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	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.
		Casimir Effect -- among other subjects), the uncertainty in the value of the energy of a particle is significant.
		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 - Wikipedia, the free encyclopedia
		The uncertainty principle is one of the cornerstones of quantum mechanics and was discovered by Werner Heisenberg in 1927.
		The uncertainty principle in quantum mechanics is sometimes explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		The uncertainty principle is stated in popular culture in many ways, for example by stating that it is impossible to know both where an electron is and where it is going at the same time.
	en.wikipedia.org /wiki/Uncertainty_principle (2161 words)

	Uncertainty principle - Open Encyclopedia (Site not responding. Last check: 2007-10-21)
		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 in quantum mechanics is sometimes erroneously explained by claiming that the measurement of position necessarily disturbs a particle's momentum.
		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 (2028 words)

	Uncertainty principle -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		The uncertainty principle in (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)) quantum mechanics 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 (Click link for more info and facts about particle in a box) particle in a box with a particular energy value; i.
		Other forms of the uncertainty principle can be formulated for the (Click link for more info and facts about Fourier transform) Fourier transform on general locally compact groups or for Fourier integral operators on manifolds.
	www.absoluteastronomy.com /encyclopedia/u/un/uncertainty_principle.htm (2319 words)

	Werner Karl Heisenberg
		Heisenberg was willing to sacrifice the idea of discrete particles moving in prescribed paths (neither particles nor paths could be observed) in exchange for a theory that would deal directly with experimental facts and lead to the quantum conditions as consequences of the theory rather than ad hoc stipulations.
		Heisenberg used the new matrix mechanics to interpret the dual spectrum of the helium atom (that is, the superposed spectra of its two forms, in which the spins of the two electrons are either parallel or antiparallel), and with it he predicted that the hydrogen molecule should have analogous dual forms.
		Indeterminacy principles are characteristic of quantum physics; they state the theoretical limitations imposed upon any pair of noncommuting (i.e., conjugate) variables, such as the matrix representations of position and momentum; in such cases, the measurement of one affects the measurement of the other.
	www.nobel-winners.com /Physics/werner_karl_heisenberg.html (1656 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.
		So, although Heisenberg did not originate the tradition of calling his relations a principle, it is not implausible to attribute the view to him that the uncertainty relations represent an empirical principle that could serve as a foundation of quantum mechanics.
	plato.stanford.edu /entries/qt-uncertainty (10377 words)

	Uncertainty Principle (Werner Heisenberg) (Site not responding. Last check: 2007-10-21)
		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)

	Heisenberg (Site not responding. Last check: 2007-10-21)
		Heisenberg presented preliminary results on the problem on turbulence at a conference in Innsbruck before going again to Göttingen to study with Born, Franck, and Hilbert while his supervisor was away.
		Heisenberg now considered the combination of all the oscillations of such a spectrum as one system, for the mathematical handling of which, he set out certain symbolical rules of calculation.
		Heisenberg hoped this mathematical property would lead to a fundamental property of nature with a 'fundamental length' as one of the constants of nature.
	www-groups.dcs.st-andrews.ac.uk /~history/Mathematicians/Heisenberg.html (2599 words)

	A Science Odyssey: People and Discoveries: Heisenberg states the uncertainty principle
		Heisenberg and Bohr's theories were compatible and became known together as the Copenhagen interpretation and accepted as the foundation for quantum theory.
		The layman without knowledge of higher mathematics, listening to Dr. Heisenberg and those who discussed his conclusions, would have decided that this particular section of the British Association is composed of quiet and polite but determined lunatics, who have created a wholly illusory mathematical world of their own.
		Planck, the originator of the quantum theory, Heisenberg, Schrödinger, and De Broglie have shown that the whole science of mechanics must be rewritten.
	www.pbs.org /wgbh/aso/databank/entries/dp27un.html (715 words)

	Werner Heisenberg - Biography
		It was probably due to his influence that Heisenberg remarked, when the Japanese physicist Yukawa discovered the particle now known as the meson and the term "mesotron" was proposed for it, that the Greek word "mesos" has no "tr" in it, with the result that the name "mesotron" was changed to "meson".
		During 1955 Heisenberg was occupied with preparations for the removal of the Max Planck Institute for Physics to Munich.
		Heisenberg's name will always be associated with his theory of quantum mechanics, published in 1925, when he was only 23 years old.
	www.nobel.se /physics/laureates/1932/heisenberg-bio.html (920 words)

	The "Heisenberg's Uncertainty Principle" Blog
		Heisenberg's famous uncertainty principle implies that the act of observation may interfere with the behavior of quantum particles; but it is the observation that creates the effect, not the uncertainty principle itself.
		Heisenberg's uncertainty principle is a key component, although one minor flaw of the movie, charged with cramming in a lot of info, is that it never explains...
		Heisenberg's uncertainty principle is a key component, although one minor flaw of the movie, charged with cramming in a lot of info, is that it never explains what that principle is.
	uncertaintyprinciple.blogspot.com (15468 words)

	Uncertainty About the Uncertainty Principle - Can't anybody get Heisenberg's big idea right? By Jim Holt (Site not responding. Last check: 2007-10-21)
		Heisenberg, one of the inventors of quantum mechanics, was the leader of Hitler's atomic bomb project during World War II.
		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 (1309 words)

	UNCERTAINTY PRINCIPLE-HEISENBERG'S UNCERTAINTY PRINCIPLE -HEISENBERG
		Heisenberg in 1927 and known as 'Heisenberg's uncertainty principle'.
		Heisenberg considered an electron that has a definite, known momentum and that passes under a powerful microscope.
		UNCERTAINTY IN Similar to uncertainty in position there is another principle of uncertainty which limits the accuracy in the measurement of time i.e.
	www.citycollegiate.com /physicsXII_17_uncertainity.htm (489 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)

	Heisenberg's Uncertainty Principle
		Heisenberg, on the other hand, started with the assumption that space and time are indefinitely divisible (i.e., the point assumption) and came up with his principle as the necessary (and ingenious) patch to reconcile the point assumption with de Broglie’s hypothesis.
		The Heisenberg’s uncertainty principle implies that my x measurements cannot be the same each time (i.e., it is impossible for me to duplicate my x measurements.) For this reason, I will end up with a range of values for x.
		This is resolved by recognizing that the measurement error in momentum, as implied by the Heisenberg’s uncertainty principle, is caused by the inability (of a classical tool) to determine the exact location of the quantum entity within its de Broglie’s wavelength.
	www.thinhtran.com /heisenberg.html (3269 words)

	uncertainty principle. The Columbia Encyclopedia, Sixth Edition. 2001-05
		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.
	www.bartleby.com /65/un/uncertai.html (380 words)

	Heisenberg Uncertainty Principle (Site not responding. Last check: 2007-10-21)
		The HUP can be stated in different ways, let me first talk in terms of momentum and position.
		The preceding is a statement of the Heisenberg Uncertainty Principle.
		A consequence of the Uncertainty Principle is that if an object's position x is defined precisely then the momentum of the object will be only weakly constrained, and vice versa.
	zebu.uoregon.edu /~imamura/208/jan27/hup.html (444 words)

	Heisenberg uncertainty principle (from quantum mechanics) -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-21)
		In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known.
		German physicist Werner Heisenberg is most famous for his statement, published in 1927, that the position and the velocity of a subatomic particle cannot both be measured exactly, at the same time, even in theory.
		He will probably be best remembered, however, for developing the uncertainty (or indeterminacy) principle, the concept that the behavior of subatomic particles can be predicted only on the basis of probability (see uncertainty principle).
	www.britannica.com /eb/article-77517 (983 words)

	SPACE.com -- Quantum Astronomy: The Heisenberg Uncertainty Principle
		However, the uncertainty principle is a fundamental property of quantum physics initially discovered through somewhat classical reasoning -- a classically based logic that is still used by many physics teachers to explain the uncertainty principle today.
		However the uncertainty principle was to turn out to be much more fundamental than even Heisenberg imagined in his first paper.
		Another way of stating this principle, using relativity in the formulation, turns out to be that one gets another version of the uncertainty principle.
	www.space.com /searchforlife/quantum_astronomy_041118.html (1652 words)

	Space.com articles - Date - SETI Institute (Site not responding. Last check: 2007-10-21)
		In scientific circles we are perhaps used to thinking of the word “principle” as “order”, “certainty”, or “a law of the universe”. So the term “uncertainty principle” may strike us as something akin to the terms “jumbo shrimp” or “guest host” in the sense of juxtaposing opposites.
		However, the uncertainty principle is a fundamental property of quantum physics initially discovered through somewhat classical reasoning—a classically based logic that is still used by many physics teachers to explain the uncertainty principle today.
		Another way of stating this principle, using relativity in the formulation, turns out to be that one gets another version of the uncertainty principle.
	www.seti.org /site/apps/nl/content2.asp?c=ktJ2J9MMIsE&b=194993&ct=295500 (1529 words)

	Math Forum - Ask Dr. Math
		As I understand, the Uncertainty Principle reads(delta)p(delta)v is approximately equal to or greater than h (Plank's constant).
		The Uncertainty Principle is wrong, Plank's constant is wrong, or my question (and an ill-formed one it is) is wrong...
		This is the essence of the Uncertainty Principle: If you have a long sample of a wave, it's spread out over time but its frequency (energy) is defined well.
	mathforum.org /library/drmath/view/51504.html (482 words)

	The musician's uncertainty principle and Heisenberg's uncertainty principle (Site not responding. Last check: 2007-10-21)
		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 (867 words)

	ipedia.com: Uncertainty principle Article (Site not responding. Last check: 2007-10-21)
		In quantum physics, the Heisenberg uncertainty principle expresses a limitation on accuracy of simultaneous measurement of observables such as the position and the momentum of a particle.
		That the role of disturbance is not essential can be seen as follows: Consider an ensemble of (non-interacting) particles all prepared in the same state for which we measure the momentum or the position (but not both).
		Albert Einstein was not happy with the uncertainty principle, and he challenged Niels Bohr with a famous thought experiment: we fill a box with a radioactive material which randomly emits radiation.
	www.ipedia.com /uncertainty_principle.html (1779 words)

	BBC - h2g2 - Heisenberg's Uncertainty Principle
		Simply put, Heisenberg's Uncertainty Principle states that it is impossible to know both the exact position and the exact velocity of an object at the same time.
		Werner Heisenberg (1901-1976) was a German physicist who helped to formulate quantum mechanics at the beginning of the 20th century.
		For larger particles, such as sand grains or buses, the percentage uncertainty in the measurements of position and momentum is insignificant.
	www.bbc.co.uk /dna/h2g2/A408638 (1064 words)

	HEISENBERG UNCERTAINTY PRINCIPLE (Site not responding. Last check: 2007-10-21)
		Heisenberg's Uncertainty Principle, or the Uncertainty Principle, is the theory that it is scientifically impossible to determine both the position and the momentum of a small particle at the same time.
		Heisenberg invented the Uncertainty Principle in 1927, and it has been exceedingly useful ever since.
		Many scientists in Heisenberg's day doubted this theory, since they refused to believe that logic could not be used to determine everything.
	www.fordhamprep.com /physics/heisen.htm (168 words)

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