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Topic: Lorentz transformation

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Lorentz transformation

Lorentz group

Special theory of relativity

Proper time

Lorentz factor

Special relativity

Frame of reference

Inertial frame of reference

Relativity

Minkowski space

Length contraction

Time dilation

Hendrik Lorentz

Theory of relativity

General relativity

	Lorentz transformation - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-11-07)
		The Lorentz transformation is a group transformation that is used to transform the space and time coordinates (or in general any four-vector) of one inertial reference frame, $A$ , into those of another one, $A'$ , with $A'$ traveling at a relative speed of ${v}$ to $A$ along the x-axis.
		The Lorentz transformations were published in 1897 and 1900 by Joseph Larmor and by Hendrik Lorentz in 1899 and 1904.
		Larmor and Lorentz believed the luminiferous aether hypothesis; it was Albert Einstein who developed the theory of relativity as a foundation for the universal application of the Lorentz transformations.
	www.arikah.net /encyclopedia/Lorentz_Boost (1183 words)

	Lorentz group - Wikipedia, the free encyclopedia
		Lorentz transformations are examples of linear transformations; general isometries of Minkowski spacetime are affine transformations.
		In the article on Möbius transformations, it is explained how this classification arises by considering the fixed points of Möbius transformations in their action on the Riemann sphere, which corresponds here to null eigenspaces of restricted Lorentz transformations in their action on Minkowski spacetime.
		The Möbius transformations are precisely the conformal transformations of the Riemann sphere (or celestial sphere).
	en.wikipedia.org /wiki/Lorentz_group (3542 words)

	Lorentz transformation: Definition and Links by Encyclopedian.com - All about Lorentz transformation (Site not responding. Last check: 2007-11-07)
		The Lorentz transformation, named after its discoverer, a Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, that has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics.
		The Lorentz transformation is a group transformation that is used to transform the space and time coordinates (or in general any four-vector) of one inertial reference frame, $S$ , into those of another one, $S'$ , with $S'$ traveling at a relative speed of ${\mathbf u}$ to $S$ .
		Lorentz believed the luminiferous aether hypothesis; it was Albert Einstein who developed the theory of relativity to provide a proper foundation for its application.
	www.encyclopedian.com /lo/Lorentz-transformation.html (449 words)

	Lorentz transformation - Wikipedia, the free encyclopedia
		The transformation describes how space and time coordinates are related as measured by observers in different inertial reference frames and are named after the Dutch physicist and mathematician Hendrik Lorentz (1853-1928).
		The composition of two Lorentz transformations is a Lorentz transformation and the set of all Lorentz transformations with the operation of composition forms a gorup called the Lorentz group.
		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 (1221 words)

	Lorentz transformation equations
		The Lorentz transformation is a set of equations that take Special relativity into account when converting the location of an event in one system of coordinates to another system of coordinates that is moving at a constant velocity with respect to the first.
		An equation which remains identical under a Lorentz transformation is known as Lorentz invariant.
		Although the equations are associated with special relativity, they were developed before special relativity and were proposed by Lorentz in 1904 as a means of explaining the Michelson-Morley experiment through contraction of lengths.
	www.ebroadcast.com.au /lookup/encyclopedia/lo/Lorentz_transformation_equations.html (218 words)

	Wikiversity:Special Relativity - Wikibooks, collection of open-content textbooks
		Lorentz suggested an aether theory in which objects and observers travelling with respect to a stationary aether underwent a physical shortening (Lorentz-Fitzgerald contraction) and a change in temporal rate (time dilation).
		While Lorentz suggested the Lorentz transformation equations, Einstein's contribution was, inter alia, to derive these equations from a more fundamental theory, which theory did not require the presence of an aether.
		The Lorentz transformation describes the way a vector in spacetime as seen by an observer O1 changes when it is seen by an observer O2 in a different inertial system.
	en.wikibooks.org /wiki/Wikiversity:Special_Relativity (3069 words)

