6-dimensional Kaluza-Klein Theory for Basic Quantum Particles and Electron-Photon Interaction

By extending original Kaluza-Klein theory to 6-dimension, the basic quantum field equations for 0-spin particle, 1-spin particle and 1/2 spin particle with mass >0 are directly derived from 6-dimensional Einstein equations. It shows that the current quantum field equations of basic particles become pure geometry properties under 6-dimension time-space. The field equations of electron and photon can be unified in one 6-dimensional extended Maxwell equation. The equations containing interactions between electron and photon will be derived from Einstein equation under 6-dimension time-space. It shows that the interactions in QED can be considered as the effect of local geometry curvature changing instead of exchange virtual photons.Comment: 5 page

A New Interpretation of Quantum Theory -- Time as Hidden Variable

Using 2 more time variables as the quantum hidden variables, we derive the equation of Dirac field under the principle of classical physics, then we extend our method into the quantum fields with arbitrary spin number. The spin of particle is shown naturally as the topological property of 3-dimensional time + 3-dimensional space . One will find that the quantum physics of single particle can be interpreted as the behavior of the single particle in 3+3 time-space .Comment: 4 pages revtex, 1 figure. [email protected]

Equations of Motion with Multiple Proper Time: A New Interpretation of Basic Quantum Physics

Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum physics: the quantum wave equation, de Broglie equations, uncertainty relation, statistical result of quantum wave-function. This shows us a possible new way to interpret quantum physics. We will also prove that physics with multiple proper time does not cause causality problem.Comment: 6 pages, 4 figure

Equations of Motion with Multiple Proper Time: A New Interpretation of Spin

The purpose of this paper is to show that: when a single particle moving under 3-proper time (three-dimensional time), the trajectories of a classical particle are equivalent to a quantum field with spin. Three-proper time models are built for spinless particle, particles with integer spin and half-integer spin respectively. The models recreate the same physical behavior as quantum field theory of free particles -- by using pure classical methods with three proper time. A new interpretation of spin is given. It provides us more evident that it is possible to interpret quantum physics by using multiple dimensional time. In the last part of this paper, Bose-Einstein statistics and Fermi-Dirac statistics are derived under classical method.Comment: 8 pages, 3 figure

Modified Kaluza-Klein Theory, Quantum Hidden Variables and 3-Dimensional Time

In this paper, the basic quantum field equations of free particle with 0-spin, 1-spin (for case of massless and mass $>$ 0) and 1/2 spin are derived from Einstein equations under modified Kaluza-Klein metric, it shows that the equations of quantum fields can be interpreted as pure geometry properties of curved higher-dimensional time-space . One will find that if we interpret the 5th and 6th dimension as ``extra'' time dimension, the particle's wave-function can be naturally interpreted as a single particle moving along geodesic path in 6-dimensional modified Kaluza-Klein time-space. As the result, the fundamental physical effect of quantum theory such as double-slit interference of single particle, statistical effect of wave-function, wave-packet collapse, spin, Bose-Einstein condensation, Pauli exclusive principle can be interpreted as ``classical'' behavior in new time-space. In the last part of this paper, we will coupling field equations of 0-spin, 1-spin and 1/2-spin particles with gravity equations

Three Dimensional Time Theory: to Unify the Principles of Basic Quantum Physics and Relativity

Interpreting quantum mechanics(QM) by classical physics seems like an old topic; And unified theory is in physics frontier; But because the principles of quantum physics and relativity are so different, any theories of trying to unify 4 nature forces should not be considered as completed without truly unifying the basic principles between QM and relativity. This paper will interpret quantum physics by using two extra dimensional time as quantum hidden variables. I'll show that three dimensional time is a bridge to connect basics quantum physics, relativity and string theory. ``Quantum potential'' in Bohm's quantum hidden variable theory is derived from Einstein Lagrangian in 6-dimensional time-space geometry. Statistical effect in the measurement of single particle, non-local properties, de Broglie wave can be naturally derived from the natural properties of three dimensional time. Berry phase, double-slit interference of single particle, uncertainty relation, wave-packet collapse are discussed. The spin and g factor are derived from geometry of extra two time dimensions. Electron can be expressed as time monopole. In the last part of this paper, I'll discuss the relation between three dimensional time and unified theory. Key words: Quantum hidden variable, Interpreting of quantum physics, Berry phase, three dimensional time, unified theoryComment: 14 pages, 3 figure

