The notion of locality - the idea that cause and effect only works when the cause somehow "bumps into" something, causing the effect - is tricky. (Say you didn't watch the Super Bowl, and so you have no idea that the Saints won. But you come across a friend - a big Saints fan - and by seeing his big grin you know instantly which team won the game. Is that weird in any way? Nope - it took news of the outcome and the sight of his smile well longer to get to you than the time the information would have traveled at the speed of light. After all, it had to go from the game to him via TV to you via the smile. No "paradox."
But take a thought experiment (much cheaper than particle accelerators and such), and imagine (as did Einstein and a couple of his collaborators in the late 1930s) that you had two "entangled" subatomic particles, one of which spins in a certain way, and the other of which necessarily spins in the opposite way. (That's how these "entangled duos work.) In the thought experiment, you send one particle off into space really far - light years! - and then you check the other nearby one. Gosh, by checking the spin of the nearby one you automatically know the spin of the other one - information apparently delivered to you instantaneously, much faster that the speed of light! Old frizzy-hair Einstein figured that such a result was nuts, thus demolishing quantum mechanics.
Trouble is, the thought experiment didn't do the job. Most physicists bought what Albert called "spooky action at the distance." They showed that their experiments and their math agreed, to astonishing precision, and moved on.
Leaving the rest of us pissed. We can't do the math, the results still don't let anybody send information faster than light, and the whole thing is a pain. Especially when the whole idea undermines our intuition regarding the (sort-of) common-sense idea of space-time itself, making it fuzz up. Drat.
Luckily, we don't have to really worry about it. After all, the Saints won ... and given Katrina, that's a really good thing. Nothing fuzzy about that.
(My Packers, however, obviously need help.)