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Topic: Dirac constant

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	Planck's constant - Wikipedia, the free encyclopedia
		Planck's constant (denoted h) is a physical constant that is used to describe the sizes of quanta.
		Planck's constant and the reduced Planck's constant are used to describe quantization, a phenomenon occurring in microscopic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values.
		Planck's constant has units of energy (joules or J) multiplied by time (seconds or s), which are the units of action (joule seconds or J·s).
	en.wikipedia.org /wiki/Planck's_constant (436 words)

	h-bar (Site not responding. Last check: 2007-11-05)
		This constant, which is pronounced as "h-bar", is sometimes (though infrequently) referred to as Dirac's constant, after Paul Dirac.
		Planck's constant is used to describe quantization, a phenomenon occurring in microscopic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values.
		On some browsers, the unicode symbol and#8462; (ℎ) is rendered as Planck's constant, and the symbol and#8463; (ℏ) is rendered as Dirac's constant.
	www.yourencyclopedia.net /H-bar.html (362 words)

	P. A. M. Dirac (Site not responding. Last check: 2007-11-05)
		Dirac was three years old when Einstein published his famous papers on relativity in 1905 and a year old when his predecessor Joseph Larmor began his tenure as Lucasian professor.
		Dirac was able to produce accurate values for the strength the magnetic field around the electron, as well as other important characteristics that had eluded everyone up to that time.
		Dirac's life was dedicated to physics with no interests outside of his work, but, besides quantum mechanics, he did work on isotope separation, magnetic monopoles, large-number hypothesis and other physics areas.
	security-books.com /lucasianchair.org/dirac.html (2525 words)

	Proper Dirac Quantization of Free Particle on D-Dimensional Sphere
		Dirac has emphasized that canonical quantization rules are consistent only in a Cartesian reference frame [1].
		Thus the modified symplectic structure proposed by Dirac, although esthetically appealing and yielding a unique result for a particle on the surface of a sphere, must be rejected on physical grounds as contradicting the established quantization via angular momentum operators and nonholonomic mapping principle.
		Dirac's new symplectic structure (5) represented by (7)-(9) accounts for this fact via its degeneracy in the embedding phase space.
	www.physik.fu-berlin.de /~kleinert/kleiner_re253/partsph.html (2308 words)

	Interview with Paul Adrian Maurice Dirac - F. David Peat
		Like Newton before him Dirac has made contributions that are respected by his colleagues not only for their depth of insight and clarity but for the power and economy with which mathematics is brought to bear upon the problems of nature.
		Dirac was able to show that the two theories were equivalent, and in the process provided quantum theory with a sound mathematical footing.
		Dirac is concerned with the occurrence of large numerical constants in physical theories.
	www.fdavidpeat.com /interviews/dirac.htm (2796 words)

	CERN Courier - Are the fundamental constant - IOP Publishing - article
		Recent observations in astrophysics suggest that α, the fine structure constant (see "The magic number " box), which is of fundamental importance in describing the electromagnetic interaction, was in earlier periods a little smaller than today.
		At around the same time, Pascal Jordan discussed the possibility that other constants could also be time-dependent (Jordan 1937; 1939), but he refused to consider that the constant of the weak interactions or the ratio of the electron and proton mass might be time-dependent.
		In the case where the coupling constant remains invariant, but the energy at which the unification takes place depends on time, one finds that the time change of the scale Λ for the strong interactions is about 31 times larger than the time change of α, but has the opposite sign.
	www.cerncourier.com /main/article/43/2/13 (2372 words)

	[No title]
		Dirac suggested that this coincidence should be explained by looking for some link between the fundamental constants and the age of the universe.
		Dicke rejected Dirac's speculation about the change of G in time and found a simpler explanation in the selection effect (on possible values of the constants) of the fact that we humans are here.
		If the physical constants being what they are is a necessary condition for there being humans (or cockroaches), and there are humans (and cockroaches), then B we can conclude B the physical constants are what they are, ie they are in the limited region of the possibility space which make humans and cockroaches possible.
	philsci-archive.pitt.edu /archive/00001609/01/Anthropic_Explanations_in_Cosmology_(2003).doc (12911 words)

