Take the tour ×  I'm having a hard time getting an intuitive
understanding of Lorentz Contraction. I understand what it is by
definition but I don't 'get it.' I'm not a physicist, just an
amateur, so sorry if this question comes across as too naïve.
Okay, I was able to understand Time Dilation with the help of
the 'light bouncing off two mirrors' experiment (the one that
uses Pythagoras' theorem to derive the equation of time
dilation) and I've noticed that this same scenario is also used
on a lot of websites to derive Lorentz Contraction. So, I'll use
it to present my question:  First, to define the setup:  Let's
assume person A is "at rest" and person B goes by in a spaceship
traveling at velocity $v$, close to the speed of light $c$.
Let's call the time measured by A $t$ and that measured by B
$t'$. So, we have:  $$t = t'/\sqrt{1-v^2/c^2}$$  I understand
that we can exchange A and B (consider B to be "at rest" instead
of A) and come up with the same relation. So, for each observer,
the other person's watc