- #1
fignewtons
- 28
- 0
Homework Statement
It is not an official question but a request for pointers. I am trying to derive the Lorentz time equation to understand the intuition behind it. My math skills are not very good so it might be an obvious question for you. Please see below for my attempt.
The variables are x, t in one inertial reference frame and x', t' in another inertial reference frame. c is the speed of light, γ is the gamma factor, and u is the relative velocity of the primed IRF, from the perspective the unprimed one.
The official equation (the end solution I want to get) is:
t'=(t-(ux/c^2))/sqrt(1-(u/c)^2)
Homework Equations
I'm using the equations:
γ=1/sqrt(1-(u/c)^2)
x'=γ(x-ut)
x=γ(x'+ut')
The Attempt at a Solution
So far I've been able to isolate t' from the equation x=γ(x'+ut') up to this state:
t'=((x/γ)-x')/u
I've tried substituting ct for x, substituting γ for 1/sqrt(1-(u/c)^2), and other substitutions that by now I've forgotten. It doesn't seem to come to the format I want in the official equation, mainly because I can't seem to isolate t in the RHS or get rid of the u in the denominator. I've been stuck on it for days :( I hope this makes sense!
Any attempts to explain the intuition behind this equation/help me visualize it is welcome too, I've asked my instructor on it but somehow he seems shocked I would ask this question and told me to just try to derive it...
Thanks for reading this over, hope everything actually makes sense!