	Bringing the Dirac Coincidences up to date
		In his paper, Dirac noted that, for some unexplained reason, the ratio of the electrostatic to gravitational force between an electron and a proton is roughly equal to the age of the universe divided by an elementary time constant, implying that
		The upshot, then, is that by combining Dirac’s empirical coincidences with standard inflation theory, one seems to arrive at a way of estimating vacuum energy densities that for the first time gives values consistent with observational constraints at all the critical cosmological epochs.
		O By linking Dirac’s coincidences to concepts drawn from inflation theory, we are led to the possibility that the most recent vacuum phase transition, due to quark-hadron confinement, led to a remnant vacuum energy making an appreciable contribution to the total mass-energy of the current universe.
	ourworld.compuserve.com /homepages/rajm/agdirac.htm (2042 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		They also suffer from uncertainties in the measurement of some of the constants on which they are based, especially of the gravitational constant G.
		The NIST (National Institute of Standards and Technology) website is a convenient source of data on the commonly-recognized constants, including Planck units.
		He himself had not yet discovered the theory of flbody radiation (first published December 1900) in which the constant h made its first appearance and for which Planck was later awarded the Nobel prize.
	www.online-encyclopedia.info /encyclopedia/n/na/natural_units.html (416 words)

	Environmental, Health & Safety: Physical constants
		Constants can take many forms: the Planck length represents a fundamental physical distance; the speed of light in a vacuum signifies a maximum speed limit of the universe; and the fine-structure constant, which characterizes the interaction between electrons and photons, is dimensionless.
		Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe.
		Constants that are independent of systems of units are typically dimensionless numbers, and are known as fundamental physical constants.
	www.christopherhaase.com /blog/2004/12/physical-constants.html (559 words)

	The Dirac Algorithm: Constant Quality Coding (Site not responding. Last check: 2007-11-05)
		The best subjective performance results from having roughly constant quality, and large variations of quality, either from frame to frame or within a frame, tend to be disliked by viewers.
		Dirac incorporates a form of constant-quality encoding by adapting RDO parameters for each type of frame until a quality metric is met.
		Constant bit rate coding (CBR) is needed when you're in a strictly bandwidth-constrained environment and you need real-time decoding - broadcasting, for example.
	www.bbc.co.uk /rd/projects/dirac/documentation/algorithm/const_qual.htm (454 words)

	[No title]
		The constant of proportionality is called G, the 'gravitational constant, the universal gravitational constant or Newton's constant.
		The gravitational constant is a fundamental physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of
		By combining the gravitational constant with Planck's constant and the speed of light in vacuum, it is possible to create a system of units known as Planck units.
	en-cyclopedia.com /wiki/Gravitational_constant (531 words)

	Physics > Physical Constants
		In science, a physical constant is a physical quantity whose numerical value is fixed.
		There are many such constants used in science, some of the most famous of which being: Planck's constant, the gravitational constant and Avogadro's constant (better known as Avogadro's number).
		Constants can take many forms; some, such as the Planck length represents a fundamental physical distance, others such as the speed of light signifies the maximun speed limit of the universe, yet others are dimensionless quantities such as the fine-structure constant which embodies the interaction between electrons and photons.
	www.physics.teleactivities.net /tables/physical_constant.htm (226 words)

	Hyperfine Structure Dirac Equation -
		The Dirac equation for a spin _ particle is of the form...
		The discovery of the Dirac equation was one of...
		Dirac equation, fine structure of the n=2 shell in hydrogen.
	equation.fabca.com /index.php?k=hyperfine-structure-dirac-equation (833 words)

	GRAVITATIONAL CONSTANT FACTS AND INFORMATION (Site not responding. Last check: 2007-11-05)
		According to the law_of_universal_gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them.
		The gravitational constant is a fundamental physical_constant which appears in Newton's law of universal gravitation and in Einstein's theory of general_relativity.
		By combining the gravitational constant with Planck's_constant and the speed of light in vacuum, it is possible to create a system of units known as Planck_units.
	www.whereintheworldisbush.com /gravitational_constant (693 words)

	Connection of Three Major Constants: fine structure constant, number pi and gold ratio. (Site not responding. Last check: 2007-11-05)
		At that, all dimensionless physical constants are very toughly connected among themselves inside own family of dimensionless constants, and their connection with dimensional fundamental physical constants is only consequence, i.e.
		When accepting of geometrical essence of fine structure constant all the dimensional and the dimensionless parameters, which characterize the microworld and universe are calculable in principle.
		At the big quantity of fundamental constants such unprecedent coincidence of calculated and experimental values is the reliable proof of the geometrical status of fine structure constant and validity of above mentioned formulas.
	www.laboratory.ru /articl/hypo/ax140e.htm (2287 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-11-05)
		The dimensionless Fine-structure constant can be thought of as taking on the value that it does because of the amount of charge, measured in natural units (Planck charge), that electrons, protons, and other charged particles happen to have been assigned by nature herself.
		This factor comes from the fact that it is the Coulomb Force Constant [ 1/(4 \pi \epsilon_0) \ ] in Coulomb's law that is normalized to 1, as is done in the cgs system of units, rather than the permittivity of free space [ \epsilon_0 \ ].
		This, and that fact that the gravitational constant [ {G} \ ] is normalized rather than [ {4 \pi G} \ ], could be considered to be an arbitrary definition and perhaps a non-optimal one from the perspective of defining the most natural physical units as the choice for Planck Units.
	www.alanaditescili.net /index.php?title=Planck_units (1528 words)

