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Topic: Galilean transformation


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  Lorentz transformation - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-07)
Under these transformations, the speed of light is the same in all reference frames, as postulated by special relativity.
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 {v} to S along the x-axis.
The Lorentz transformations were first published in 1904, but their formalism was at the time imperfect.
www.newlenox.us /project/wikipedia/index.php/Lorentz_transformation_equations   (792 words)

  
 Galilean transformation - Wikipedia, the free encyclopedia
The Galilean transformation is used to transform between the coordinates of two coordinate systems in a constant relative motion in Newtonian physics.
Unlike the Galilean transformation, the relativistic Lorentz transformation can be shown to apply at all velocities so far measured, and the Galilean transformation can be regarded as a low-velocity approximation to the Lorentz transformation.
Under the Erlangen program, the space-time (no longer spacetime) of nonrelativistic physics is described by the symmetry group generated by Galilean transformations, spatial and time translations and rotations.
en.wikipedia.org /wiki/Galilean_transformation   (368 words)

  
 Lorentz transformation - Wikipedia, the free encyclopedia
This is in contrast to the more intuitive Galilean transformation, which is sufficient at non-relativistic speeds (i.e.
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 v to S along the x-axis.
Beneath the Foundations of Spacetime The Lorentz transformation can be derived with moving rulers in such a way that the astonishing connection between space and time can be clearly understood.
en.wikipedia.org /wiki/Lorentz_transformation   (705 words)

  
 Invariant Galilean Transformations (FAQ) On All Laws
In particular, the Principle of Relativity is embodied in the form of the Galilean transformation, which relates the original x, y, z, t to x', y', z', t' by the transform equations x'=x-vt, y'=y, z'=z, t'=t in the simplified case where attention is focused only on transforming the x-axis, and not y and z.
As the transform equations say, the relationship of t', x' to t, x is based on the relative velocity between the two systems, but neither the original (eq-99) equation nor the M observer equation is about a relationship between coordinate systems or observers.
Their process, which says (x'+vt') is the transform of x, says that (x'+vt') is the moving system location of x, but it can't be because x is moving further in the negative direction from the moving viewpoint.
www.cs.uu.nl /wais/html/na-dir/physics-faq/criticism/galilean-invariance.html   (6572 words)

  
 Math Forum - Ask Dr. Math
You're quite right: the Galilean transformation is a simple thing expressed in complex (or at least unfamiliar) terminology, and it doesn't work right for frames traveling near the speed of light.
The Galilean transformation, underneath its disguise, is old, familiar stuff, _not_ relativistic physics - which is why it doesn't work right (in relativistic terms) near the speed of light.
The Galilean transformation is: (1) x' = x - vt (2) t' = t where v is the relative speed between two reference frames (x, t) and (x',t').
mathforum.org /library/drmath/view/51487.html   (1058 words)

  
 Science Fair Projects - Principle of relativity
In Galilean relativity, reference frames are related to each other in an intuitive way: to transform the velocity of an object from one frame to another, the vector representing the velocity of the object is added to the vector representing the velocity difference between the two reference frames.
Einstein saw, as did his contemporaries, that if one assumes that both the Maxwell equations are valid, and that Galilean transformation is the appropriate transformation, then it should be possible to measure velocity absolutely.
Einstein saw that if one assumes that the Lorentz transformations are the appropriate transformations for transforming between inertial reference frames, then that constitutes a principle of relativity that is compatible with the Maxwell equations.
www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Galilean-Newtonian_relativity   (944 words)

  
 Galilean transformation -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07)
The Galilean transformation is used to transform between the coordinates of two coordinate systems in constant relative motion in (Click link for more info and facts about Newtonian physics) Newtonian physics.
The equations below, although apparently obvious, break down at speeds that approach the (The speed at which light travels in a vacuum; the constancy and universality of the speed of light is recognized by defining it to be exactly 299,792,458 meters per second) speed of light.
Unlike the Galilean transformation, the (Click link for more info and facts about relativistic) relativistic (Click link for more info and facts about Lorentz transformation) Lorentz transformation can be shown to apply at all velocities so far measured, and the Galilean transformation can be regarded as a low-velocity approximation to the Lorentz transformation.
www.absoluteastronomy.com /encyclopedia/G/Ga/Galilean_transformation.htm   (521 words)