Impinging Jet Dynamics

In this fluid dynamics video, Ray-tracing data visualization technique was used to obtain realistic and detailed flow motions during impinging of two liquid jets. Different patterns of sheet and rim configurations were presented to shed light into the underlying physics, including liquid chain, closed rim, open rim, unstable rim and flapping sheet. In addition, stationary asymmetrical waves were observed and compared with existing theories. The generation of stationary capillary wave in respect to the liquid rim were explained by the classic shallow water wave theory. The atomization process caused by development of the impact waves were observed in detail, including fragmentation of liquid sheet, formation of liquid ligaments, and breakup of ligament into droplet. The locking-on feature of the wavelength of impact wave were also found to be similar to that of perturbed free shear layers

Model-free Nonconvex Matrix Completion: Local Minima Analysis and Applications in Memory-efficient Kernel PCA

This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite matrix without any assumptions on the rank-matching, the condition number or eigenspace incoherence parameter. Furthermore, under certain assumptions on rank-matching and well-boundedness of condition numbers and eigenspace incoherence parameters, a corollary of our main theorem improves the state-of-the-art sampling rate results for nonconvex matrix completion with no spurious local minima in Ge et al. [2016, 2017]. In addition, we investigated when the proposed nonconvex optimization results in accurate low-rank approximations even in presence of large condition numbers, large incoherence parameters, or rank mismatching. We also propose to apply the nonconvex optimization to memory-efficient Kernel PCA. Compared to the well-known Nystr\"{o}m methods, numerical experiments indicate that the proposed nonconvex optimization approach yields more stable results in both low-rank approximation and clustering.Comment: Main theorem improve

An Enhanced MPPT Method based on ANN-assisted Sequential Monte Carlo and Quickest Change Detection

The performance of a photovoltaic system is subject to varying environmental conditions, and it becomes more challenging to track the maximum power point (MPP) and maintain the optimal performance when partial shading occurs. In this paper, we propose an enhanced maximum power point tracking (MPPT) method utilizing the state estimation by the sequential Monte Carlo (SMC) filtering which is assisted by the prediction of MPP via an artificial neural network (ANN). A state-space model for the sequential estimation of MPP is proposed in the framework of incremental conductance (I-C) MPPT approach, and the ANN model based on the observed voltage and current or irradiance data predicts the global MPP (GMPP) to refine the estimation by SMC. Moreover, a quick irrandiance change detection method is applied, such that the SMC-based MPPT method resorts to the assistance from ANN only when partial shading is detected. Simulation results show that the proposed enhanced MPPT method achieves high efficiency and is robust to rapid irradiance change under different noise levels

On Finite Block-Length Quantization Distortion

We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we derive a lower bound on the quantization distortion under finite block-length, which is shown to be greater than the asymptotic distortion given by the rate-distortion theory. We also derive two upper bounds on the quantization distortion based on random quantization codebooks, which can achieve any distortion above the asymptotic one. Moreover, we apply the new upper and lower bounds to two types of sources, the discrete binary symmetric source and the continuous Gaussian source. For the binary symmetric source, we obtain the closed-form expressions of the upper and lower bounds. For the Gaussian source, we propose a computational tractable method to numerically compute the upper and lower bounds, for both bounded and unbounded quantization codebooks.Numerical results show that the gap between the upper and lower bounds is small for reasonable block length and hence the bounds are tight