	ModPhy1
		By applying this transformation to every event of interest, it is possible to transform the whole time-varying three-dimensional world perceived by one observer into the time-varying three-dimensional world perceived by another observer.
		By the way, notice that the Lorentz transformation equations reduce to the classical Galilean transformation equations in the limit of small velocities exactly as required by the correspondence principle.
		Derive the inverse Lorentz transformation equations by solving the Lorentz transformation equations algebraically for the respective unprimed coordinates.
	physics.tamuk.edu /~hewett/ModPhy1/Unit1/SpecialRelativity/RelativeView/LorentzTransform/LorentzTransform.html (1114 words)

	Hendrik A. Lorentz - Biography
		From Lorentz stems the conception of the electron; his view that his minute, electrically charged particle plays a rôle during electromagnetic phenomena in ponderable matter made it possible to apply the molecular theory to the theory of electricity, and to explain the behaviour of light waves passing through moving, transparent bodies.
		The so-called Lorentz transformation (1904) was based on the fact that electromagnetic forces between charges are subject to slight alterations due to their motion, resulting in a minute contraction in the size of moving bodies.
		It may well be said that Lorentz was regarded by all theoretical physicists as the world's leading spirit, who completed what was left unfinished by his predecessors and prepared the ground for the fruitful reception of the new ideas based on the quantum theory.
	nobelprize.org /physics/laureates/1902/lorentz-bio.html (1070 words)

	Chapter 11. The Lorentz Transformation. Einstein, Albert. 1920. Relativity: The Special and General Theory
		This system of equations is often termed the “Galilei transformation.” The Galilei transformation can be obtained from the Lorentz transformation by substituting an infinitely large value for the velocity of light c in the latter transformation.
		Aided by the following illustration, we can readily see that, in accordance with the Lorentz transformation, the law of the transmission of light in vacuo is satisfied both for the reference-body K and for the reference-body K'.
		Of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.
	www.bartleby.com /173/11.html (1012 words)

	Lorentz transformation - Wikipedia
		The group transformation known as the Lorentz transformation, after physicist H.
		The Lorentz transformation, as a set of equations governing two reference frames in space-time, S and S', with S' traveling at a relative speed of u to S; an event has space-time coordinates of (x,y,z,t) in S and (x',y',z',t') in S':
		In cases where u does not point along the x-axis of S, it is generally easier to perform a rotation so that u does point along the x-axis of S than to bother with the general case of the Lorentz transformation.
	nostalgia.wikipedia.org /wiki/Lorentz_invariance (233 words)

	Appendix 1. Simple Derivation of the Lorentz Transformation. Einstein, Albert. 1920. Relativity: The Special and ... (Site not responding. Last check: 2007-11-07)
		Thus we have obtained the Lorentz transformation for events on the x-axis.
		The Lorentz transformation represented by (8) and (9) still requires to be generalised.
		from Lorentz transformations in the special sense and from purely spatial transformations, which corresponds to the replacement of the rectangular co-ordinate system by a new system with its axes pointing in other directions.
	www.bartleby.com /173/a1.html (927 words)

	A Question of Time: The Lorentz Transformation
		In essence, Lorentz’s argument, using the analogy of the plane trip, intends to shorten the distance between SF and NY to 2880 miles.
		Lorentz, in 1904, based his derivation of the LT and the gamma factor on the thinking that prevailed at the time of the Michelson-Morely (M&M) experiment.
		The Lorentz transform, properly derived, using Lorentz’s assumptions of the aether as the carrier of light, should end up with the square of gamma as the correct formula for one way shrinkage of time to account for the M&M experiment.
	www.aquestionoftime.com /lorentz.htm (2199 words)

