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	Lorentz Transformation Equations
		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)

	Inconsistency of Lorentz Transforms With Einstein Relativity Postulates
		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.
		Equation 14 gives the equation for the synchronization of the clocks in coordinate system S in terms of the time and space coordinates of S. It represents the equation of synchronization for an observer in S in terms of his space coordinates.
		This arises because the Lorentz and inverse Lorentz transformations are mathematically inconsistent.
	www.mrelativity.net /Papers/18/Ricker2.htm (7175 words)

	Lorentz transformation Summary
		The main objective in formulating the equations that comprise the Lorentz transformations was to preserve the velocity of light and hence the invariance of the space-time interval under all reference frames.
		The Lorentz transformations are a general group of equations that comprise a four-dimensional transformation, a transformation that involves the three-dimensions of space and time as the fourth dimension, that is satisfied by all four-vectors, a four-element vector.
		In the Galilean transformations, which predate the Lorentz transformations, it is implicitly assumed that measurements of lengths and time intervals are not affected by the relative motion of the observers, and that the speed of light may have different values depending on the observer's motion.
	www.bookrags.com /Lorentz_transformation (2963 words)

	STR: The Symmetry of the Lorentz Distortions
		And as the symmetry of the two sets of Lorentz transformation equations implies, what makes it impossible to detect absolute motion by such global experiments is that the Lorentz distortions always appear to be occurring in the other inertial frame as a function of the velocity of the two references relative to one another.
		The symmetry of Lorentz distortions is, therefore, a symmetry betwen real distortions in reference frames in absolute motion and apparent distortions in the reference frame at absolute rest, and it is a thoroughgoing symmetry, which holds for all the basic ways of measuring the other frame's clocks and measuring rods.
		Lorentz and Poincaré both expected to explain time dilation and length contraction as the result of an interaction between material objects and an ether at rest in absolute space (as if material objects were made of nothing but electrons that interact with the electromagnetic ether as they move through it).
	www.twow.net /ObjText/OtkCaLbStrD.htm (4752 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)

	chapter 1 Modern Relativity modernrelativity special general black hole mass energy Einstein wormhole time light
		Lorentz was one such person who empirically derived the Lorentz transformation equations by introducing length contractions and time dilations into a transformation which would leave the speed c invariant to frame so that one could not use it to determine a speed with respect to the medium.
		What actually distinguishes Lorentz transformations and special relativistic physics from Galilean transformations and Newtonian physics is that in the Lorentz transformations the invariant speed c is finite.
		This set of transformation equations results in Lorentz transformation on the way out as well as on the way in and gives the solution that the ship clocks read less time upon their arrival back at Earth.
	www.geocities.com /zcphysicsms/chap1.htm (2990 words)

	The expanding sphere of light
		The absence of vitally important details in the formulation of the special theory of relativity is shown to result in the conclusions that there cannot be any physical observers present in that theory and that the light used in Einstein’s derivation of the special theory cannot be the light of common scientific experience.
		In Lorentz’s case by an axiomatic statement to do with forces, and in Einstein’s by a statement that is so vague that it amounts to the assumption that the neutron displays charge-like behaviour, a seemingly ridiculous statement about a neutral particle.
		The introduction of Maxwell’s equations, given this experimental scenario, would have necessitated a direct causal connection between a neutral mass particle that is supposed not to radiate, and a charged particle that does radiate.
	www.wbabin.net /physics/max2.htm (3784 words)

	Dr. George J. Marklin
		The Lorentz transformation will be shown to follow from the contraction of the length unit, the dilation of the time unit, and the adoption of local time zones according to the Einstein synchronization convention.
		Equation (12) can be put into a more familiar form by using (8) to replace the x' term and then simplifying, to get: t' = g (t - u x/ c^2) (13) The symmetrical appearance of (8) and (13) is related to an important property of the LTE's called the group property.
		Equations (16) through (18) give the expressions for the invariant position, time and velocity in terms of relative coordinates and they are all Lorentz invariant.
	perso.orange.fr /mluttgens/marklin6.htm (1949 words)

	metric2lorentz.nb
		To get the metric equation, one simply adds in a "side" of length icdt, where c is the speed of light, dt is a time interval measured with respect to the same "map frame of motion" whose yardsticks measured the sides (e.g.
		The equations for time-like intervals in the frame of a moving observer are quite important.
		The resulting "inverse Lorentz transform" equations are c dt = γ (c dt' + β dx'), and dx = γ (β c dt' + dx').
	www.umsl.edu /~fraundor/anyspeed/metric2lorentz/index.html (800 words)

