Lorentz transformation

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A set of equations proposed by H. A. Lorentz for transforming the position and motion parameters from a frame of reference with origin at O and coordinates (x,y,z) to a frame moving relative to it with origin at O′ and coordinates (x′,y′,z′). They replace the Galilean transformations used in Newtonian mechanics and are used in relativistic mechanics. They are:

x′ = β(xvt)

y′ = y

z′ = z

t′ = β(tvx/c2),

where v is the relative velocity of separation of O and O′, c is the speed of light, and β = 1/√(1 − v2/c2). The above equations apply for constant v in the xx′ direction with O and O′ coinciding at t = t′ = 0.

Subjects: Physics — Mathematics.

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