	Lorentz and AD transformation
		If Lorentz’s transform from T1 to T3 forms a “group," it also forms a “group” in AD, even though in AD the concept is physically irrelevant, because the concept of groups is only a mathematical concept unrelated to any physical phenomenon.
		When Carezani found the physical contradiction in Lorentz’s transform, he simultaneously discovered that to achieve relativity, it is not necessary to “introduce” two systems of coordinates to observe a phenomenon, even though he respected the Lorentz mathematical transformation for ONE Observer (O’) that sees the object's (wave front) motion from position X to X’(Fig 2).
		Equation (28) is equivalent to Lorentz equation (6) and equation (29) to equation (7).
	www.autodynamicsuk.org /AutodynamicsL-and-A-am3.htm (3232 words)

	The Lorentz Transformation
		LORENTZ RULE 1:(invariance of lateral distances) In two inertial frames in relative motion, the distance between any two given points measured in a direction perpendicular to the relative motion will be the same for observers in both frames.
		LORENTZ RULE 2B:(Lorentz-Fitzgerald contraction) An object moving relative to some observer appears to that observer to be shorter in the direction of relative motion than it does to an observer at rest in its inertial frame, the moving length being equal to the stationary length divided by the Lorentz factor between the two inertial frames.
		Lorentz Rule 2B does not appear in those equations directly because, although we made it part of the deductive chain that leads to the Lorentz Transformation, it is not strictly a part of it.
	www.bado-shanai.net /Map%20of%20Physics/moplortrans.htm (3308 words)

	Relativity
		Transformations relate quantities in sytems that are in relative motion.
		A peculiar effect of Einstein's postulates is the transformation that connects space-time in two inertial frames.
		Directly from Lorentz transformations, one obtains the concepts of length contraction, time dilation, relativistic Doppler effect, and relativistic addition of velocities.
	nobelprize.org /physics/educational/relativity/transformations-1.html (125 words)

	Mobius Transformations and The Night Sky
		This leads to the remarkable fact that the combined effect of any proper orthochronous (and homogeneous) Lorentz transformation on the incidence angles of light rays at a point corresponds precisely to the effect of a particular LFT on the Riemann sphere via ordinary stereographic projection from the extended complex plane.
		If we apply a Lorentz transformation of the form (1) to this observer, specified by the four complex coefficients a,b,c,d, the resulting change in the directions of the incoming rays of light is given exactly by applying the LFT (also known as a Mobius transformation)
		This is certainly a proper orthochronous Lorentz transformation, because the determinant is +1 and the coefficient of t is positive.
	www.mathpages.com /rr/s2-06/2-06.htm (1843 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.
		After a century, it is astonishing to discover that the Lorentz transformation, that requires a distortion between the X and Y axis, does not lead to a constant (one-way) velocity of light when "measured" in the moving frame.
	www.newtonphysics.on.ca /lorentz/lorentz.html (4367 words)

	New Transformation Equations and the Electric Field Four-vector
		A four-dimensional orthogonal transformation matrix is used as the starting point for the replacement of the Lorentz transformation equations, allowing the electric field to be described by a four-vector and forcing Maxwell's equations to include extra terms.
		Lorentz introduced a set of coordinate transformation equations that revolutionized our perception of space and time.
		Contrary to the Lorentz transformation, there is a rotation of the y'-z' plane relative to the y-z plane.
	www.softcom.net /users/der555/original.html (1304 words)

	The Lorentz Transformation
		This means that matter waves should also undergo the Doppler effect and the Lorentz transformation.
		Lorentz was not aware of the wave nature of matter, and so he could not explain why such a contraction should occur.
		Lorentz also showed that clocks should slow down to half of their original rate, according to the same g value.
	www.glafreniere.com /sa_Lorentz.htm (409 words)

