As a physicist, I get emails from people who get very upset that something as counterintuitive as special relativity is how the Universe works. They give lots of arguments about why things couldn't or shouldn't work that way. But, it turns out they do. More importantly, it turns out that you can pretty easily show that, in order for electromagnetism to work, special relativity is the only option. This is why Einstein's paper on special relativity is titled "On the Electrodynamics of Moving Bodies."

Relativity is profoundly unintuitive to humans. Our brain seem hardwired to visualize geometry in at most 3 dimensions, and 3 Euclidean dimensions at that. This is probably because we evolved in an environment where objects move at non-relativistic speeds. Similarly since we evolved in an environment where actions were much larger than the Planck constant, our brains just do not think naturally in terms of quantum mechanics. We are, at our core, creatures who think in classical physics. And that is good enough if you're a naked ape looking to hit a gnu with a rock, or even an engineer building the Hoover Dam, but that physical intuition falls apart when you get to the physics of the very fast, the very big, or the very small. And since the Universe is really quantum and relativistic, those limits are where things get fun.

Let's look at one of those fun things: the Twin Paradox. First in Special Relativity, and then again in General Relativity. 

In science fiction, it is pretty standard fare to introduce some form of faster-than-light communication or travel. After all, space is big, and you can't write your swashbuckling Hornblower-in-space novel if you have to wait for a generation ship to crawl painfully slowly between the nearest stars, much less try to cross a galaxy.

However, faster-than-light communication (which includes travel) breaks something very fundamental about physics, something that is often ignored by sci-fi, and difficult for non-physicists to understand. If you allow faster-than-light (FTL), then you break causality: you are allowing time-travel.