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Deriving Linear Transformations - Special Relativity

  • Thread starter erok81
  • Start date
  • #1
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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.

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.
 

Answers and Replies

  • #2
464
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Would any more information help? I'm not sure if what I am saying makes total sense. :)
 
  • #3
464
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Ok...I finally figured this out and can do it.

So how about this question instead.

I don't think I've really done linear transformations. What class are these usually taught in?
 

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