- #1
erok81
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I wasn't sure if this counted as intro physics. Feel free to move if I have it in the wrong place.
In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light.
Describing the reference frames:
s' -> x'=u't'
s-> x=ut
Boundary conditions:
x=x'=t=t'=0
Therefore at the origin of x we have x=ut=0, x'=u't', x=-vt'
Using these for the transformations:
x'=Ax+Bt
t'=Cx+Dt
Final transforms:
[tex]x'=\gamma(x-vt)[/tex]
[tex]t'=\gamma(\frac{-vx}{c^2}+t)[/tex]
[tex]x=\gamma(x'+vt')[/tex]
[tex]t=\gamma(\frac{vx'}{c^2}+t')[/tex]
So I can solve these as long as I have my notes that I can follow so I know what to solve for and when. My professor ended up solving for the A,B,C,D first then subbing in gamma etc to arrive at the final results.
My questions is: I'd love to be able to derive these on my own. My problem I don't know what I am trying to solve for or the point of what I am solving for. Point may not be the best word - I understand the end result and know how it is used, I just don't understand the steps/method to get there. (the algebra I get, not the method.
Homework Statement
In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light.
Describing the reference frames:
s' -> x'=u't'
s-> x=ut
Boundary conditions:
x=x'=t=t'=0
Therefore at the origin of x we have x=ut=0, x'=u't', x=-vt'
Using these for the transformations:
x'=Ax+Bt
t'=Cx+Dt
Homework Equations
Final transforms:
[tex]x'=\gamma(x-vt)[/tex]
[tex]t'=\gamma(\frac{-vx}{c^2}+t)[/tex]
[tex]x=\gamma(x'+vt')[/tex]
[tex]t=\gamma(\frac{vx'}{c^2}+t')[/tex]
The Attempt at a Solution
So I can solve these as long as I have my notes that I can follow so I know what to solve for and when. My professor ended up solving for the A,B,C,D first then subbing in gamma etc to arrive at the final results.
My questions is: I'd love to be able to derive these on my own. My problem I don't know what I am trying to solve for or the point of what I am solving for. Point may not be the best word - I understand the end result and know how it is used, I just don't understand the steps/method to get there. (the algebra I get, not the method.