal component of the momentum of the helically-circulating charged photon, while the relativistic energy of the electron equals the energy of the circulating charged photon. The circulating charged photon has a relativistically invariant transverse momentum that generates the z-component of the spin  of a slowly-moving electron. The charged photon model of the electron is found to generate the relativistic de Broglie wavelength of the electron. This result strongly reinforces the hypothesis that the electron is a circulating charged photon. Wave-particle duality may be better understood due to the charged photon model--electrons have wavelike properties because they are charged photons. New applications in photonics and electronics may evolve from this new hypothesis about the electron.

Today, we are capable of measuring the position of an object with unprecedented accuracy, but quantum physics and the Heisenberg uncertainty principle place fundamental limits on our ability to measure. Noise that arises as a result of the quantum nature of the fields used to make those measurements imposes what is called the "standard quantum limit." This same limit influences both the ultrasensitive measurements in nanoscale devices and the kilometer-scale gravitational wave detector at LIGO. Because of this troublesome background noise, we can never know an object's exact location, but a recent study provides a solution for rerouting some of that noise away from the measurement. [8]
The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories.
The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry.
The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.

Ce livre développe des réflexions sur la possibilité, l’actualité, la pragmatique de la langue et les pratiques de l’expérimentation scientifique, centrées sur le cas de la théorie quantique. Il peut être lu comme un développement naturel de mon précédent livre "Mécanique quantique: une introduction philosophique".

1-Pensée des possibles ou expérience des possibles?
2-Choses, lois et mondes: une généalogie humaniste de la nature
3-Héritage et fondations de la théorie quantique
4-Critique de la pluralité des mondes
5-Les corrélations d'Einstein-Podolsky-Rosen sans non-localité
6-L'événement, germe du temps et de l'irréversibilité
7-Une connaissance sans distance et sans dualité

We investigate cross-correlations in the tunneling currents through two parallel quantum dots coupled to independent electrodes and gates and interacting via an inter-dot Coulomb interaction. The correlations reveal additional information, beyond what can be learned from the current or conductance, about the dynamics of transport processes of the system. We find qualitatively different scenarios for the dependence of the cross-correlations on the two gate voltages. Reducing the temperature below the inter-dot Coulomb interaction, regions of a given sign change from spherical shapes to angular L-shapes or stripes. Similar shapes have been observed in recent experiments. 

The pursuit of an understanding of the base machinery of the mind led early researchers to anatomical exhaustion. With neuroscience now in the throes of molecular mayhem and a waning biochemical bliss, physics is spicing things up with a host of eclectic quantum, spin, and isotopic novelties. While increases in electron spin content have been linked to anesthetic effects, nuclear spins have recently been implicated in a more rarefied and subtle phenomenon— neural quantum processing. [7]
The hypothesis that there may be something quantum-like about the human mental function was put forward with “Spooky Activation at Distance” formula which attempted to model the effect that when a word’s associative network is activated during study in memory experiment; it behaves like a quantum-entangled system. The human body is a constant flux of thousands of chemical/biological interactions and processes connecting molecules, cells, organs, and fluids, throughout the brain, body, and nervous system. Up until recently it was thought that all these interactions operated in a linear sequence, passing on information much like a runner passing the baton to the next runner. However, the latest findings in quantum biology and biophysics have discovered that there is in fact a tremendous degree of coherence within all living systems.
The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories.
The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry.
The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to understand the Quantum Biology.

Gravity is  posed to be a radial flow of compressible fluid space, whose local speed defines a relative scale factor - a metric providing not only a measure of distance and time, but of dimension as well.The fluid space approach to gravity, and a reliance upon special relativity, provide a novel scientific theme - a structural basis - for how elementary particles, and their properties, such as mass and charge, evolve along with energy-borne space.

The reader will find this narrative to be circular - without a starting point and without an end. We find ourselves witnessing the physical universe - a creative work in progress - an ongoing theatrical composition - without an informing prelude to suggest a purposeful theme; yet, with a sense that a finale has taken place; and, will ensue as an epoch of cosmic proportion.

Our narrative will discuss both space and time, with some disregard for the latter either being linear, simply connected, sequential or even present when crossing spatial or temporal boundaries called horizons. Our narrative focus is upon energy and all of its forms and manifestations - a property of both space and the objects enclosed within and without - but, a property which cannot be created or destroyed.

Realistic earth-based observation is subject to the spatial conditions existing at the locality where measurements are taken. Theoretical findings, predicated upon Lorentz invariance, across inertial frames of reference, are subject to critical review when applied to terrestrial  based observations. An earth supported frame of reference is not an inertial frame; an object free to move will fall to the earth's surface. Relative to the freely falling object in the earth's gravitational field, the earth supported observer is accelerating radially outward; and, at an ever increasing rate.

Non-zero gravity is nowhere spatially uniform. The radial gravitational field approaching the earth's surface is varying non-linear with the distance relative to any supported reference frame. The radial spatial flow, is likewise accelerating inward at an ever increasing rate. This assures that the radial spatial flow will develop an event horizon. unless it encounters a counter support against the flow.

Although the variance between a local inertial frame and the earth supported frame is small, this is not the case near a black hole. Nor is this the case in the immediate proximity of the atomic nucleus and in subatomic space. Findings using the fluid model are consistent with solutions of Einstein's field equations applied  at astronomical scales; the advantage being that  the fluid model can be applied to microscopic scales where quantum effects arise and take hold; and do so in harmony.

Quantum physics tell us that even massive particles can behave like waves, as if they could be in several places at once. This phenomenon is typically proven in the diffraction of a matter wave at a grating. Researchers have now carried this idea to the extreme and observed the delocalization of molecules at the thinnest possible grating, a mask milled into a single layer of atoms. [6]
Researchers in Austria have made what they call the "fattest Schrödinger cats realized to date". They have demonstrated quantum superposition – in which an object exists in two or more states simultaneously – for molecules composed of up to 430 atoms each, several times larger than molecules used in previous such experiments1. [5]
Patrick Coles, Jedrzej Kaniewski, and Stephanie Wehner made the breakthrough while at the Centre for Quantum Technologies at the National University of Singapore. They found that 'wave-particle duality' is simply the quantum 'uncertainty principle' in disguise, reducing two mysteries to one. [4]
The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories.
The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry.