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	Bell test experiments - Wikipedia, the free encyclopedia
		The term "Bell inequality" can mean any one of a number of inequalities — in practice, in real experiments, the CHSH or CH74 inequality, not the original one derived by John Bell.
		One of the main achievements of this new branch of physics is showing that violation of Bell's inequalities leads to the possibility of a secure information transfer, which utilizes the so-called quantum cryptography (involving entangled states of pairs of particles).
		The second was the first application of the CHSH inequality, the third the famous one (originally suggested by John Bell) in which the choice between the two settings on each side was made during the flight of the photons.
	en.wikipedia.org /wiki/Bell_test_experiments (1590 words)

	Bell's theorem - Wikipedia, the free encyclopedia
		Bell test experiments to date overwhelmingly show that the inequalities of Bell's theorem are violated.
		John Bell's papers examined both John von Neumann's 1932 proof of the incompatibility of hidden variables with QM and Albert Einstein and his colleagues' seminal 1935 paper on the subject.
		Bell's inequalities are tested by "coincidence counts" from a Bell test experiment such as the optical one shown in the diagram.
	en.wikipedia.org /wiki/Bell's_theorem (3074 words)

	CHSH inequality - Wikipedia, the free encyclopedia
		In physics, the CHSH Bell test is an application of Bell's theorem, intended to distinguish between quantum mechanics (QM) and local hidden variable theories.
		They derived the CHSH inequality, which, as with John Bell's original one (Bell, 1964), applies to a statistical property of counts of "coincidences" in a Bell test experiment that follows from the assumption that there exist underlying local hidden variables.
		It would appear from both these later derivations that the only assumptions really needed for the inequality itself (as opposed to the method of estimation of the test statistic) are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently.
	en.wikipedia.org /wiki/CHSH_inequality (1376 words)

	bell.htm (Site not responding. Last check: 2007-10-19)
		Nevertheless, the quantum mechanical violation of Bell's inequality, which was proven experimentally in the 1980s, is yet another example of how God has cooked up a universe that is stranger than anything we could have imagined.
		Because Bell's inequality will not be violated by quantum mechanics, and I wouldn't be writing this.) So let's set it up this way: after the particles are created, they fly off to the left and right, where we have our spin measuring devices waiting for them.
		Their laboratory investigations conclusively demonstrated that Bell's inequality was violated (in one experimental run it was violated by nine standard deviations), so quantum mechanics was proved to be correct.
	www.weylmann.com /bell.htm (3514 words)

	Quantum Stuff
		Bell's theorem is based in the idea that the total measurement for two analyzers cannot be more than the sum of the changes in each, if the local view of Einstein holds since changes at A should have no effect on the results measured at B and vice versa.
		Bell's logic appears to be correct from a QM point of view because of the fact that QM assumes the two photons or particles are somehow entangled with each other and still have a connection with each other after they are separated.
		Bell's inequality is graphed as a straight line which represents the upper limit in the summation of the 'errors' from both ends of the experiment but Bell mistakenly believes he can plot the maximum measurement of the EPR tests to this same point.
	www3.sympatico.ca /saburns/pg9020.htm (4557 words)

	The EPR Paradox and Bell's Inequality Principle
		In 1964 John Bell proposed a mechanism to test for the existence of these hidden variables, and he developed his inequality principle as the basis for such a test.
		This is Bell's Inequality Principle, and it is proved to be true if there are real (perhaps hidden) variables to account for the measurements.
		Some physicists argue that there are assumptions in derivations of Bell's Inequality and that it may be possible to construct a local theory that does not respect those assumptions.
	math.ucr.edu /home/baez/physics/Quantum/bells_inequality.html (2076 words)

	Mesons violate Bell’s inequality (November 2003) - News - PhysicsWeb
		Experiments to test Bell’s inequality involve measuring the properties of pairs of particles that are space-like separated in the sense of special relativity: in other words, there is no time for a light signal to travel between them within the duration of the experiment.
		In a typical Bell’s inequality experiment the polarizations of a pair of photons are measured as the relative angle between the axes of polarizers making the measurements is varied.
		Bell and others showed that it was possible to distinguish between quantum mechanics and these hidden-variable theories in a certain type of experiment that measure a parameter known as S. Put simply, the local theories predict that S will always be less than two, whereas the quantum prediction is S = 2√2.
	physicsweb.org /article/news/7/11/3 (441 words)

	Quantum Wierdness III: Bell's Inequality
		Bell's work addressed the case of coupled particles, first used by Einstein, Podolsky, and Rosen to argue that quantum mechanics must be an incomplete theory.
		Although this inequality is rather subtle, it has a profound implication, because quantum mechanics does predict that the error rate may more than double when the angle between the polarizers is doubled.
		The predictions of quantum mechanics are confirmed; Bell's Inequality is violated.
	www.telp.com /qw3.htm (2218 words)

	Experimental tests of Bell's inequality
		For timing in a test of Bell's inequality to be conclusive requires that we time the occurrence of a macroscopic event.
		In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements.
		Bell's inequality tests necessitate major improvements of technology in order to finally, after more than 15 years, go significantly beyond the 1982 experiment of Aspect et al.
	www.mtnmath.com /whatrh/node81.html (2118 words)

	The EPR Paradox and Bell's Inequality Principle
		In 1964 John S. Bell proposed a mechanism to test for the existence of these hidden variables, and he developed his inequality principle as the basis for such a test.
		Additional inequality relations can be written by just making the appropriate permutations of the letters A, B and C and the two signs.
		Some physicists argue that there are assumptions in derivations of Bell's inequality and that it may be possible to construct a local theory which does not respect those assumptions.
	www2.corepower.com:8080 /~relfaq/bells_inequality.html (2063 words)

	EPR paradox - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-19)
		And so, in 1964, John Stewart Bell showed that the whole class of theories known as hidden variable theories have to be non-local if they are to agree with the quantum-mechanical prediction for ideal experiments.
		If such a theory is local it must satisfy Bell's inequality, but Quantum mechanics predicts that the inequality is not satisfied.
		However examples of local realist theories can be constructed which do not conform to the requirements of a hidden variable theory needed for the proof of Bell's inequality and such theories thus escape Bell's theorem.
	www.netipedia.com /index.php?title=Bell_inequality&redirect=no (2400 words)

	Bell's inequality
		Bell suspected there was something wrong with von Neumann's proof and, in the early sixties, he wrote a refutation[4].
		The inequality relates the angles between the polarizer to the probability that there will be a joint detection of two events.
		The inequality is only predicted to hold if a change in the probability of joint detections occurs in less time that it takes light to travel from either polarizer to the more distant detector.
	www.mtnmath.com /book/node27.html (683 words)

	Kip Ingram Online :: April :: 2003 (Site not responding. Last check: 2007-10-19)
		To apply Bell’s Inequality, we’d like to measure the spin of a large ensemble of particles at three different angles.
		Bell's Theorem applies the inequality in a manner that allows us to study the fundamental structure of physical reality.
		Then Bell's Inequality states that the number of blonde women plus the number of short men is greater than or equal to the number of short blondes.
	www.kipingram.com /index.php?m=200304 (1652 words)

	Bell's Theorem
		The fact that our final form of Bell's inequality is experimentally violated indicates that at least one of the three assumptions we have made have been shown to be wrong.
		The results of these tests are the same as the previous experiments: Bell's inequality is violated and the predicted Quantum correlations are confirmed.
		What is actually found [in the experimental tests of Bell's theorem] is that the behavior of the two [electrons] is correlated in a way that is rather similar to that of the two television images of the fish, as described earlier.
	www.upscale.utoronto.ca /PVB/Harrison/BellsTheorem/BellsTheorem.html (6569 words)

	List Of Articles (Site not responding. Last check: 2007-10-19)
		It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle.
		Considering an extended type of Bohm's version of EPR thought experiment, we derive Bell's inequality for the case of factorizable contextual hidden variable theories which are consistent with the predictions of quantum theory.
		In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role.
	theory.ipm.ac.ir /papers/shafiee.html (801 words)

	Quantum Physics
		John Bell imagined that instead of measuring equal and opposite momenta, a process emits two particles with equal and opposite spin.
		Quantum mechanics predicts that the choice of the axis for the first measurement of spin will alter the results of measurement of spin of the second particle, in a manner which is not consistent with the notion that the two particles have separated and become independent.
		The experiment had been carried out a number of times and it has been found that Bell's inequality is violated, and the predictions of quantum mechanics supported.
	www.kheper.net /cosmos/quantum_physics/quantum_physics.htm (3060 words)

	Bell's Inequality
		It was then that John S. Bell published a remarkable mathematical equation (or rather an inequation) (see [2]), very general in nature, by which we can test any experiment of this type for "telepathy".
		Bell's inequality can take many different forms, but the following is one of the simplest.
		It is because the abandonment of either of these "obvious" precepts is so strongly opposed to intuition, and involves such a major change in one's philosophy, that so much effort has been devoted to testing the EPR results experimentally, and so much ink and sweat devoted to their analysis.
	www.tribunes.com /tribune/art98/parr.htm (2953 words)

	Experimental violation of a Bell's inequality with efficient detection : Nature
		The correlation values and resulting Bell's signals from five data runs are given in Table 2.
		We have thus presented experimental results of a Bell's inequality measurement where a measurement outcome was recorded for every experiment.
		Lamehi-Rachti, M. and Mittig, W. Quantum mechanics and hidden variables: a test of Bell's inequality by the measurement of the spin correlation in low-energy proton-proton scattering.
	www.nature.com /nature/journal/v409/n6822/full/409791a0.html (2993 words)

	Bell's Paradox
		In 1964 John S. Bell proposed a mechanism to test for the existence of these hidden parameters, and he developed his inequality principle as the basis for such a test.
		This is Bell's inequality principle, and it is proved to be true if there are real (perhaps hidden) parameters to account for the measurements.
		Bell: "On the Einstein Podolsky Rosen paradox" Physics 1 #3, 195 (1964).
	phoenixandturtle.net /excerptmill/EPRBELL.HTM (2920 words)

	Objective Science - Quantum Mechanics and Dissidents By Eric Dennis (Site not responding. Last check: 2007-10-19)
		Bell contemplated an experiment involving a pair of entangled particles shot in opposite directions from a common source, one toward a measuring device at A and the other toward a separate measuring device at B.
		Indeed, the advocates of TEW subsequently admitted that TEW could not account for the experimental results in question [7], namely those for which the device settings at A and B are made quickly enough as not to allow the device setting at A to (sub-luminally) affect the measurement result at B and vice versa.
		This is a particularly clear and rigorous treatment of Bell's inequality.
	www.objectivescience.com /articles/ed1_quantum_dissidents.htm (2062 words)

	Tsirelson : "My bound"
		The stunning implications of Bell's theorem caused an outbreak of theoretical activity, including some wild speculations that I shall not discuss.
		On the serious side, Bell's work led to a systematic search for other inequalities with the same universal character.
		Cirel'son raised the question whether quantum theory imposed an upper limit to correlations between distant events (a limit which would of course be higher than the classical one, given by Bell's inequality).
	www.tau.ac.il /~tsirel/Research/mybound/main.html (220 words)

	On the Violation of Bell's Inequality in Quantum Theory (Site not responding. Last check: 2007-10-19)
		Elementary considerations concerning Bell's inequality are presented and applied to the quantum theory of local observables.
		If R violates Bell's inequality then no classical description in terms of a joint distribution is possible.
		That is, Bell's inequality may be violated by the maximum amount 2
	www.mth.kcl.ac.uk /~llandau/Homepage/Math/bell.html (679 words)

	"My bound" : citing
		1984 A.A. Grib, "Bell's inequalities and experimental verification of quantum correlations at macroscopic distances." Soviet Phys.
		1987 L.J. Landau, "On the violation of Bell's inequality in quantum theory." Phys.
		1997 A. Peres, "Bell inequalities with postselection." In: Boston Stud.
	www.tau.ac.il /~tsirel/Research/mybound/cit_a.html (1317 words)

	An Introduction to Bell's Inequalities and Non-Locality by Travis Norsen
		This is a general statement of Bell's inequality.
		This inequality should hold if the assumptions we have made leading up to it are correct -- in particular, if the measurement result on each side is independent of the choice of direction to measure along at the distant experiment.
		Given the analysis presented here, the experimentally-observed violation of Bell's inequalities proves that the correlations between the results of Alice's and Bob's measurements are too strong to be explained by anything in the shared past of the two particles -- that is, the correlations are too strong to be explained by any purely local theory.
	www.objectivescience.com /articles/tn_bell_4.htm (2454 words)

	Cycles Research Institute - David Elm's EPR Explanation
		What it tells me is that Bell's inequality cannot be applied to just a special subset of the data, rather it must apply to the entire data set.
		Bell's inequality is violated only when all the data are not included in the math.
		This rejection is obviously a problem since Bell's theorem _doesn't follow_ if other types of detection events are allowed (such as when only A or only B detector triggers, or when two A detectors trigger, etc).
	www.cyclesresearchinstitute.org /physics/elm.html (7299 words)

	"Bell's Theorem is Invalid for Cellular Automata..." by Plamen Petrov
		In the present paper, we demonstrate that Bell's inequality is invalid for cellular automata by giving a concrete example of a one-dimensional (non-quantum) CA that clearly violates it.
		Applying Bell's theorem, it is easy to deduce that if the settings of the switches are random then the same colors will flash at least 5/9 of all the runs, i.e.
		The restriction proposed by J. Bell with his famous inequality may be something that shocks physicists traditionally operating with notions like "continuity" and "randomness", but it is not at all a problem for perfectly local and deterministic mathematical models like CAs that replace these notions with the corresponding notions of finitely divisible space/time and pseudo-randomness.
	digitalphysics.org /Publications/Petrov/Pet02m/Pet02m-InterJournal.htm (3309 words)

	INI : Abstracts : QISW04 : The Bell inequality and the coincidence-time loophole (Site not responding. Last check: 2007-10-19)
		INI : Abstracts : QISW04 : The Bell inequality and the coincidence-time loophole
		A generalized inequality is derived for the case when coincidence and non-coincidence (and hence whether or not a pair contributes to the actual data) is controlled by timing that depends on the detector settings.
		Needless to say, this inequality is violated by quantum mechanics and could be violated by experimental data provided that the loss of measurement pairs through failure of coincidence is small enough, but the quantitative bound is more restrictive in this case than in the previously analyzed "efficiency loophole".
	www.newton.cam.ac.uk /programmes/QIS/Abstract4/Larsson.html (133 words)

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