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kwestion

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I started to study Simple Derivation of the Lorentz Transformation

In this derivation, I gather that there are two rays of light being tracked--one going to the right of the origin and one going to the left of the origin.

The right-going light is described by x=ct and x'=ct'.

The left-going light is inferred to be described by x=-ct and x'=-ct'.

This is bothersome that both rays are described by the same symbol x. Perhaps that could be overlooked as long as the statements are kept in context of right-going light and left-going light, but in step 5 the left and right x's are mixed together as the same. I think this means that from step 5 forward, the symbol x represents an intersection of the rays at time t. I think that the initial constraints on x,t,x',t' are required to continue to hold. In particular, I think that from step 5 forward, the intersection x is such that

Wouldn't justification for step 5 also require that it be accompanied by the initial constraints which would collectively imply that x=0, t=0, x'=0, t'=0? I think this may have been just an everyday error, but maybe there is something silly or deep that I'm missing.

In this derivation, I gather that there are two rays of light being tracked--one going to the right of the origin and one going to the left of the origin.

The right-going light is described by x=ct and x'=ct'.

The left-going light is inferred to be described by x=-ct and x'=-ct'.

This is bothersome that both rays are described by the same symbol x. Perhaps that could be overlooked as long as the statements are kept in context of right-going light and left-going light, but in step 5 the left and right x's are mixed together as the same. I think this means that from step 5 forward, the symbol x represents an intersection of the rays at time t. I think that the initial constraints on x,t,x',t' are required to continue to hold. In particular, I think that from step 5 forward, the intersection x is such that

*both*initial constraints x=ct and x=-ct must be satisfied, which in turn implies that both x and t can only be zero when c is non-zero. Likewise x' and t' must equal zero to satisfy the initial conditions.Wouldn't justification for step 5 also require that it be accompanied by the initial constraints which would collectively imply that x=0, t=0, x'=0, t'=0? I think this may have been just an everyday error, but maybe there is something silly or deep that I'm missing.

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