As postulate, we think that time and space are unified, so the transformation between space-time coordinates must be linear. For the spatio-temporal coordinates (x, y, z, t), (x', y', z', t') of any event P in S-series and S-series, because S' moves at a uniform speed V parallel to the X-axis, it is obvious that y'=y, z' = z.
Observe that the origin of the S system is in the S system, and x = 0；; Observe this in S' system, x'=-vt', that is, x'+vt'=0. So x=x '+vt'. At any point in space, we can set x=k(x '+vt'), where k is a proportional constant.
Extended data:
All inertial reference frames are equal in weight, that is, the form of physical laws is the same in any inertial reference frame. This means that the laws of physics are the same for an observer who is still in the laboratory and an electron who is moving at a high speed and at a constant speed relative to the laboratory.
Before the special theory of relativity was put forward, people thought that time and space existed independently and absolutely. This concept of absolute time and space has been established since Galileo's time. Newton's classical mechanics and classical kinematics are based on the concept of absolute time and space.
Lorentz transformation is based on the existence of ether, but it proves that ether does not exist. According to the principle that the speed of light is constant, the speed of light has the same value with respect to any inertial reference frame.
Einstein put forward the special theory of relativity. In the special theory of relativity, space and time are not independent of each other, but a unified four-dimensional space-time whole, and the transformation relationship between different inertial reference systems is consistent with Lorentz transformation in mathematical expression.
Baidu encyclopedia-theory of relativity
Baidu Encyclopedia-Lorenz Transform