In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?
Concerning Rapidity, if tanh(Fi) = v/c, can it be concluded in general that the relative angle of two frames in combination with Lorentz Transformation is tan(theta) = tanh(Fi) = v/c, where theta is the relative angle?
Mathematically if you would use iterate many infinitesimal transformations, then the transf. by exp. form would be exp(e1.B+ e2.R) (e=infinitesimal amount), but it would be interesting to see the proof that the outcome of changing the order of R and B would lead to equal transformation
Let's be more clear, if a particle moves in a single direction in one coordinate e.g. boost, then an observer has a finite rotation, then the transformation in his frame is simply the product of a boost and rotation, then what are the considerations as regards the order?
As per group property, one could make a product of gr members e.g. Lorentz boost (B) and rotation R, as they Commutativity is not valid, R.B or B.R, what should be considered and which order should be preferred? Generally it is known R.B1= B2.R .