2,063 research outputs found

### Scale invariant quantum potential leading to globally self-trapped wave function in Madelung fluid

We show in spatially one dimensional Madelung fluid that a simple requirement
on local stability of the maximum of quantum probability density will, if
combined with the global scale invariance of quantum potential, lead to a class
of quantum probability densities globally being self-trapped by their own
self-generated quantum potentials, possessing only a finite-size spatial
support. It turns out to belong to a class of the most probable wave function
given its energy through the maximum entropy principle. We proceed to show that
there is a limiting case in which the quantum probability density becomes the
stationary-moving soliton-like solution of the Schr\"odinger equation.Comment: 11 pages; changed conten

### Spatiotemporally-localized-stationary typical wave function satisfying Klein-Gordon equation with emergent mass

Starting from relativistic mass-less Madelung fluid, we shall develop a class
of typical wave functions by imposing it to maximize Shannon entropy given its
finite average quantum potential. We show that there is a class of solutions in
which the wave function is spatiotemporally localized with finite spacetime
support, uniformly moving hence stationary. It turns out that the quantum
amplitude satisfies Klein-Gordon equation with emergent mass term proportional
to the square root of average quantum potential. We show that there is physical
time uncertainty which decreases as the mass increases. We also rederive the
classical energy-momentum relation provided the de Broglie-Einstein relation
holds. In this case, the time uncertainty is proportional to the inverse of
classical energy.Comment: 10 pages, content change

### Quantum fluctuations from a local-causal information dynamics

We shall show that the abstract and formal rules which govern the quantum
kinematic and dynamics can be derived from a law of change of the information
content or the degree of uncertainty that the system has a certain
configuration in a microscopic time scale, which is singled out uniquely, up to
a free parameter, by imposing the condition of Macroscopic Classicality and the
principle of Locality. Unlike standard quantum mechanics, however, the system
always has a definite configuration all the time as in classical mechanics,
following a continuous trajectory fluctuating randomly in time.Comment: A large part of text of the previous version is omitted. A longer
version is accepted for publication in Physica A. arXiv admin note:
substantial text overlap with arXiv:1301.534

### Is nonlocality responsible for the violation of Bell's inequalities?

Bell's theorem has been widely argued to show that some of the predictions of
quantum mechanics which are obtained by applying the {\it Born's rule} to a
class of {\it entangled states}, are {\it not} compatible with {\it any}
local-causal statistical model, via the violation of Bell's inequalities. On
the other hand, in the previous work, we have shown that quantum dynamics and
kinematics are {\it emergent} from a statistical model that is singled out {\it
uniquely} by the principle of Locality. Here we shall show that the
local-causal model supports entangled states and give the statistical origin of
their generation. We then study the Stern-Gerlach experiment to show that the
Born's rule can also be derived as a mathematical theorem in the local-causal
model. These results lead us to argue that nonlocality is {\it not} responsible
for the quantum mechanical and most importantly experimental violation of
Bell's inequalities. The source(s) of violation has to be sought somewhere
else.Comment: 29 pages, accepted for publication in International Journal of
Theoretical Physic

### Quantum dynamics and kinematics from a statistical model selected by the principle of Locality

Quantum mechanics predicts correlation between spacelike separated events
which is widely argued to violate the principle of Local Causality. By
contrast, here we shall show that the Schr\"odinger equation with Born's
statistical interpretation of wave function and uncertainty relation can be
derived from a statistical model of microscopic stochastic deviation from
classical mechanics which is selected uniquely, up to a free parameter, by the
principle of Local Causality. Quantization is thus argued to be physical and
Planck constant acquires an interpretation as the average stochastic deviation
from classical mechanics in a microscopic time scale. Unlike canonical
quantization, the resulting quantum system always has a definite configuration
all the time as in classical mechanics, fluctuating randomly along a continuous
trajectory. The average of the relevant physical quantities over the
distribution of the configuration are shown to be equal numerically to the
quantum mechanical average of the corresponding Hermitian operators over a
quantum state.Comment: 33 pages, no figure, major changes, accepted for publication in
International Journal of Theoretical Physic

