- #1

- 73

- 2

I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating:

x

^{2}+y

^{2}+z

^{2}-c

^{2}t

^{2}= x'

^{2}+ y'

^{2}+z'

^{2}-c

^{2}t'

^{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'=a

_{1}x+a

_{2}t and t'=b

_{1}x + b

_{2}t )while y=y' and z=z'. Doing some boring algebraic manipulation, a

_{1}, a

_{2},b

_{1}and b

_{2}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

x

^{2}-c

^{2}t

^{2}= x'

^{2}- c

^{2}t'

^{2}

So of course it does not leave anywhere. My naive question is then: where's the flaw in my reasoning?