epkid08 said:
Anyways, has the Lorentz transformation been proven?
Every time you watch your TV and use your cell phone;)
You probably need to pick up an introductory book electromagnetism. Einstein also wrote a very readable layman's introduction to the relativity bits calls "Relativity, the Special and General theory". As a new learner myself I found that very palatable (it's probably available in your public library ... that's where I found it).
The way that I have found for myself that I like the best for an initial introduction of the Lorentz transformation is to look at the wave equation. Light appears as a wave regardless of your velocity, so if you take the wave equation for an electromagnetic field (ie: propagation of a signal at the speed of light) :
\partial_{xx} + \partial_{yy} + \partial_{zz} - \frac{1}{c^2}\partial_{tt}
, and perform a change of variables using the chain rule introducing a
along one direction x' = x - vt, then you don't get the wave equation anymore (you get a bunch of mixed terms too). This would imply a curious distortion of light signals with the velocity of the observer (ie: one that we don't observe). If you do the math for a linear change of variables in the above, then lo and behold, out falls the Lorentz transformation, as the linear transformation required to maintain the wave equation with respect to motion of the "observer".
You can do the same thing (with less math) by looking at invarience of the speed of a spherical light shell:
x^2 + y^2 +z^2 -c^2t^2 = {x'}^2 + {y'}^2 +{z'}^2 -c^2{t'}^2
and look for linear transformations that retain this form (ie: no mixed terms). My Berkeley physics mechanics book introduces the transform this way, but it was not all obvious to me that this was a sensical starting point when I first tried learning the subject (later I started to understand the somewhat subtle statement of what it really meant for the speed of light to be constant ... understanding or acceptance of that justifies the spherical shell equation above).
