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1. Let S be a stationary x-coordinate system. Let S' be a stationary x'-coordinate system. Let the x'-axis of system S' coincide with the x-axis of system S. Let system S' move along the x-axis of system S with constant velocity v in the direction of increasing x. Let observers (every one of them with the ability to count the time t in such a way that each count is exactly 1s, being synchronous to each other) be stationed along every point on the x-axis of S. Let observers (every one of them with the ability to count the time t' in all respects like the observers which are stationed along the x-axis of S) be stationed along every point on the x'-axis of S'. Let the origin of the moving system S' coincide with the origin of the stationary system S at the time t = t' = 0s.
2. If a ray of light is emitted from the origin of the moving system S' at the time t' = 0s to a point x' on the positive side of the origin of S', then the time t' that the ray of light takes to travel the distance x' from the origin of S' is given by the equation
t' = x'/c.
With respect to the stationary system S, the time t of t' is given by the Lorentz transformation equation
t = (t' + v*x'/sq(c))/sqrt(1 - sq(v/c)).
With respect to the stationary system S, the distance x of x' is given by the Lorentz transformation equation
x = (x' + v*t')/sqrt(1 - sq(v/c)).
3. If the ray of light is emitted from the origin of the stationary system S at the time t = 0s to a point x on the positive side of the origin of S, then the time t that the ray of light takes to travel the distance x from the origin of S is given by the equation
t = x/c.
With respect to the moving system S', the time t' of t is given by the Lorentz transformation equation
t' = (t - v*x/sq(c))/sqrt(1 - sq(v/c)).
With respect to the moving system S', the distance x' of x is given by the Lorentz transformation equation
x' = (x - v*t)/sqrt(1 - sq(v/c)).
2. If a ray of light is emitted from the origin of the moving system S' at the time t' = 0s to a point x' on the positive side of the origin of S', then the time t' that the ray of light takes to travel the distance x' from the origin of S' is given by the equation
t' = x'/c.
With respect to the stationary system S, the time t of t' is given by the Lorentz transformation equation
t = (t' + v*x'/sq(c))/sqrt(1 - sq(v/c)).
With respect to the stationary system S, the distance x of x' is given by the Lorentz transformation equation
x = (x' + v*t')/sqrt(1 - sq(v/c)).
3. If the ray of light is emitted from the origin of the stationary system S at the time t = 0s to a point x on the positive side of the origin of S, then the time t that the ray of light takes to travel the distance x from the origin of S is given by the equation
t = x/c.
With respect to the moving system S', the time t' of t is given by the Lorentz transformation equation
t' = (t - v*x/sq(c))/sqrt(1 - sq(v/c)).
With respect to the moving system S', the distance x' of x is given by the Lorentz transformation equation
x' = (x - v*t)/sqrt(1 - sq(v/c)).