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I've seen several derivations of it and I understand them, specially the one in two dimensions with the right angled triangle, but when I try it in 1 dimension, I always find that the condition that the speed of light is the same in all the inertial frames, isn't enough to specify what the Lorentz Factor is. Here's my problem:

Take the Lorentz Transformation eq.:

x'=y(x-vt)

t'=y(t-vx/c^2)

Now focus on a light signal, so that in S, x/t=c. We then want x'/t'=c in S' too:

x'/t'=(x-vt)/(t-vx/c^2)=c

As you can see the Lorentz Factor always drops out of the eq...so it seems like it doesn't matter what its value is. But then using other methods and the same assumptions, you do get a definite expression. I think there must be something wrong in my derivation above, but I don't know what it can be. Any ideas?

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# Issue with deriving the Lorentz Factor

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