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Topic: Uncertainty principle

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	Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Principle
		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 (966 words)

	The Uncertainty Principle (Stanford Encyclopedia of Philosophy)
		The uncertainty principle played an important role in many discussions on the philosophical implications of quantum mechanics, in particular in discussions on the consistency of the so-called Copenhagen interpretation, the interpretation endorsed by the founding fathers Heisenberg and Bohr.
		This should not suggest that the uncertainty principle is the only aspect of the conceptual difference between classical and quantum physics: the implications of quantum mechanics for notions as (non)-locality, entanglement and identity play no less havoc with classical intuitions.
		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.
	plato.stanford.edu /entries/qt-uncertainty (10573 words)

	Uncertainty principle - Wikipedia, the free encyclopedia
		Uncertainty is the characterization of the relative narrowness or broadness of the distribution function applied to a physical observation.
		The uncertainty principle in quantum mechanics is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		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 (3427 words)

	Uncertainty - Wikipedia, the free encyclopedia
		Often, the uncertainty of a measurement is found by repeating the measurement enough times to get a good estimate of the standard deviation of the values.
		In metrology, measurement uncertainty is a central concept quantifying the dispersion one may reasonably attribute to a measurement result.
		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 (1127 words)

	Uncertainty Principle - MSN Encarta
		Uncertainty Principle, in quantum theory, the principle that it is impossible to precisely specify certain quantities simultaneously.
		The uncertainty principle was discovered by the German physicist Werner Heisenberg in 1927.
		To Bohr the uncertainty principle did not describe an inability of physicists to measure quantities, but a limitation of the way in which momentum and position could be defined.
	uk.encarta.msn.com /encyclopedia_761578486/Uncertainty_Principle.html (684 words)

	uncertainty principle - HighBeam Encyclopedia (Site not responding. Last check: )
		According to the uncertainty principle, the mathematical product of the combined uncertainties of simultaneous measurements of position and momentum in a given direction cannot be less than Planck's constant h divided by 4π.
		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.
		Redistributing the burden of scientific uncertainty: implications of the precautionary principle for state and nonstate actors.
	www.encyclopedia.com /html/u1/uncertai.asp (477 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.
	www.seop.leeds.ac.uk /archives/spr2002/entries/qt-uncertainty (10240 words)

	Uncertainty Principle
		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 principle applies to other related (conjugate) pairs of observables, such as energy and time: the product of the uncertainty in an energy measurement and the uncertainty in the time interval during which the measurement is made also equals h/(2) or more.
		The uncertainty principle, developed by W. Heisenberg, is a statement of the effects of wave-particle duality on the properties of subatomic objects.
	zebu.uoregon.edu /~js/21st_century_science/lectures/lec14.html (3556 words)

	Uncertainty Principle - Uncyclopedia
		The Uncertainty Principle was with 78% probability postulated by Werner Heisenberg, probably because the quantum theory was by that time so hopelessly confused that he needed a way to explain the self-contradictory results.
		The principle was revived by Marty McFly in 1955 (every 1955 except the first) during his famous time travel experiment, in which he temporarily reached a translucent state of superposition during a school dance.
		The Uncertainty Principle was further extrapolated to the future in the said 1984, the year of Nixon and Reagan's presidency, when Kyle Reese reformulated it in its current form, saying that the future is uncertain.
	uncyclopedia.org /wiki/Heisenberg_Uncertainty_Principle (1532 words)

	Heisenberg Uncertainty Principle
		The equations (7.16) and (7.17) show that uncertainty in the present and future positions of a particle are complimentary.
		On the other hand, a broad-scale initial wave packet means that the present position is poorly known, but the uncertainty in position, poor as it is, doesn't rapidly increase with time, since the wave packet has a small uncertainty in wave vector and thus disperses slowly.
		In this case the uncertainties induced by the uncertainty principle are unimportant.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node77.html (575 words)

	The musician's uncertainty principle and Heisenberg's uncertainty principle (Site not responding. Last check: )
		Heisenberg's Uncertainty Principle follows from a classical result, which is at least as old as Fourier.
		Js), so the consequences of the uncertainty principle are usually only important for photons, fundamental particles and phonons.
		There is also a discussion of how chemistry depends upon the uncertainty principle at Why there would be no chemistry without relativity, which is part of our site on relativity.
	www.phys.unsw.edu.au /~jw/uncertainty.html (858 words)

