Relativity
The Special and General Theory

i.e. with the velocity c. According to the equations of the Lorentz transformation, this simple relation between x and t involves a relation between x' and t'. In point of fact, if we substitute for x the value c·t in the first and fourth equations of the Lorentz transformation, we obtain:

x' =   (c - v)t  √  1 - v2/c2

t' =   (1 - v/c)t  √  1 - v2/c2

from which, by division, the expression

x' = c·t'

immediately follows. If referred to the system K', the propagation of light takes place according to this equation. We thus see that the velocity of transmission relative to the reference-body K' is also equal to c. The same result is obtained for rays of light advancing in any other direction whatsoever. Of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.