	Special relativity:lortra
		Transformations are mathematical equations that allow us to transform from one coordinate system to another.
		The motivation for this, once again, is to mix the x and t transformations in such a way that the undesirable terms cancel in the equation of the spherical wave front in the unprimed coordinate system.
		The form of the equation describing the wave front is the same in all frames moving with uniform relative velocity.
	library.thinkquest.org /C005644/lortra.htm (848 words)

	Physics Myths and physics facts
		Fourier Transformation/ Coherence: The Fourier theorem is frequently used to associate a certain time dependence of a physical quantity with the corresponding frequency spectrum.
		Saha-Equation: The Saha equation describes the ratio of different stages of ionization of an atom under the assumption of LTE and, like the latter, suffers therefore from the limitation that it is strictly only applicable if elastic collisions are responsible for establishing the energetic distribution of particles.
		Special Relativity: The special theory of relativity, as developed by Einstein, is directly based on the Lorentz Transformation formula and attempts to transfer the 'equation of motion' for light signals to the space- time coordinates of moving material bodies.
	www.physicsmyths.org.uk (8102 words)

	Lorentz Transformation
		Deriving time dilation from the Lorentz transform is pretty simple--just pick two events in Alice's system separated by a time interval of t, then figure out what the time interval between the two event's would be in Bob's system.
		Lorentz contraction is a little more subtle, because the different coordinate systems disagree about simultaneity (two events that happen at the same time-coordinate in one happen at different time-coordinates in the other), and "length" is about looking at the distance between the front and back of an object at a single moment.
		Remember that in the Lorentz transform equations given above, the "v" refers to the velocity of the origin of the x'-y'-z' axes as seen in the x-y-z-t system.
	www.physicsforums.com /showthread.php?t=99910 (2685 words)

	Einstein's Mistake? Re: Relativity Theories (Site not responding. Last check: 2007-10-28)
		If classical mechanics transformation equations had been used instead of Lorentz’s, the length of the rod would have been independent of the relative velocity, and the length of the rod would not have been shorter when in motion than when at rest.
		By using the Lorentz transformation equation for time, he showed that the greater the relative velocity of one body or coordinate system to another, the slower its time is with respect to it.
		However, the Lorentz transformation time equation is based upon the time of the observance of a phenomenon, not on the time of its occurrence.
	members.aol.com /rhrrr/einstein.htm (8781 words)

	New Transformation Equations and the Electric Field Four-vector
		The Lorentz transformation equations are replaced by a new set of transformation equations, the electric field is described by a four-vector, and the analog of Maxwell's electromagnetic field tensor contains nonzero terms along the main diagonal, causing any relation that contains its components to include extra terms.
		Since these equations are used to determine the covariance of the laws of physics, any change in their form requires a change in the form and scope of these laws.
		Equations (12.5) include terms related to the time component of the electric field four-vector, unlike the Lorentz equations.
	www.softcom.net /users/der555/full.html (3920 words)

	Special Relativity (Site not responding. Last check: 2007-10-28)
		In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation.
		The Lorentz transformation equations applied to the laws of physics cannot be used unless and until it has been established that K and K' are different energies, i.e., a K is more at rest than a K'.
		Thus, the meter stick of K' obtained from K in accordance with the Lorentz transformation equations would be 1 meter long in K' - as measured in K' - have the same number of atoms - but its atoms would be expanded because of greater energy.
	home.att.net /~j.neergaard/SR/SR.html (1424 words)

	Lorentz Derivation
		These equations are limited, however, since they apply only to a particular situation: one in which both events occur at the same place (x’=0) in the spaceship.
		Under these circumstances, it is impossible to satisfy equation 7.0 with a single choice of values of B and G unless these values make the coefficient of x’t’ on the left side of equation 7.0 vanish as it does on the right:
		In summary, the Lorentz transformation equations rest fundamentally on the required linearity of the transformation and on the invariance of the spacetime interval.
	skybooksusa.com /time-travel/physics/lorentz1.htm (557 words)

	SPECIAL RELATIVITY
		Equations (30) and (31) are the heart of the relativistic kinematics of elementary particles.
		The equation for m allows the mass of a particle to be obtained (and the particle identified) if E and p have been determined for it by, say, using energy and momentum conservation in a collision where all but one of the particles are known.
		Show that equation (10) may be obtained by considering the motion of the origin of the S frame, rather than the S' frame.
	www.physics.gatech.edu /people/faculty/gatland/relativity.html (4072 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)

