- #1
member 11137
My two questions are related to the title. The problematic is: "How can we connect the coordinates ... xα... for α = 0, 1, 2 and 3 to the coordinates of the same object in another frame, say ...yλ for λ = 0, 1, 2, 3 in preserving the quantity η(x)αβ. dxα.dxβ = η(y)λμ. dyλ. dyμ?
Can someone explain clearly:
1°) why we have supposed that the coordinates transformations should absolutely be linear (and not, e.g. a Taylor's developpment including terms of highter degree)? -> Poincaré group;
2°) why didn't we preferred to work with the relations proposed in 1869 by E.B. Christoffel for such problematic?
Thanks
Can someone explain clearly:
1°) why we have supposed that the coordinates transformations should absolutely be linear (and not, e.g. a Taylor's developpment including terms of highter degree)? -> Poincaré group;
2°) why didn't we preferred to work with the relations proposed in 1869 by E.B. Christoffel for such problematic?
Thanks