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Topic: Uncertainty

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	Uncertainty principle - Wikipedia, the free encyclopedia
		The uncertainty principle in quantum mechanics is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		The fundamentally non-classical characteristics of the uncertainty measurements in quantum mechanics were clarified due to the EPR paradox which arose from Einstein attempting to show flaws in quantum measurements that used the uncertainty priciple.
		In 1927, to develop the standard deviation for the uncertainty principle, Heisenberg took the gaussian distribution or bell curve for the imprecision in the measurement of the position q of a moving electron to the corresponding bell curve of the measured momentum p.
	en.wikipedia.org /wiki/Uncertainty_principle (3734 words)

	Uncertainty - Wikipedia, the free encyclopedia
		In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result.
		The expected measurement uncertainty of many measuring instruments (scales, oscilloscopes, force gages, rulers, thermometers, etc) is often stated in the manufacturers specification.
		Uncertainty has been a common theme in art, both as a thematic device (see, for example, the indecision of Hamlet), and as a quandary for the artist (such as Martin Creed's difficulty with deciding what artworks to make).
	en.wikipedia.org /wiki/Uncertainty (807 words)

	The Uncertainty Principle
		In many expositions of the subject, the ‘uncertainty’ may refer sometimes to a lack of knowledge of a quantity by an observer, or to the experimental inaccuracy with which a quantity is measured, or to some ambiguity in the definition of a quantity, or to a statistical spread in some ensemble of similarly prepared systems.
		Popper argued that the uncertainty relations cannot be granted the status of a principle, on the grounds that they are derivable from the theory, whereas one cannot obtain the theory from the uncertainty relations.
		It must be remembered, however, that the uncertainty in question is not simply a consequence of a discontinuous change of energy and momentum say during an interaction between radiation and material particles employed in measuring the space-time coordinates of the individuals.
	plato.stanford.edu /entries/qt-uncertainty (10377 words)

	Encyclopedia topic: Uncertainty principle (Site not responding. Last check: 2007-11-06)
		The uncertainty principle in quantum mechanics (The branch of quantum physics that accounts for matter at the atomic level; an extension of statistical mechanics based on quantum theory (especially the Pauli exclusion principle)) is sometimes explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		The uncertainty principle (as initially considered by Heisenberg) is concerned with cases in which neither of these two descriptions is fully and exclusively appropriate, such as a particle in a box (additional info and facts about particle in a box) with a particular energy value; i.
		Therefore, if the uncertainty principle is the result of some deterministic process, it must be the case that particles at great distances instantly transmit information to each other to ensure that the correlations in behavior between particles occur.
	www.absoluteastronomy.com /encyclopedia/u/un/uncertainty_principle.htm (2410 words)

	Uncertainty Principle Encyclopedia Article, Description, History and Biography @ ArtisticNudity.com (Site not responding. Last check: 2007-11-06)
		In quantum physics, the Heisenberg uncertainty principle states that one cannot assign with full precision values for certain pairs of observable variables, including the position and momentum, of a single particle at the same time.
		The uncertainty principle in quantum mechanics is sometimes explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		Within the widely but not universally accepted Copenhagen interpretation of quantum mechanics, the uncertainty principle is taken to mean that on an elementary level, the physical universe does not exist in a deterministic form—but rather as a collection of probabilities, or potentials.
	www.artisticnudity.com /encyclopedia/Uncertainty_principle (2466 words)

	Uncertainty principle - Open Encyclopedia (Site not responding. Last check: 2007-11-06)
		In quantum physics, the Heisenberg uncertainty principle expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle.
		The uncertainty principle alternatively derives as an expression of the Cramer-Rao inequality of classical measurement theory.
		Albert Einstein was not happy with the uncertainty principle, and he challenged Niels Bohr with a famous thought experiment (See the Bohr-Einstein debates for more details): we fill a box with a radioactive material which randomly emits radiation.
	open-encyclopedia.com /Uncertainty_principle (1965 words)

	Uncertainty Principle (Werner Heisenberg)
		Since the momentum of a particle is the product of its mass and velocity, the principle is sometimes stated differently, however, its meaning remains the same: The act of measuring one magnitude of a particle, be it its mass, its velocity, or its position, causes the other magnitudes to blur.
		The uncertainty relation describes the "blur" between the measurable quantities of a particle in mathematical terms.
		This conflict is the philosophical essence of the uncertainty principle.
	www.thebigview.com /spacetime/uncertainty.html (1435 words)

	Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Principle (Site not responding. Last check: 2007-11-06)
		Heisenberg's route to uncertainty lies in a debate that began in early 1926 between Heisenberg and his closest colleagues on the one hand, who espoused the "matrix" form of quantum mechanics, and Erwin Schrödinger and his colleagues on the other, who espoused the new "wave mechanics."
		His analysis showed that uncertainties, or imprecisions, always turned up if one tried to measure the position and the momentum of a particle at the same time.
		(Similar uncertainties occurred when measuring the energy and the time variables of the particle simultaneously.) These uncertainties or imprecisions in the measurements were not the fault of the experimenter, said Heisenberg, they were inherent in quantum mechanics.
	www.aip.org /history/heisenberg/p08.htm (958 words)

	UNCERTAINTY (Site not responding. Last check: 2007-11-06)
		The uncertainty resulting from two or more sets of categories is the sum of the uncertainties of the sets of categories taken independently.
		Since the categories must be specified by an observer, the uncertainty of a system may be different as seen by different observers.
		Since the categories within which events are observed are always specified by an observer, the notion of uncertainty emphasizes the cognitive dimension of information processes, specifically in the form of measures of variety, statistical entropy including noise and equivocation.
	pespmc1.vub.ac.be /ASC/UNCERTAINTY.html (273 words)

	[No title]
		Uncertainty may involve things that are completely unknown, whereas risks are often understood via calculable probabilities.
		Uncertainty is a major factor in matters of science, technology, health, and the environment.
		Uncertainty and risk are academically rich topics, so there is an enormous amount of literature available on the subjects.
	www.beyondintractability.org /m/fact_finding_limits.jsp (3464 words)

	Uncertainty Principle (Site not responding. Last check: 2007-11-06)
		The uncertainty principle also called the Heisenberg Uncertainty Principle, or Indeterminacy Principle, articulated (1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory.
		The uncertainty principle, developed by W. Heisenberg, is a statement of the effects of wave-particle duality on the properties of subatomic objects.
		While the uncertainty principle means that quantum objects have to be described by probability fields, this doesn't mean that the microscopic world fails to conform to deterministic laws.
	zebu.uoregon.edu /~js/21st_century_science/lectures/lec14.html (3556 words)

	Agilent \| Uncertainty for Beginners
		Assuming both the specification and uncertainty have Gaussian distribution at 95% confidence and that the TAR is 4:1, a test result at the specification limit means that there would be a 0.8% chance that it was, in reality, out-of-tolerance.
		To explain, the specification will contribute to the user's uncertainty budget by quadratic summation and, therefore, the setting of the acceptance limit by simple arithmetic is inappropriate.
		In these conditions and at 95% confidence level for specification and uncertainty, the chance of incorrect declaration of conformance to specification is 0.8%.
	metrologyforum.tm.agilent.com /uncert.shtml (839 words)

	AllRefer.com - uncertainty principle (Physics) - Encyclopedia
		The value of Planck's constant is extremely small, so that the effect of the limitations imposed by the uncertainty principle are not noticeable on the large scale of ordinary measurements; however, on the scale of atoms and elementary particles the effect of the uncertainty principle is very important.
		Because of the uncertainties existing at this level, a picture of the submicroscopic world emerges as one of statistical probabilities rather than measurable certainties.
		The uncertainty principle has been elevated by some thinkers to the status of a philosophical principle, called the principle of indeterminacy, which has been taken by some to limit causality in general.
	reference.allrefer.com /encyclopedia/U/uncertai.html (429 words)

	Choice under Risk and Uncertainty: Introduction
		The formal incorporation of risk and uncertainty into economic theory was only accomplished in 1944, when John von Neumann and Oskar Morgenstern published their Theory of Games and Economic Behavior - although the exceptional effort of Frank P. Ramsey (1926) must be mentioned as an antecedent.
		For instance, they argue that in Knightian uncertainty, the problem is that the agent does not assign probabilities, and not that she actually cannot, i.e.
		that uncertainty is really an epistemological and not an ontological problem, a problem of "knowledge" of the relevant probabilities, not of their "existence".
	cepa.newschool.edu /het/essays/uncert/intrisk.htm (1817 words)

	Thoughts on DOI #3 - Uncertainty
		We settled on uncertainty as the one single word which best captured the essence of the problem.
		Uncertainty in this context means from variation to chaos, as defined by De Meyer et al, Managing Project Uncertainty: from Variation to Chaos, and shown in this diagram
		In the new paradigm, uncertainty is a facet of planning and scheduling.
	www.agilemanagement.net /Articles/Weblog/ThoughtsonDOI3.html (245 words)

