I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage..
2. Homework Equations / attempt
c = velocity of light.
v = the velocity as observed from where time t is measured.
D = distance AB.
t = time light occupies to pass from A to B.
t1 = time light occupies to return from B to A.
Firstly we can see that
So for the total distance,
Make a common denominator and add the two fractions,
Expand the brackets,
Simplify, cancel out where possible,
And take out the factor of 2D
t+t1=2D(c/(c^2-v^2)) or 2D(1/(c-(v^2/c))
( I am unsure whether or not taking it that far is right yet..)
Above is where i have arrived and the next step i am supposed to arrive at..
2D (c^2 / (c^2 - v^2)) = 2D (1 + (v^2 / c^2)]
Any help asap please?