	Planck's constant - FreeEncyclopedia (Site not responding. Last check: 2007-11-05)
		Planck's constant, denoted h, named after the physicist Max Planck, is a physical constant which appears in all quantum mechanical equations.
		Js Planck's constant can be seen as a conversion factor between frequency and energy, especially for photons.
		The constant $\hbar$ is sometimes referred to as Dirac's constant after Paul Dirac.
	openproxy.ath.cx /pl/Planck's_constant.html (139 words)

	We consider the three body dirac equation with linear scalar one body potentials as the Hamiltonian for a three quark ... (Site not responding. Last check: 2007-11-05)
		Abstract: A variant of a squared three body Dirac equation is used to determine center of mass energy effects in independent particle motion approximations for three quarks in the nucleon.
		With a quark model of the nucleon, this potential is a reasonable model of a flux tube potential [11] which minimizes the flux tube length connecting and confining the three quarks within the nucleon.
		We consider the three body Dirac equation with linear scalar one body potentials as the Hamiltonian for a three quark model of the nucleon.
	www.physast.uga.edu /~gstrobel/fujita.html (2691 words)

	Articles - Coupling constant (Site not responding. Last check: 2007-11-05)
		In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction.
		is the permittivity of free space, â is Dirac's constant and c is the speed of light) is such a dimensionless coupling constant that determines the strength of the electromagnetic force on an electron.
		However, in the case of string theory, these coupling constants are not pre-determined, adjustable, but universal parameters, but rather dynamical scalar fields that can depend on the position in space and time and whose values are determined dynamically.
	www.lastring.com /articles/Coupling_constant?mySession=27b8a9e460516ddb5ab914117cce5b92 (1029 words)

	Archimedes Plutonium (Site not responding. Last check: 2007-11-05)
		Another dimensionless constant is the ratio of the mass of the proton to the mass of the electron, that is to say, Mp/Me That constant has the value somewhere near 1840.
		And, I share that sentiment with Dirac that the meaning of the fine-structure marker of physics is one of the most important unsolved, outstanding problems of physics.
		Going beyond Dirac in his statement above, it is now experimentally known in high energy physics that the fine-structure marker is not a constant but a variable.
	www.iw.net /~a_plutonium/File002c.html (2441 words)

	Numerical Constants - Mathematics & Physics - Numericana
		Planck's constant: The ratio of a photon's energy to its frequency.
		The attribution of this irrational constant to Ramanujan was made by Simon Plouffe, as a monument to a famous 1975 April fools column by Martin Gardner in Scientific American (where it was claimed that the above had been proven to be exactly an integer, as conjectured by Ramanujan in 1914 [sic!]).
		Some other set of independent constants could have been used to define the 7 basic units (for example, a conventional value of the electron's charge could replace the conventional permeability of the vacuum) but the following one was chosen after careful considerations.
	home.att.net /~numericana/answer/constants.htm (4599 words)

	Abstracts of PDE and QM papers
		The behavior of the operator near the critical coupling constant $Z_c$ is studied and the essential spectrum is determined in the case of $Z=Z_c$.
		We study the asymptotic behavior, as Planck's constant $\hbar \to 0$, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field $\mu\mathbf{B}(x)$ and an electric field.
		Two main types of results are established: in the first $\mu\hbar\le constant$ as $\hbar\to 0$, with magnetic fields of arbitrary direction; the second results are uniform with respect to $\mu\ge 0$ but the magnetic fields have constant direction.
	www.math.ku.dk /~solovej/PDE-QM/abstracts.html (7877 words)

	MULTIDIM QC CORRESPONDENCE
		Clearly there is no Planck's constant in classical mechanics and hence what possible classical structure could give rise to this experimentally observed dicrete energy spectrum.
		Dirac proposed a possible quantization which must be familiar if you have had quantum mechanics.
		A natural question is whether Dirac quantization is the only possible quantization - this is a subtle question and mathematicians have been worrying over this for a while now.
	www.chem.cornell.edu /gse1/multidqc.html (1164 words)

	Dirac Centenary Conference (Site not responding. Last check: 2007-11-05)
		I shall argue that the resolution of these difficulties demands actual changes to the theory, and that the nature of these changes will be guided by principles coming from that other great achievement of 20th century physics: Einstein's general theory of relativity.
		Recent observations have strongly indicated that there is a small positive a cosmological constant required in Einstein's equation.
		Several cosmologists have expressed a puzzlement that the effective density that this additional term provides is comparable to the density of actual matter, a feature that can hold only in the present cosmological epoch.
	www.baylor.edu /dirac/Presenters/penrose_abstracts.htm (183 words)

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