### No-signaling non-unitary modification of quantum dynamics within a deterministic model of quantization

We have developed in the previous works a statistical model of quantum
fluctuation based on a chaotic deviation from infinitesimal stationary action
which is constrained by the principle of Locality to have a unique exponential
distribution up to a parameter that determines its average. The unitary
Schr\"odinger time evolution with Born's statistical interpretation of wave
function is recovered as a specific case when the average deviation from
infinitesimal stationary action is given by $\hbar/2$ for all the time. This
naturally suggests a possible generalization of the quantum dynamics and
statistics by allowing the average deviation fluctuates effectively randomly
around $\hbar/2$ with a finite yet very small width and a finite time scale. We
shall show that averaging over such fluctuation will lead to a non-unitary
average-energy-conserving time evolution providing an intrinsic mechanism of
decoherence in energy basis in macroscopic regime. A possible cosmological
origin of the fluctuation is suggested. Coherence and decoherence are thus
explained as two features of the same statistical model corresponding to
microscopic and macroscopic regimes, respectively. Moreover, noting that
measurement-interaction can be treated in equal footing as the other types of
interaction, the objective locality of the model is argued to imply
no-signaling between a pair of arbitrarily separated experiments.Comment: accepted for publication in Annals of Physics. arXiv admin note: text
overlap with arXiv:1310.6028, arXiv:1301.5345, arXiv:1404.152

### Quantum mechanics is a calculus for estimation under epistemic restriction

Consider a statistical model with an epistemic restriction such that, unlike
in classical mechanics, the allowed distribution of positions is fundamentally
restricted by the form of an underlying momentum field. Assume an agent
(observer) who wishes to estimate the momentum field given information on the
conjugate positions. We discuss a classically consistent, weakly unbiased, best
estimation of the momentum field minimizing the mean squared error, based on
which the abstract mathematical rules of quantum mechanics can be derived. The
results suggest that quantum wave function is not an objective
agent-independent attribute of reality, but represents the agent's best
estimation of the momentum, given the positions, under epistemic restriction.
Quantum uncertainty and complementarity between momentum and position find
their epistemic origin from the trade-off between the mean squared errors of
simultaneous estimations of momentum field and mean position, with the Gaussian
wave function represents the simultaneous efficient estimations, achieving the
Cram\'er-Rao bounds of the associated mean squared errors. We then argue that
unitary time evolution and wave function collapse in measurement are normative
rules for an agent to update her/his estimation given information on the
experimental settings.Comment: 38 pages, comments welcom

### A class of traveling-envelope solutions of free Schr\"odinger equation generated by Lorentz transformation

We develop a class of traveling-envelope solutions of Schr\"odinger equation
for a free particle whose amplitude is moving with constant group velocity
while keeping its shape undistorted. We show that solution with arbitrary
finite group velocity is obtained by Lorentz boosting the solution with
vanishing group velocity, if the quantum average energy $E$ and momentum $p$
are related to the rest-mass $m$ of the particle by Einstein formula
$E^2/c^2-p^2=m^2c^2$. The wave function is spatially localized with finite-size
support which is decreasing as the rest-mass and/or group velocity are
increased. For a particle with vanishing rest-mass yet finite momentum, we show
that the group and phase velocities are equal to the velocity of light and the
wavelength is given by Einstein another formula $\lambda_P=h/p$.Comment: 4 pages, content change

### A stochastic model for quantum measurement

We develop a statistical model of microscopic stochastic deviation from
classical mechanics based on a stochastic processes with a transition
probability that is assumed to be given by an exponential distribution of
infinitesimal stationary action. We apply the statistical model to
stochastically modify a classical mechanical model for the measurement of
physical quantities reproducing the prediction of quantum mechanics. The
system+apparatus always have a definite configuration all the time as in
classical mechanics, fluctuating randomly following a continuous trajectory. On
the other hand, the wave function and quantum mechanical Hermitian operator
corresponding to the physical quantity arise formally as artificial
mathematical constructs. During a single measurement, the wave function of the
whole system+apparatus evolves according to a Schr\"odinger equation and the
configuration of the apparatus acts as the pointer of the measurement so that
there is no wave function collapse. We will also show that while the result of
each single measurement event does not reveal the actual value of the physical
quantity prior to measurement, its average in an ensemble of identical
measurement is equal to the average of the actual value of the physical
quantity prior to measurement over the distribution of the configuration of the
system.Comment: 12 pages, accepted for publication in Journal of Statistical
Mechanics: Theory and Experiment. arXiv admin note: substantial text overlap
with arXiv:1301.534

### Thermodynamics analogue for self-trapped spinning-stationary Madelung fluid

We discuss two-dimensional Madelung fluid dynamics whose irrotational case
reduces into the Schr\"odinger equation for a free single particle. We show
that the self-trapped spinning-stationary Madelung fluid reported in the
previous paper can be analogically identified as an equilibrium thermodynamics
system. This is done by making correspondence between Shannon entropy over
Madelung density and internal energy to be defined in the main text,
respectively with thermal-entropy and thermal-internal energy of equilibrium
thermodynamics system. This leads us to identify a Madelung fluid analog of
thermal-temperature at the vanishing value of which the stationary Madelung
fluid will be no more spinning and is equal to the quantum mechanical ground
state of a particle trapped inside a cylindrical tube external potential.Comment: changed content, Revtex 17 page

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