Lorentz transformation written in same format as Galilean transformation.
Consider two inertial frames of reference, S and S'. Frame S' is moving at a constant velocity V with respect to S. Define a quantity Γ,
Γ=1/(1-V2/c2)1/2
where
c is the speed of light. Γ is known as the
Lorentz transformation Gamma.
If the frame S' is moving at a constant speed V along the x-axis and the two frames coincide at t=0 then the transformation may be written as follows
x=Γ(x'+Vt')
y=y'
z=z'
t=Γ(t'+Vx'/c2)
This transformation agrees with the experimental observation that the speed of light is constant whether measured in the reference frame S or the moving frame S' (and as postulated by the theory of Special Relativity). It can also be shown that Maxwell's equations are covariant under the transformation. Therefore, Electromagnetism is consistent with the requirements of Special Relativity.
The above transformation reduce to the Galilean case when V is much less than c (Γ->1). However, several effects arise that are outside our daily experience when V is a significant fraction of c (Γ>1). See time dilation, length contraction and the twin paradox.