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| The '''Lorentz transformation''' is the set of equations relating the space and time coordinates assigned to an event by two observers in uniform relative motion, in such a way that the speed of light comes out the same for both. It replaced the Galilean transformation as the kinematic core of twentieth-century physics, and almost every disputed result of [[Special relativity|special relativity]] — [[Length Contraction|length contraction]], [[Time Dilation|time dilation]], the relativity of [[Simultaneity|simultaneity]] — is a direct consequence of it.
| | #REDIRECT [[Lorentz transformation]] |
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| ==The standard account==
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| For motion along the ''x'' axis at speed ''v'', the transformation is
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| : ''x' = γ(x − vt)'', ''t' = γ(t − vx/c²)'', ''y' = y'', ''z' = z''
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| with the Lorentz factor ''γ = 1/√(1 − v²/c²)''.
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| The equations predate [[Albert Einstein|Einstein]]. Voigt wrote a similar set in 1887; Larmor and [[Hendrik Lorentz|Lorentz]] arrived at the modern form between 1897 and 1904 as the transformation leaving Maxwell's equations invariant, and Poincaré named it after Lorentz and showed the transformations form a group. For Lorentz they described how measuring rods and clocks are physically affected by motion through a stationary aether, which remained a real preferred frame. Einstein's 1905 derivation dispensed with the aether: he obtained the same equations from two postulates — the equivalence of all inertial frames and the invariance of the speed of light — and read them as statements about space and time themselves rather than about apparatus.
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| That reinterpretation, not the algebra, is what is chiefly contested. The transformations are mathematically well-defined and their group structure is not in dispute; the disagreement is over whether they describe physical reality, a measurement convention, or an artefact of how coordinates were assigned.
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| ==On this wiki==
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| Critiques catalogued here fall into roughly three families.
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| '''Derivational.''' [[Neil E Munch]] devoted a series of papers to the logic of the derivations themselves — ''[[The Derivations of the Einstein-Lorentz Transformation]]'' (with [[Robert J Hannon]], 1995), ''[[Consequences of Relativity's Failure To Control Assumptions]]'' (2005), ''[[Conflicts in Special Relativity Resulting from Assumption Shifts]]'' and ''[[Incompatibility of Lorentz Transformations with Michelson-Morley Data]]'' — arguing that the standard derivations shift the meaning of their symbols mid-argument. [[Steven Bryant]] makes a parallel case in ''[[Namespace Analysis in Evaluating the Validity of the Einstein-Lorentz Transformation Equations]]'' (2008). [[John E Chappell]] makes the same charge specifically about simultaneity in ''[[Simultaneity Cannot Possibly be Relative to Motion]]'', following Melbourne Evans and Rosser: a symbol that first denotes a ''length'' is later reassigned to denote a ''point''. [[Alex Ceapa]] and [[Bernard Guy]] examine what the transformations presuppose about the joint definition of space and time.
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| '''Internal consistency.''' [[Hartwig Wolfgang Thim]]'s ''[[Three Major Inconsistencies of the Lorentz Transformations]]'' ([[Proceedings of the NPA]], 2011) states three: a logical error in the light-speed postulate, the intransitivity of the transformations, and a transverse Doppler shift he reports as experimentally refuted by his own microwave measurements. [[Stephan J G Gift]] argues from the [[GPS]] that the transformations fail operationally (''[[Faster West than East: The GPS Invalidates Special Relativity]]''). [[Georg Galeczki]]'s ''[[Dynamic Gamma Factor: Yes; Lorentz Transformation: No]]'' takes an unusually precise position: the γ factor is real as a ''dynamical'' effect — mass increase with absolute velocity, confirmed in the Bertozzi experiment — but the ''kinematic'' gamma equals one, so no non-Galilean coordinate transformation is licensed.
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| '''Replacement.''' [[Curtis E Renshaw]] argues in ''[[The Restoration of Space and Time from a Galilean Approach to Relativity's Second Postulate]]'' (1998) that Maxwell's equations fix only the combination ''c = 1/√(ε₀μ₀)'' and say nothing about the frame in which that speed is measured; relaxing Einstein's second postulate yields an aether-free Galilean-invariant solution with no length contraction or time dilation, developed further in ''[[The Restoration of Space and Time: Galilean-Newtonian Relativity in the 21st Century]]''. [[Sidney Bertram]]'s ''[[The Lorentz Transform]]'' derives the transformation from retarded elementary forces between charge fields, concluding that what is observed is a "surrogate" image rather than the charge itself, so that neither mass nor clock rate actually changes. [[Steven Bryant]] holds that the whole family of effects arises from applying length-based equations to wavelength-based observations. [[Franco Selleri]] and [[Thomas E Phipps]] instead retain a transformation but with absolute simultaneity restored.
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| See [[:Category:Relativity]] for the full body of work.
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| ==See also==
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| * [[Special relativity]]
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| * [[Length Contraction]]
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| * [[Time Dilation]]
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| * [[Simultaneity]]
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| * [[Twin Paradox]]
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| * [[Hendrik Lorentz]]
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| [[Category:Relativity]]
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| [[Category:Theory & Models]]
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| [[Category:Time]]
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