Absolute time is the same for all observers. Thus the time part of the Galilean transformation is:
Einstein made space and time relative and symmetric (at least in one dimension) by assuming an absolute speed of light, c. With β = v/c and γ = (1 − 1/(1 − β²), the Lorentz transformation is
A linear transformation would be simpler. This is a rigid or Euclidean transformation of time, with a dual one for space. Let w = 1/v, then
An illustration of this transformation is how time on the Earth is defined by the relative position of the Sun. At Noon the Sun is directly overhead, and so on. This has been standardized with time zones but the physical background is continuous. In this case w = 1 hour per 15 degrees of Longitude or 4 minutes per degree. With distance measured by degrees of Longitude, this is a rigid transformation.