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Topic: Lorentz equation

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Lorentz force

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	STR: A Brief History of Einstein's Special Theory of Relativity
		The transformation equations that Lorentz constructed to describe the effects of absolute motion on material objects predict the outcomes of other experiments, such as attempts to measure directly the lengths of high-velocity measuring rods and the rate at which high-velocity clocks are ticking away.
		Lorentz meant his transformation equations to be a way of describing the length contraction and time dilation in material objects with absolute motion, for that would explain the Michelson-Morley experiment, that is, why absolute motion cannot be detected by measuring the velocity of light in different directions.
		Lorentz’s explanation of length contraction assumed that the ether is totally unaffected by the motion of material objects through it, and he had no explanation of such first order effects except to state transformation equations by which one could obtain the coordinates used on the moving object from those used at absolute rest.
	www.twow.net /ObjText/OtkCaLbStrB.htm (8622 words)

	The Theory of the Electron
		Lorentz constructed a microscopic theory by using Maxwell's equations and adding to it an expression for the force which a charged particle experiences in the presence of electric and magnetic fields.
		Since this equation is almost exactly the Lorentz equation in the point particle limit, and in order to avoid confusion with Dirac's equation for the electron in relativistic quantum mechanics, this equation is referred to as the "Lorentz-Dirac Equation." In fact, the radiation term was also known long before Dirac.
		That means that the equations which permit the computation of the gravitational field from the motion of the masses also determine the motion of these masses under the influence of the gravitational fields.
	www.philsoc.org /1962Spring/1526transcript.html (6306 words)

	ricker2
		Equation 7 gives the equation for the motion of the origin of the coordinate system S’, the coordinate x’=0, in terms of the time and space coordinates of S. It represents the equation of motion obtained by an observer in S in terms of his coordinates.
		Equations 11 and 13 are interpreted in terms of the Lorentz contraction hypothesis, which explains the null result of the Michelson-Morley experiment as a physical contraction of the experimental apparatus.
		Equations 9 and 11 indicate that the observer in the opposite reference frame views the distances in the moving frame as contracted, while equations 9 and 15 give the result that they are dilated.
	www.wbabin.net /physics/ricker2.htm (13618 words)

	The Collapse of the Lorentz Transformation
		The aim of the Lorentz transformations (1) is to calculate the relationships between the lengths and time units between a frame supposedly at rest and another frame in motion, assuming that the same velocity of light is measured in both frames.
		In fact, the Lorentz transformations predicts only the transformation that gives an “average” velocity of light equal to c, which means that the velocity of light is slower in the forward direction and faster in the backward direction, in the moving frame, just as illustrated in equation 17.
		Equation 28 shows that the “average velocity of light”;, during the sum of the two light paths in the forward and backward directions, is equal to c.
	www.newtonphysics.on.ca /lorentz/lorentz.html (4352 words)

	The Lorentz Oscillator Model
		Lorentz was a late nineteenth century physicist, and quantum mechanics had not yet been discovered.
		Lorentz was not positing the existence of a physical spring connecting the electron to an atom; however, he did postulate that the force binding the two could be described by Hooke's Law, i.e.,
		Lorentz understood the origin of all the terms in eq:LE except for the damping term.
	webphysics.davidson.edu /Projects/AnAntonelli/node5.html (968 words)

	Demonstration of the Lorentz Equations without Einstein's Rrelativity Principles
		We must notice that in both cases (equations 3.5 and 3.6), the constant h refers to a measurement done in the stationary frame (meaning that the measurement is made from a frame having zero velocity and using rest units) so that the parameter h must have the subscript o.
		Equation 3.46 shows that the proper value of the velocity of the moving frame with respect to the rest frame is the same (negative) as the proper value of the velocity of the rest frame with respect to the moving frame.
		Equation 3.55 gives the relationship between the coordinate x' on the moving frame and the coordinate x, the velocity V and the time t on the rest frame.
	www.newtonphysics.on.ca /EINSTEIN/Chapter3.html (6428 words)

	EcEn 360 Tutorials-Maxwell's Law-Lorentz Force Equation (Site not responding. Last check: 2007-10-11)
		Lorentz found that a magnetic field would exert a force on an electric charge only if it was moving.
		He then found that the force on a moving charge is proportional to the strength of the magnetic field and the speed of the charge.
		The direction of the force is always perpendicular to both the magnetic field and the velocity of the charge.
	www.ee.byu.edu /em/lorentz.htm (191 words)