	[Xplor-nih] The Uncertainty Principle Is Untenable
		THE UNCERTAINTY PRINCIPLE IS UNTENABLE By re-analysing Heisenberg's Gamma-Ray Microscope experiment and the ideal experiment from which the uncertainty principle is derived, it is actually found that the uncertainty principle can not be obtained from them.
		Except for the factor of 4pi and an equal sign, this is Heisenberg's uncertainty relation for the simultaneous measurement of the position and momentum of an object.
		For example, the Law of Conservation of Momentum is based on the collision of two stretch ball in the vacuum; the Principle of equivalence(general relativity) is besed on the Einstein's laboratory in the lift.
	nmr.cit.nih.gov /pipermail/xplor-nih/2003-December/000124.html (1255 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 (1447 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 PRINCIPLE (Site not responding. Last check: )
		A principle in quantum physics, formulated by Heisenberg: "It is impossible to simultaneously measure the position and the momentum of atomic particles with an arbitrary degree of accuracy".
		The principle recognizes the fact that, on the atomic level, any measuring process involves energy which by necessity interferes with the energy measured.
		A less quantifiable uncertainty principle exists in the social sciences: "Any interaction between an observer and the observed changes both.
	pespmc1.vub.ac.be /ASC/UNCERT_PRINC.html (125 words)

	"The New Uncertainty Principle"
		Critics asserted that the principle's definition and goals are vague, leaving its application dependent on the regulators in charge at the moment.
		What is more, scientists whose work butts up against the precautionary principle will have "to do a very good job of expressing the uncertainty in their information," points out William W. Fox, Jr., director of science and technology for the National Marine Fisheries Service.
		Those wide limits are the crux of the issue, the point at which proponents of the precautionary principle say decisions should be taken from the realm of science and into politics.
	www.biotech-info.net /uncertainty.html (1207 words)

	Heisenberg's Uncertainty Principle
		Heisenberg’s Uncertainty Principle is one of the fundamental concepts of Quantum Physics, and is the basis for the initial realization of fundamental uncertainties in the ability of an experimenter to measure more than one quantum variable at a time.
		Attempting to measure an elementary particle’s position to the highest degree of accuracy, for example, leads to an increasing uncertainty in being able to measure the particle’s momentum to an equally high degree of accuracy.
		Specifically, the “unfortunately unspecified” interaction of an electron with the rest of the universe, as specified by Mach’s Principle, is contained within the Heisenberg Uncertainty Principle as a continuously fluctuating exchange of energy or momentum.
	www.halexandria.org /dward159.htm (953 words)

	Uncertainty Principle (Site not responding. Last check: )
		There is an analogous uncertainty >relation between the uncertainty in the simultaneous measurement of the >energy and time, which is dimensionally equivalent [Joule*sec].
		The uncertainty principle places a lower limit on >the product of the uncertainties of two simultaneous measurements on >the same system, and not just any two measurements, but specifically >measurements of "incompatible" [my word, not a technical term] observables.
		The difference is that in everyday >situations, you could, in principle, achieve an arbitrarily small >measurement uncertainty (e.g., use a very small thermometer in a huge >bowl of soup).
	www.newton.dep.anl.gov /askasci/phy00/phy00072.htm (466 words)

	The Uncertainty Principle
		One important consequence of the wave-particle duality of nature was discovered by Heisenberg, and is called the uncertainty principle.
		We recall in the last chapter that there is a limit to the resolving power of the light used to see the particle given by the wavelength of light used.
		As with de Broglie waves, for everyday macroscopic objects such as bowling balls the uncertainty principle plays a negligible role in limiting the accuracy of measurements, as we shall see in some examples.
	theory.uwinnipeg.ca /physics/quant/node7.html (247 words)

	UNCERTAINTY PRINCIPLE IS UNTENABLE
		By reanalysing the experiment of Heisenberg Gamma-Ray Microscope and one of ideal experiment from which uncertainty principle is derived, it is found that actually uncertainty principle can not be obtained from these two ideal experiments.
		And it is found that uncertainty principle is untenable.
		These yield the highest resolution, for according to a principle of wave optics, the microscope can resolve (that is, "see" or distinguish) objects to a size of dx, which is related to and to the wavelength L of the gamma ray, by the expression:
	www.incunabula.org /blog/uncertain.html (1343 words)

	Uncertainty Principle
		Using ∆n for the frequency spread (uncertainty in frequency) and ∆t for the duration of the pulse (uncertainty in the time domain), the frequency-time uncertainty relation is given by
		The uncanny similarity between the shape of the frequency spectrum and the intensity distribution of the single-slit diffraction pattern is remarkable.
		The similarity is not entirely an accident since the spreading out of the diffraction pattern (while narrowing the slit-width) is, of course, another example of the ubiquitous uncertainty principle rearing its head and is described in the Optical Analog of Uncertainty Principle demo.
	www.fas.harvard.edu /~scdiroff/lds/QuantumRelativity/UncertaintyPrinciple/UncertaintyPrinciple.html (1066 words)

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