OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:and so the moving observer measures the speed of light as:
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