Lorentz Transformation

Lorentz Transformation: Since Galilean transformation do not satisfy the postulate that the speed of light is a universal constant, Lorentz transformation equations are developed. Let x, y, z and t be the space and time coordinate in rest system or standard system. The system with moves with velocity along the x-axis. The origins at coincide. The most general transformation equations relating the coordinates of an event in two system can be written as,

The transformations are linear. If they are not linear one system would predict acceleration while in other system velocity was even constant. We have assumed that and axes are left unchanged by the transformation for reasons of symmetry. Using the following boundary conditions we will work out the constants.

(i) Observers in S and S' see the origin of S' as respectively
                        
(ii) Observer in S' and S see the origin of S as respectively
                        
(iii) A light pulse is sent out from the origin of S towards x at t=0, its location is given by
                           

(iv) A light pulse is emitted along y axis in S system at t=0, its coordinate in both systems are