H1: Introduction to Relativity

H1: Frame of reference: It is a system of coordinates that allows the position of various objects to be defined and measurements to be made.



From: http://www.patana.ac.th/secondary/science/anrophysics/relativity_option/commentary.html#intro_to_SR

If object A is moving due east at 20 ms^-1 and object B is moving towards it due west at 15 ms^-1 then

  V_{a rel B} means the velocity of A relative to B i.e. B is the observer and A is the object. 

V_{a rel B} = V_a - V_b = 20 – (-15) = 35 ms^‑1. 

This is an example of a Galilean transformation where time is assumed to be independent of the observer.

Consider:

As they are moving towards each other their relative velocities with respect to each other are twice their original velocities by Galilean transformation = 0.9800c + 0.9800c = 1.960c. This is faster than the speed of light which is not physically possible; therefore at speeds greater than 1c, Galilean transformations break down and consequentially the Theory of Relativity was 'invented.'

But in our everyday life we do not deal with speeds close to the speed of light; therefore the Galilean transformations hold.

The photon moving in the same direction as the pion (photon R) will have a speed of 1c (speed of light/photon)+ 0.900c which is 1.90c. 

The photon moving in the opposite direction as the pion (photon Q) will have velocity 1c - 0.900c = 0.100c.