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(x − vt)
y′ = y
z′ = z
t′ = β(t − vx/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.