5,313 research outputs found
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
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