	Uncertainty in continuous system simulation
		That algorithm generated trajectories inside the RS, but the control variable was being modified to obtain a mostly uniform possible distribustion of ponts inside the RS at the endo of the simulated time interval.
		The method was applied in some uncertainty problems, for example to simulate the growth of the number of computer science specialists in the former "Socialistic Countries" block (project sponsored by COMECON, Moscow).
		Managing uncertainty in operational control of water distribution systems, in Integrated Computer Applications, Vol 2, (Ed.) B Coulbeck, J Wiley, 1993, ISBN: 0 471 94232 2, pp 353-363.
	www.raczynski.com /pn/uncertainty.htm (2021 words)

	Uncertainty About the Uncertainty Principle - Can't anybody get Heisenberg's big idea right? By Jim Holt (Site not responding. Last check: 2007-11-06)
		Two years later he announced, in what is probably the most quoted paper in the history of physics, his "uncertainty principle." Today, even the greatest physicists admit to bafflement at Heisenberg's mathematical non sequiturs and leaps of logic.
		There the principle is often taken to mean that the very act of observing a phenomenon inevitably alters that phenomenon in some way; that is why, say, Margaret Mead could never know the sexual mores of the Samoans—her very presence on the island distorted what she was there to observe.
		Heisenberg himself opted for this kind of interpretation, which is called "epistemic," since it places the burden of uncertainty on the knower.
	slate.msn.com /?id=2062844 (1328 words)

	FRB: Speech, Greenspan--Risk and Uncertainty in Monetary Policy--January 3, 2004
		Despite those uncertainties, the trauma of the 1970s was still so vivid throughout the 1980s that preventing a return to accelerating prices was the unvarying focus of our efforts during those years.
		The term "uncertainty" is meant here to encompass both "Knightian uncertainty," in which the probability distribution of outcomes is unknown, and "risk," in which uncertainty of outcomes is delimited by a known probability distribution.
		In practice, one is never quite sure what type of uncertainty one is dealing with in real time, and it may be best to think of a continuum ranging from well-defined risks to the truly unknown.
	www.federalreserve.gov /boarddocs/speeches/2004/20040103/default.htm (5653 words)

	Relative Uncertainty and Evidence Sets: A Constructivist Framework (Site not responding. Last check: 2007-11-06)
		Several measures of uncertainty, in its various forms of nonspecificity, conflict, and fuzziness, valid both in finite and infinite domains are investigated.
		It is defended that this framework should be built around the notion of relative uncertainty, that is, when the uncertainty content of some situation is related to the information content of the universal set on which the situation is defined.
		The uncertainty content of evidence sets is described with the measures of uncertainty defined in sections 3 through 5, which establish a three dimensional uncertainty space.
	informatics.indiana.edu /rocha/ijgs_unc.html (488 words)

	Agilent \| Uncertainty Made Easy
		In some companies with small calibration departments it might be possible for all of the engineers to be re-educated in assessment of uncertainties, however, in larger laboratories it is more usual for various engineers to become specialist in certain aspects of the calibration process.
		A list of contributions to the uncertainty budget can be used in place of the measurement equation and each term may be partially differentiated by varying the quantity over its range and measuring its influence on the measurand.
		In this case we have measurement uncertainties expressed in two different units; measurements of amplitude are expressed as an amplitude ratio (usually in dB units) and measurements of frequency (in Hz.).
	metrologyforum.tm.agilent.com /easy.shtml (2554 words)

	fUSION Anomaly. Uncertainty Principle
		A principle in quantum mechanics holding that increasing the accuracy of measurement of one observable quantity increases the uncertainty with which other quantities may be known.
		Albert Einstein, believed that the uncertainty involved in observation in no way contradicted the existence of laws governing the behavior of the particles or the ability of scientists to discover these laws.
		The uncertainty principle can also be derived from the fact that when taking a measurement of matter or it's particles, the tools to do so can change the particles.
	fusionanomaly.net /uncertaintyprinciple.html (591 words)

	uncertainty
		Uncertainty relations are mathematical theorems as well as physical statements so if we begin with a proof we should end up with an exact definition of what we are trying to understand.
		Here the ``uncertainty'' in time is expressed as the average time taken, starting in state x, for the expectation of some arbitrary operator A to change by its standard deviation.
		This is reasonable as a definition for time uncertainty, because it gives the shortest time scale on which we will be able to notice changes by using A in state x.
	math.ucr.edu /home/baez/uncertainty.html (797 words)

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