Yesterday we have studied the Lorentz transformation in school. So we have two frames of reference, $S$ and $S'$ . $S$ is stationary and $S'$. $S'$ has a constant velocity $v$, relative to the $S$ frame. $v$ is directed along the Ox axis. Ox is parallel to Ox' and Oy is parallel to Oy'.
If we apply the Galilran Transformations we get:
$x = x' + ut' $ $y = y'$ $z = z'$ $t = t'$
$ x' = x - ut $ $y'=y$ $z'=z$ $t' = t$
Now, our physics teacher, assumed that:
$ x=k(x'+ut')$ $ x'=k(x-ut)$ with k being a constant.
Why did he do that? I didn't understand. I undrstood that the length of an object depends o the frame of reference and that the speed of light is the same in the two frames.
Assuming the above facts, we can derive the $k$ constant:$$\frac{1}{\sqrt{1-\frac{u^2}{c^2}}}$$
But why did we make that first assumptikn? I didn't get the logic. Could somebody explain, please?
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