Special relativity - frames of reference

AI Thread Summary
The discussion focuses on deriving the Lorentz transformations for two frames of reference, K and K', where K' moves with a velocity vector of v = v [1/√2, 1/√2]. The proposed transformations are t' = (t - (v_x * x + v_y * y)/c^2) / √(1 - v^2/c^2), x' = (x - v_x * t) / √(1 - v^2/c^2), and y' = (y - v_y * t) / √(1 - v^2/c^2), with v_x and v_y both equal to v/√2. The solution appears to be correct, confirming the application of special relativity principles. The discussion concludes with appreciation for the clarity of the transformations provided.
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Homework Statement


We have two frames of reference: K (x,y,t) and K' (x',y',t') such that initially x=x'=y=y'=t=t'=0. Now let K' move with a velocity \vec{v} = v [\tfrac{1}{\sqrt{2}},\tfrac{1}{\sqrt{2}}]
Write Lorentz transformations in such a case.

Homework Equations





The Attempt at a Solution


My try is:
t' = \frac{t - (\vec{v} \circ (x, y))/c^2}{\sqrt{1 - \frac{v^2}{c^2}}}, \; x' = \frac{x - v_x t}{\sqrt{1 - \frac{v^2}{c^2}}}, y' = \frac{y - v_y t}{\sqrt{1 - \frac{v^2}{c^2}}}

where v_x = v_y = \frac{v}{\sqrt{2}}
 
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Looks good to me.
 
Great, thank you!
 
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