Help with deriving Lorentz Factor

  • Thread starter Joeirvin
  • Start date
  • #1
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Homework Statement


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
Let:
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
t= D/(c+v)
And
t1= D/(c-v)
So for the total distance,
t+t1=D/(c+v)+D/(c+v)
Make a common denominator and add the two fractions,
t+t1=(D(c-V)+D(c+v))/((c+v)(c-v))
Expand the brackets,
(Dc+Dv+Dc-Dv)/(c^2+cv-cv-v^2)
Simplify, cancel out where possible,
(2Dc)/(c^2-v^2)
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?

thankyou
 

Answers and Replies

  • #3
Fredrik
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Science Advisor
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t = time light occupies to pass from A to B.
t1 = time light occupies to return from B to A.
What's A and B? Are they events? Points in space? Wouldn't this make t=t1?

Firstly we can see that
t= D/(c+v)
And
t1= D/(c-v)
I'm not sure what you're doing, but this looks wrong.
 
  • #4
4
0
It doesn't matter now, i decided to start over using a light clock idea, and it seemed to work perfectly. Thanks anyway
 

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