410(2): Precession from Length Contraction and Time Dilatation

410(2): Precession from Length Contraction and Time Dilatation

The discussion by Marion and Thornton reproduced in this Note leads to the remarks by Horst below. I think that the easiest and simplest way of dealing with time dilation or “dilatation” as it is called in the physics literature, is to use the infinitesimal line element (9), which gives dt = gamma d tau directly,  Eq.(10). Here dt is the infinitesimal of observer time, the time in frame K, and dtau is the infinitesimal of proper time, the time as measured in the moving frame K’. This result is also given by Eq. (21) from the inverse Lorentz transform (14). I think that the method used by Marion and Thornton is not as clear as the line element method. The result dt = gamma dtau is the basis for the relativistic momentum, the relativistic kinetic energy and the Einstein energy equation…