The Uncertainty Principle from the Complex Point of View. First Examples

1994 ◽  
pp. 119-195
Author(s):  
Victor Havin ◽  
Burglind Jöricke
Keyword(s):  
Uncertainty Principle ◽  
Point Of View ◽  
Complex Point

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

TAKING IT ON TRUST: REASON AND OBSERVABILITY IN QUANTUM COMPUTING

2005 ◽  
Vol 03 (01) ◽  
pp. 49-56
Author(s):  
ROSSELLA LUPACCHINI
Keyword(s):  
Quantum Computing ◽  
Uncertainty Principle ◽  
Natural Process ◽  
Point Of View ◽  
Basic Question ◽  
Logical Point ◽  
Characteristic Features ◽  
Definition Of ◽  
Locality Conditions ◽  
Theoretical Computing

If quantum computing is located somewhere between physics and theoretical computing, a basic question concerns which characteristic features are derived from the latter. From a logical point of view, the concept of computation provides a definition of the natural process of calculare. It rests on trust that a procedure of reason can be reproduced mechanically. Turing argues for the adequacy of the concept by introducing a requirement of "observability," which is expressed through finiteness and locality conditions. However, according to the uncertainty principle, no computational path can be observed. How does quantum computing contend with Turing's constraints? What observables are relevant to the computation? This is an attempt to sharpen such questions.

scholarly journals GALILEO GALILEI´S THESIS EXPANDED

2021 ◽  
Vol 5 (1) ◽  
pp. 26-31
Author(s):  
Walter GOMIDE ◽  
Keyword(s):  
Uncertainty Principle ◽  
Point Of View ◽  
Real Numbers ◽  
Short Article ◽  
Galileo Galilei ◽  
Mathematical Point ◽  
Physical Laws

In this short article, I try to show alternative maths to real numbers in such a way that these maths (especially Transreal Numbers by James Anderson and Arithmetic of Infinity by Yaroslav Sergeyev) can also be considered as legitimate instruments for presenting the structure of reality. I call this thesis of expanding the possibilities of understanding Nature mathematically the "Galileo Galilei´s thesis extended". As an example of the application of the thesis that the mathematics that is at the base of Nature must be extended to a better assessment of the scope of physical laws, here we present the Heisenberg´s Uncertainty Principle, approached in an alternative way from a mathematical point of view.

GENERALIZED UNCERTAINTY PRINCIPLE AND PARIKH–WILCZEK TUNNELING

2009 ◽  
Vol 24 (30) ◽  
pp. 5669-5680 ◽  
Author(s):  
S. HAMID MEHDIPOUR
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Statistical Correlation ◽  
Point Of View ◽  
The Other ◽  
Black Hole Radiation ◽  
Black Hole Remnant ◽  
De Broglie Wavelength

We investigate the modifications of the Hawking radiation by the Generalized Uncertainty Principle (GUP) and the tunneling process. By using the GUP-corrected de Broglie wavelength, the squeezing of the fundamental momentum cell, and consequently a GUP-corrected energy, we find the nonthermal effects which lead to a nonzero statistical correlation function between probabilities of tunneling of two massive particles with different energies. Then the recovery of part of the information from the black hole radiation is feasible. From the other point of view, the inclusion of the effects of quantum gravity as the GUP expression can halt the evaporation process, so that a stable black hole remnant is left behind, including the other part of the black hole information content. Therefore, these features of the Planck-scale corrections may solve the information problem in black hole evaporation.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

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