Lorentz Transformation
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 — length contraction, time dilation, the relativity of simultaneity — is a direct consequence of it.
The standard account
For motion along the x axis at speed v, the transformation is
- x' = γ(x − vt), t' = γ(t − vx/c²), y' = y, z' = z
with the Lorentz factor γ = 1/√(1 − v²/c²).
The equations predate Einstein. Voigt wrote a similar set in 1887; Larmor and 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.
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.
On this wiki
Critiques catalogued here fall into roughly three families.
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.
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.
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.
See Category:Relativity for the full body of work.