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Consider the Lorentz transformations

x=g(x’+Vt’) (1)

t=g(t’+Vx’/c2). (2)

They relate the space-time coordinates of the same events E(x,t) and E’(x’,t’) i.e. the space coordinates of the points M(x,0) and M’(x’,0) where the events take place and the readings of the clocks C(x,0) and C’(x’,0) located at that points when they read t and t’ respectively. In each of the involved inertial reference frames I and I’, the corresponding clocks are synchronized a la Einstein. We mention the clocks C0(0,0) and C’0(0,0) of the two reference frames located at theirs origins display the same running time as C(x,0) and C’(x’0) do respectively, as a result of the synchronization procedure. It is obvious that

t=x/c (3)

t’=x’/c. (4)

Multiplying both sides of (2) by c and taking into account (3) and (4) we obtain

x=g(x’+Vx’/c)=g(x’+Vt’) (5)

and we recover (1)!

Dividing (1) with c and taking into account (3) and (4) we obtain

t=g(t’+Vt’/c)=g(t’+Vx’/c2)

and we recover 2)! Is it correct to say that equation (1) is self contained in (2) and vice-versa?