  
 Comments on Problem Set #4   (Site not responding. Last check: 2007-11-07)
The principle of Galilean relativity states that the laws of motion are the same as viewed from any inertial frame of reference.
The Galilean transformation has the property that when it is applied to Newton's laws of motion, the result is unchanged (that is, you get Newton's laws of motion).
The Galilean transformation (referred to as the ``classical transformation'' in Einstein and Infeld) turns out to be incompatible with the postulates of Special Relativity.
www.physics.nyu.edu /courses/V85.0020/node83.html   (1534 words)

  
 Staircase Wit
In addition, we notice that the rotational transformations maintain the orthogonality of the coordinate axes, whereas the lack of an invariant measure for the Galilean transformations prevents us from even assigning a definite meaning to “orthogonality” between the time and space coordinates.
Since the velocity transformations leave the laws of physics unchanged, Minkowski reasoned, they ought to correspond to some invariant physical quantity, and their determinants ought to be unity.
It is certainly true that we are led toward the Lorentz transformations as soon as we consider the group of velocity transformations and attempt to identify a physically meaningful invariant corresponding to these transformations.
www.mathpages.com /rr/s1-07/1-07.htm   (3507 words)

  
 Notes on Relativity
A coordinate transformation is the set of equations for converting the space and time coordinates of an event as measured in one reference frame to the coordinates measured in another frame.
Galilean transformation is implied by the writings of Galileo, although he did not write the equations.
The Lorentz transformation is equivalent to length contraction and time dilation (which had been proposed by Fitzgerald and by Lorentz earlier).
phys-astro.sonoma.edu /people/faculty/tenn/P314/RelativityNotes.html   (421 words)

  
 Newtonian physics - Wikipedia
In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute in all reference frames.
The space-time coordinates of an event in Galilean-Newtonian relativity are governed by the set of formulas which defines a group transformation known as the Galilean transformation:
The set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform).
nostalgia.wikipedia.org /wiki/Newtonian_physics   (398 words)

  
 The Theory of Relativity: An Error of the Transformation of Coordinates *
the principle of existence and of transformation of coordinates: there are no coordinates and no transformation of coordinates in general, and there exist the coordinates and transformation of the coordinates of the object only.
The Galilean transformation relates the coordinates of the point $M$ in the systems $S$ and $E$: $x_{M} = Vt + x^{\prime }_{M}$ where $V$ is the velocity of motion of the system $E$ relative to the system $S$ in the positive direction of the axis $Ox$ ($V < c$).
Introduction (insertion) of the Galilean transformation into the equation for the front of the light beam means equality between the coordinates:
wbabin.net /physics/theoryrel.htm   (597 words)

  
 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.
If c is taken to be infinite, the Galilean transformation is recovered, such that it may be indentified as a limiting case.
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.
www.city-search.org /lo/lorentz-transformation.html   (882 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)

  
 Encyclopedia: Galilean-transformation   (Site not responding. Last check: 2007-11-07)
The Galilean symmetries (interpreted as active transformations): An active transformation is one which actually changes the physical state of a system and makes sense even in the absence of a coordinate system whereas a passive transformation is merely a change in the coordinate system of no physical significance.
In mathematics, a Lie algebra is an algebraic structure whose main use lies in studying geometric objects such as Lie groups and differentiable manifolds.
representation theory of the Galilean group, Poincaré group In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin as follows: The spacetime symmetry group of nonrelativistic mechanics is the Galilean group.
www.nationmaster.com /encyclopedia/Galilean_transformation   (1381 words)

  
 Invariant Galilean Transformations (FAQ) On All Laws   (Site not responding. Last check: 2007-11-07)
Below, in the sci.math subject, we see that all sci.math respondents agree with the basic "controversial" position of this faq: every coordinate is transformed, whether a supposed "constant" or not.
What does sci.math have to say about x0'=x0-vt? The crackpots' positions/arguments were put to sci.math in such a way that at least two or three who posted re- sponses thought it was your faq-er who was on the idiot's side of the questions.
A linear transformation, A, on the space is a method of corr- esponding to each vector of the space another vector of the space such that for any vectors U and V, and any scalars a and b, A(aU+bV) = aAU + bAV.
omicron.felk.cvut.cz /FAQ/articles/a3503.html   (6587 words)

  
 ModPhy1
Therefore, the Lorentz transformation equations must reduce to the following Galilean transformation equations in the limit of small velocities.
The Galilean transformation equations and their implications are discussed in greater detail on page 4 in
principle of relativity.) Hint: The Galilean transformations pertain to two arbitrary inertial frames, so any law that is invariant under a Galilean transformation takes on the same form in all inertial frames.
physics.tamuk.edu /~hewett/ModPhy1/Unit1/SpecialRelativity/RelativeView/LorentzTransform/GalileanTransform/GalileanTransform.html   (491 words)