	Lorentz transformation - Wikipedia, the free encyclopedia
		Although physicists such as Lorentz, Larmor, and Voigt had been discussing ideas such as these for nearly 20 years by the time Einstein published his theory of relativity, their interpretation of them was couched in the concepts of classical physics.
		Larmor and Lorentz, who believed the luminiferous aether hypothesis, were seeking the transformations under which Maxwell's equations were invariant when transformed from the ether to a moving frame.
		Larmor's (1897) and Lorentz's (1899, 1904) final equations were not in the modern notation and form, but were algebraically equivalent to those published (1905) by Henri Poincaré, the French mathematician, who revised the form to make the four equations into the coherent, self-consistent whole we know today.
	en.wikipedia.org /wiki/Lorentz_transformation (1589 words)

	special relativity
		Likewise, data from particle accelerators is dependent upon these equations to yield useful information, and many unresolvable situations have occurred, unexplainable with the current Lorentz transformations and the field equations derived from them.
		The Lorentz equations for x and t (that Einstein derives from this thought experiment) are-- or should be-- equations for only one degree of relativity.
		The Lorentz equations came from precisely this sort of diagram, and the Michelson-Morley experiment accepts it as a given.
	www.wbabin.net /mathis/spec.htm (9243 words)

	special relativity
		Einstein imported an equation that Galileo would have used to find the total distance from the origin to the front of the caboose after time t, and applied it to find the length of the caboose as seen from the origin.
		The Lorentz equations came from precisely this sort of diagram or visualization, and the Michelson-Morley experiment accepts it as a given.
		The velocity that this equation yields is the velocity of the man as seen by the embankment.
	geocities.com /mileswmathis/long.html (9990 words)

	PowerPedia:Lorentz force - PESWiki
		In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field.
		The Lorentz force can act on a current carrying conductor, in this case called Laplace Force, by the interaction of the conduction electrons with the atoms of the conductor material.
		The Lorentz force equation can be written in covariant form in terms of the field strength tensor (cgs units).
	peswiki.com /index.php/PowerPedia:Lorentz_force (394 words)

	Lorenz dynamical system
		This is a numerical simulation of the Lorenz equations.
		These are a system of first order differential equations given by:
		These equations are integrated using a fourth order Runge Kutta method for the parameter values: sigma = 10.0, rho = 28.0, beta = 2.6667.
	www.geom.uiuc.edu /~worfolk/apps/Lorenz (107 words)

	Lorentz Invariance
		is a scalar, the Klein-Gordon equation is Lorentz invariant.
		Since the Klein-Gordon operator does not change under continuous Lorentz transformations, we can reason that the wave function is multiplied by a factor with absolute value of unity in these transformations.
		The pi-meson (pion) is an example of a pseudoscalar meson that obeys the Klein-Gordon equation.
	www.phys.ualberta.ca /~gingrich/phys512/latex2html2/node23.html (177 words)

	Physics 16: Lecture 1
		By the beginning of the twentieth century, it was recognized that the speed of light does not depend on the velocity of the source.
		Einstein had the genius to recognize this was the problem, and by doing away with these transformations in favor of Lorentz transformations, he was able to abolish the ether theory and give us a whole new insight into the nature of space and time.
		Imaging there is some sort of Lorentz contraction, so that the bullet is narrow as it passes through the hole.
	cmtw.harvard.edu /Courses/Phys16/l1_latex/l1_latex.html (2768 words)

	[physics/9911027] The critical manifold of the Lorentz-Dirac equation (Site not responding. Last check: 2007-10-11)
		We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena.
		The physical solutions of the Lorentz-Dirac equation lie on the critical surface.
		Thereby one obtains an effective second order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap.
	www.arxiv.org /physics/9911027 (136 words)

	Lorentz-Lorenz equation - Wikipedia, the free encyclopedia
		The Lorentz-Lorenz equation, also known as the Clausius-Mossotti equation and the Maxwell equation, relates the refractive index of a dilute gas to its temperature, pressure, and molar refractivity.
		The index of refraction n is given by
		The Lorentz-Lorenz formula is named after the Danish mathematician and scientist Ludwig Valentine Lorenz, who published it in 1869, and the Dutch physicist Hendrik Lorentz, who discovered it independently in 1870.
	en.wikipedia.org /wiki/Lorentz-Lorenz (124 words)

	Lorentz Force (Site not responding. Last check: 2007-10-11)
		The general solution of the Lorentz equation of motion contains six arbitrary integration constants.
		and can be used to eliminate time from the remaining equations.
		This means that the above equation need not be integrated, and only five integration constants are important (one of them is H).
	rkb.home.cern.ch /rkb/PH14pp/node104.html (138 words)

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