	A Reform-minded Seventh-day Adventist forum - View topic - Must the Lorentz Transformation Equations be Linear?
		The Lorentz transformation then couldn't possibly be the correct rule to express how events (x, t) get mapped into events (x', t') in moving frames of reference.
		The end result is a group of nonlinear transformations that obviously contain the same physical content as the original Lorentz transformations.
		The point of the Lorentz transformation is to give a rule expressing how events (x,y,z,t) in one frame of reference translate into events (x',y',z',t') for moving frames of reference.
	www.everythingimportant.org /viewtopic.php?t=221 (2066 words)

	Extended Maxwell's Equations: compact formulations in physics
		Maxwell's equations as a subset of the relativistic quantum unified equation
		of Maxwell's equations (1a), (2a), (3a) and (4a).
		in the Maxwell equations (1a) or (1) and (2a) or (2)
	www.wolfram-stanek.de /maxwell_equations.htm (2516 words)

	chapter 2 definition Modern Relativity modernrelativity special black hole mass energy Einstein time Schwarzschild light
		Therefor when modeling the general laws of physics with equations we must use equations that do not change their basic form when transformed from one frame to another.
		If such an equation does transforms like this then it is not one of the fundamental equations of physics.
		Notice that since we model the laws of physics with tensor equations whose expressions are tensors defined by the transformation properties of the coordinates and since the Lorentz coordinate transformations are one to one invertable, there can be no true paradox's in special relativity.
	www.geocities.com /zcphysicsms/chap2.htm (1419 words)

	Lorentz Transformation (Site not responding. Last check: 2007-10-28)
		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)

	[No title] (Site not responding. Last check: 2007-10-28)
		According to the Lorentz transformation equations referred to a system moving with respect to the lever system, the couples are no longer equal so the lever should be seen to rotate, which is, of course, absurd.
		The Lorentz transformations have proved not to be the necessary formulation of the principle of relativity, as Poincaré believed, since physical interpretations of them have contradicted the principle.
		But the Lorentz transformation equations were first derived and used by Voigt in 1887 in connection with elasticity, and later, again by Lorentz in connection with the electron theory of matter, and do not depend on 'relativity' for their derivation.
	homepage.ntlworld.com /academ/whatswrongwithrelativity.html (4975 words)

	Direction of electric and magnetic fields in electromagnetic waves - Advanced Physics Forums (Site not responding. Last check: 2007-10-28)
		I would say that you should consider the transformation of the coordinates as well (and possibly what you mean by \"perpendicular\").
		Sure, when you Lorentz transform the field components, things get shifted into different directions, but I\'m suspicious of the arguement of the sinusoid picking up an x term.
		In other words, the field may still be perpendicular to the direction of the wave, but the direction of the field as well as the direction of the wave both change in a Lorentz transformation.
	www.advancedphysics.org /forum/showthread.php?t=281 (477 words)

	Einstein Light: module 4
		For relativity, we need new transform equations because, as we have seen in Module 3, when v becomes comparable with the speed of light, Zoe and Jasper disagree on time and length.
		Now that we have the transformation equations, that is just a matter of taking derivatives.
		So the relativistic equations are consistent with our common sense, even at 300 kilometres per second, which is much faster than everyday objects (1000 times faster than an airliner).
	www.phys.unsw.edu.au /einsteinlight/jw/module4_Lorentz_transforms.htm (1601 words)

	Null Coordinates
		The singularity of the Lorentz transformation is most clearly expressed in terms of the underlying Minkowski pseudo-metric. Recall that the invariant space time interval dt between the events (t,x) and (t+dt, x+dx) is given by
		Pictorially, the locus of points whose squared distance from the origin is ±1 consists of the two hyperbolas labeled +1 and -1 in the figure below.
		- 1 = cos(2q), and the equation of the hyperbola is R
	www.mathpages.com /rr/s1-09/1-09.htm (964 words)

	Incompatibility Between the Lorentz Transformation Equations and General Relativity
		The Lorentz transformation equations exhibit serious problems when we try to reconcile them with General Relativity.
		And as it approaches the speed of light, everything in it, including the container of gas and the gas in the container, should increase in mass according to the Lorentz transformation equations.
		Of course to the people in the spaceship, who remain stationary with respect to the gas container, the dimensions of the container will not have changed one bit.
	homepage.mac.com /ardeshir/LorentzTransformationProbs.html (789 words)

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