I am now studying the Lorentz transformation which shares some commonality with the Galiliean transformation. What I'm confused about is how they only seem to transform the x axis. It will help if I write it out. The Galilean transformation looks like:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] x' = x-vt [/tex]

[tex] y' = y [/tex]

[tex] z' = z [/tex]

[tex] t' = t [/tex]

Although most of the books I have read do not bother, I will put this in matrix form because I will eventually do that with the Lorentz transformation.

[tex]

\left(\begin{array}{cccc}

1 & 0 & 0 & -v &

0 & 1 & 0 & 0 &

0 & 0 & 1 & 0 &

0 & 0 & 0 & 1

\end{array} \right)

\letf(\begin{array}{c}

x &

y &

z &

t

\end{array} \right) =

\letf(\begin{array}{c}

x' &

y' &

z' &

t'

\end{array} \right)

[/tex]

Pay no attention to the stange layout of the 1 by 4 arrays. I could not figure out how to make them. It is clear that veolocity effects only the x component of the resulting vector. To me that makes no sense. Does anyone know why it is set up this way. I have had no classes on matrices but I work with computer graphics programming and have taught myself much over the summer. I am thinking the book is assuming I also transform the coordinates of the object so that it is traveling only with respect to x and then transform the coordinate space back to the orginal for the final transformation. In that case giving the Lorentz transformation as first listed is not adaquate. Am I right?

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# Homework Help: Lorentz Transformation

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