	An Extension of the Concept of Inertial Frame and of Lorentz Transformation -- Kerner 73 (5): 1418 -- Proceedings of ...
		It is shown how particular kinds of fractional-linear (or projective) transformations generalize the notion of inertial frame in that they ensure that free-particle motion goes over into free-particle motion.
		A ten-parameter group of such transformations is produced which generalize Lorentz transformations, and which involve besides c (velocity of light) a new fundamental length b; they encompass the ordinary Lorentz group in the limit that b becomes infinite.
		These extended Lorentz transformations are most simply understood as a type of rotation in the space of homogeneous coordinates, a rotation that unifies 3-space rotations, frame-shifts to moving frames, and space- as well as time-translations.
	www.pnas.org /cgi/content/abstract/73/5/1418 (215 words)

	[No title]
		In 1919, Lorentz was appointed Chairman of the Committee.
		Lorentz based his transformation on the fact that electromagnetic forces between charges are subject to slight alterations due to their motion.
		In mathematics, a transformation is considered the replacement of variables in an algebraic expression by their values in terms of another set of variables or a mapping of one space onto another or onto itself.
	www.saintjoe.edu /~karend/m441/SteveFinalPaper.doc (3714 words)

	MATHEMATICAL INVALIDITY OF THE LORENTZ TRANSFORMATION EQUATIONS
		The Lorentz transformation equations were originally devised to ensure that the speed of light remains a constant for all observers in all inertial frames, regardless of their relative rectilinear motions.
		Now remember that the Lorentz transformation equations require that in the frame of the lady in the capsule, the spaceship will have contracted in length by a factor of : i.e., to the lady in the capsule, the spaceship should appear to be five times shorter than it would be if it were at rest.
		Now according to the Lorentz Transformation equations, time should be running slower on board the spaceship by a factor of , which as we said, happens to be 5.0.
	homepage.mac.com /ardeshir/LorentzTransformation.html (1506 words)

	Can You See the Lorentz-Fitzgerald Contraction?
		The above article on Penrose-Terrell rotations mentions in passing the fact that every Lorentz transformations act on the celestial sphere the same way that the corresponding Moebius transformation acts on the Riemann sphere, but it is not very explicit.
		To understand the how the appearance of the night sky (apparent positions of stars and galaxies on the celestial sphere) is altered by a Lorentz transformation, we must look at null lines (one dimensional subspaces spanned by null vectors).
		Lorentz transformations may be classified into four types according to their geometric effect on the night sky:
	math.ucr.edu /home/baez/physics/Relativity/SR/penrose.html (1653 words)

	Physics: Hendrik Lorentz: Explaining the Lorentz Transformation
		Lorentz imagined that the ether exists throughout Space and that fields existed as a 'state' of this ether.
		It is this change in velocity, ellipsoidal shape and wavelength of the In-wave which causes the apparent motion of the wave-center and the Lorentz Transformations.
		This is a general principle, and is the foundation of Einstein's principle of special relativity and thus his postulate that the velocity of light is always measured to be the same.
	www.spaceandmotion.com /Physics-Hendrik-Lorentz.htm (2460 words)

	Lorentz Transformation Equations (Site not responding. Last check: 2007-11-07)
		In the introduction I mentioned that classical mechanics required the use of Galilean Transformation equations to transform the results in one inertial frame of reference into another inertial frame.
		However, as was already shown, this transformation becomes less and less accurate as the velocity of the body approaches the speed of light.
		The equations for transforming into a moving frame of reference (x prime, y prime, z prime, and t prime coordinates) are on the left.
	ffden-2.phys.uaf.edu /212_fall2003.web.dir/Eddie_Trochim/Lorentztransform.htm (393 words)

	Lorentz Transformation (Site not responding. Last check: 2007-11-07)
		The Lorentz transformation is powerful; it brings the technical ability to transform coordinates from frame to frame.
		The equations for this transformation, known as the Lorentz transformation equations, were adopted by Einstein, but he gave them an entirely new interpretation.
		According to this relativistic transformation, not only would lengths in the line of a moving object be altered but also time and mass.
	skybooksusa.com /time-travel/physics/lorentz.htm (244 words)

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