  
 The Ultimate Galilean invariance Dog Breeds Information Guide and Reference
Galilean invariance is a principle which states that the fundamental laws of physics are the same in all inertial (uniform-velocity) frames of reference.
Specifically, the term Galilean invariance today usually refers to this principle as applied to Newtonian mechanics, under which all lengths and times remain unaffected by a change of velocity, which is described mathematically by a Galilean transformation.
At the low relative velocities characteristic of everyday life, Lorentz invariance and Galilean invariance are nearly the same, but for relative velocities close to that of light they are very different.
www.dogluvers.com /dog_breeds/Galilean_invariance   (197 words)

  
 Galilean transformation: Definition and Links by Encyclopedian.com - All about Galilean transformation   (Site not responding. Last check: 2007-11-07)
Galilean transformation: Definition and Links by Encyclopedian.com - All about Galilean transformation
For example, if the frames in Fig.11.1 were exactly lined up at t = t' = 0, then the coordinate of the explosion in frame O would be equal to the coordinate x' as measured by O' plus the distance that the frames had moved relative to each other in that time interval:
Eqs[11.1] and [11.2] constitute the so-called Galilean transformations relating coordinates as measured in two different frames.
www.encyclopedian.com /ga/Galilean-transformation.html   (931 words)

  
 [No title]
Galilean transformations Although we still accept MaxwellÕs equations today in the same form as in the 19th century, their interpretation is completely different.
 transforms as a contravariant 4-vector  transforms as a covariant 4-vector.
This is one reason for discarding the Lorentz transformation with F = -1, considered earlier, because such a transformation on the light cone would take us from a timelike ordering of events to a spacelike one, or vice versa.
www3.baylor.edu /Physics/open_text/classical/ch13.2003.doc   (4041 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)

  
 [No title]   (Site not responding. Last check: 2007-11-07)
Galilean transformation (Common sense)  2.4 Consequences of Einstein’s Postulates 2.4.1 The relativity of time We consider a timing device which ticktack by light flashed from a bulb and reflected by a mirror.
Thus, transforming to the reference frame of O’,  EMBED Equation.3  Where x,y,z are the coordinate at the reference frame of O, and x’,y’,z’ are the coordinate at reference frame of O’.
The equation of the Lorentz transformation, derived from these treatments, are  EMBED Equation.3  Where x is the rest (proper) distance measured by O at the reference frame of O, and x’ is the distance measured by O’ at the reference frame of O’.
vega.icu.ac.kr /~ois/download/ICE2251/ICE2251_2.doc   (1992 words)

  
 Einstein's Theory of Relativity - Scientific Theory or Illusion?
A similar transformation can also be derived when the axes of these two systems are at a certain angle, that is when they are not parallel.
The above mentioned transformation is called Galilean transformation in honor of the founder of mechanics.
So, at the transformation of coordinates, the equation for the inertial law has remained the same, which means that with Galilean transformation is maintained the invariability of the equation for acceleration in the case of an inertial system.
users.net.yu /~mrp/chapter2.html   (365 words)

  
 Special Relativity Explained by Diagrams   (Site not responding. Last check: 2007-11-07)
In the first section, we present the Galilean relativity and the associated space-time diagrams to illustrate various events.
The position of the light wave front along the x axis in the K-frame is given by x=ct, where c is the speed of light in this frame.
K' moves at constant speed (v) along the x axis relative to the K-frame, and t = t' = 0 when O' coincides with O and event E is happening somewhere in space at a given moment in time.
www.colvir.net /prof/richard.beauchamp/rel-an/rela.htm   (1588 words)

  
 Is a Crystal-clear Theory Preferable to Dogmatic Riddles?
Essentially ==he takes Galilean transformations, and then does a change of ==variables to put it in the form of the Lorentz transformation, ==then claims to have derived the Lorentz transformation from the ==Galilean transformation.
Essentially = he takes Galilean transformations, and then does a change of = variables to put it in the form of the Lorentz transformation, = then claims to have derived the Lorentz transformation from the = Galilean transformation.
Essentially he takes = Galilean transformations, and then does a change of variables to put it in = the form of the Lorentz transformation, then claims to have derived the = Lorentz transformation from the Galilean transformation.
www.pych-one.com /new-6421194-4388.html   (8125 words)

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