Actually, the basic train-lightning gedanken-experiment (simultaneity of event observations) can be shown with Trigonometry (as long as you 'believe' that the speed of light 'c' isn't infinite or doesn't change with the motion of the observer. As noted, kawecki isn't buying the latter premise). :)

But, yes, Special Relativity is an exercise in variance of measurements between systems moving with respect to one another - that is all.  Einstein starts off with clocks (important since time is based on events and recognition of events is based upon observation - usually via some form of energy transmission (sound or light, e.g.)) and moves onto distance (as they are tied together in a system where light doesn't act instantaneously at a distance).  In normal, everyday life, the train isn't moving at 0.8c compared to the observer on the platform so that the disparity becomes evident.  In other words, the effect of Relativity is a curvilinear one that ramps up the closer one gets to 'c' relative motion and the effect is negligible at small percentages of 'c'.

I'll admit that the one place Relativity fails is with subatomic particles themselves, of which light particles (photons) are involved.  This is why it has been impossible to combine Relativity and Quantum Physics.  Relativity is using the subatomic particles/waves grossly as part of the phenomenal study while Quantum Physics is studying them directly (as it were).  Relativity in no way explains why subatomic particles are always moving so fast, can't move faster, are apparently massless. and why they aren't affected by their own Relativistic speeds (when observed) even when slowed a bit by a medium.  Neither theory is particularly satisfying as a unifying model of the fabric of the universe (space-time and the subatomic realm).  There has been some headway into explaining macroscopic interactions with the subatomic processes via Quantum Physics but we're not there yet.  I don't want to hear anything about having finally arrived at the end of all understanding within Physics.  There are still tons of mysteries out there, large and small, to be solved and possibly relevant to changing paradigms.

C makes it easy to shoot yourself in the foot. C++ makes it harder, but when you do, you blow your whole leg off.

 -- Bjarne Stroustrup

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