This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a sphere of light radiating from the point where both coordinates coincide should have the same radius. Also, the assumption is made that x' and t' can be expressed as a linear combination of x and t, (x'=a1x+a2t and t'=b1x + b2t )while y=y' and z=z'. Doing some boring algebraic manipulation, a1, a2 ,b1 and b2 are found. So I thought: why bother with y and z coordinates since they are the same? So let's concentrate on events happening along the x and x' axis. I don't need the sphere, I just need to consider the ray of light along the axis and write instead: x-ct =x'-ct' But that is obviously different from x2-c2t2 = x'2 - c2t'2 So of course it does not leave anywhere. My naive question is then: where's the flaw in my reasoning?