Genady Posted February 24 Posted February 24 I've arrived to an expected answer, but I am not sure at all that the process was what the problem statement wants. First, I considered \(0=(t+\delta t)^2-(x+vt)^2-(t^2-x^2) \approx 2t \delta t - 2xvt - v^2t^2\). Ignoring \(O(v^2)\) gives \(\delta t=vx\), i.e., \(t \rightarrow t+vx\). Keeping \(O(v^2)\) gives \(t \rightarrow t+vx+\frac 1 2 v^2t\), which is the correct expansion of the full transformation to the second order. Now, taking \(x \rightarrow x+ \delta x, t \rightarrow t+vx\) gives by the similar calculation \(x \rightarrow x+vt+\frac 1 2 v^2x\). Is it what the exercise means?
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