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[en] Uncertainty analysis is a method or methods for determining the uncertainties of given responses due to uncertainties in the input parameters. An inverse uncertainty analysis is a method or methods for determining the uncertainties of the input parameters due to the uncertainties of given responses. An approach for estimating the covariance-variance matrix of the input parameters is presented. It is assumed that the sensitivities and covariance-variance matrix of the responses are given, and that the responses are linear functions of the input parameters. (author)
[en] The basic characteristics of determining acceptable risk are discussed. Technical, political, and social aspects of the problem add much complexity. The appropriate manner to reach responsible decisions regarding acceptable risk is suggested. This explicity address the alternatives, the objectives, the uncertainty, and the values which constitute the information necessary to arrive at any solution. The inappropriateness of many ''solutions'' currently in use or ''suggested'' is exposed
[en] The quantum logic approach to axiomatic quantum mechanics is used to analyze the conceptual foundations of the traditional quantum theory. The universal quantum of action h>0 is incorporated into the theory by introducing the uncertainty principle, the complementarity principle, and the superposition principle into the framework. A characterization of those quantum logics (L,S) which may provide quantum descriptions is then given. (author)
[en] The concept of the uncertainty principle that position and momentum cannot be simultaneously specified to arbitrary accuracy is somewhat difficult to reconcile with experience. This note describes order-of-magnitude calculations which quantify the inadequacy of human perception with regards to direct observation of the breakdown of the trajectory concept implied by the uncertainty principle. Even with the best optical microscope, human vision is inadequate by three orders of magnitude. 1 figure
[en] We report a proof-of-principle experimental demonstration of quantum lithography. Utilizing the entangled nature of a two-photon state, the experimental results have beaten the classical diffraction limit by a factor of 2. This is a quantum mechanical two-photon phenomenon but not a violation of the uncertainty principle
[en] The subject of this thesis is the uncertainty principle (UP). The UP is one of the most characteristic points of differences between quantum and classical mechanics. The starting point of this thesis is the work of Niels Bohr. Besides the discussion the work is also analyzed. For the discussion of the different aspects of the UP the formalism of Davies and Ludwig is used instead of the more commonly used formalism of Neumann and Dirac. (author). 214 refs.; 23 figs
[en] We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum joint uncertainty states for some fluctuation measures are the maximum joint uncertainty states of other fluctuation measures, and vice versa.
[en] We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.