A few days ago some friends and I were watching a lecture on modern physics, presented by a college physics instructor and intended to educate the general public on what is possible and impossible according to the laws of nature. I won't embarrass the speaker by naming him, but I will say that most of what he said was wrong. As a theoretical physicist, it quickly became clear to me that he did not have a solid understanding of the topics he was trying to present. As such, I was inspired to write a few articles on loopholes in the laws of physics that might help to clarify exactly what is and is not possible at the leading edge of knowledge...

One of the most commonly quoted rules of Einstein's theory of relativity (both the special and the general theory) is that nothing can travel faster than the speed of light in vacuum. You might add infinite amounts of energy, or build exotic machines and matter, but nothing will travel faster than light.

It is commonly quoted, and it is wrong.

The actual rule is that information cannot be sent faster than light in a vacuum, relative to the spacetime in its vicinity, unless (and this is still speculative) it cannot interact with anything travelling slower than light. Consider three legitimate systems that violate the usual FTL rules:

1. Quantum Effects (ie EPR Paradox): This is one of the most common counterexamples given, as it relies on very sound physics. If you take two particles, and entangle them together in certain ways, then they remain connected even at great distances. For example if you take two electrons which can either spin clockwise or counterclockwise (relative to a common axis), entangle them, and then move one to the opposite side of the galaxy, then when you measure the spin of one of them the other will instantly assume the opposite spin direction. The 'signal' has travelled faster the speed of light. 
So why doesn't this violate the theory of relativity? Because it is random. There is no way of controlling which spin will be measured, and so you are effectively flipping a coin that affects both electrons. And worse still, when either electron is observed the system collapses so the recipient of the message cannot check it until they are certain it has been received. And when they collapse the system, they don't even know whether a signal was received first or not. So the best you can say is that a random event may or may not have traveled faster than light, but you gain no information from it.

2. Warp Drive: The second loophole is that, while speed is restricted, distances can be changed. In the general theory of relativity, space can be expanded and contracted by the presence of energy or matter. In theory at least, it is possible to compress space in front of a spaceship, cross it at less than the speed of light, and then expand it behind the ship. (This has been studied, and it does work in theory, but at present all models require enormous quantities of energy, and usually also require exotic types of matter that are not known to exist yet). At the end of the trip you have arrived at your destination before a light beam would, making it appear as though you had traveled faster than light.
Another variation on this method is to make spacetime itself move faster than light relative to some distant reference point. The Universe is not only expanding, but is accelerating. Distant galaxies are known to be receding from us faster than light from this effect, but the galaxies are being pulled along by space itself rather than actually moving quickly through space. And so a space ship could effectively surf along on a spacetime wave at high speed.
So why doesn't this violate the laws of relativity? Because at no time are you actually travelling faster than light in your local frame of reference.  Distant observers will see your ship moving faster than light, but you yourself are never exceeding the speed of light relative to the patch of space around your ship.

TOP: A spaceship moves through spacetime under its own power. (the lines are added to give a sense of the 
shape of spacetime near the spaceship).
MIDDLE: The spaceship is travelling at the same speed relative to the lines, but the lines themselves are moving analogous to spacetime moving or expanding around the space ship.
BOTTOM: A spaceship with a warp drive contracts the region of space in front of it, crosses it at the same speed at in the other two diagrams, and then expands the spacetime behind it to effectively travel faster.

3. Tachyons: This is the most controversial of the loopholes, but it is still an interesting piece of theoretical physics. In particle physics, it is quite easy to create particles that travel faster than the speed of light, known as tachyons. They cannot slow down, and in fact the more energy that is added to a tachyon the slower it travels! And it is possible (in theory at least) that they could interact with light, which then interacts with ordinary matter. In this way, there arises the possibility that matter could interact superluminally through an intermediate tachyon. However as with the EPR paradox, it is most likely that only random events can occur and so once again, no information can be transferred. But this is still an area of research, and who can tell what the future holds...

So there are three systems that allow faster than light travel, but not faster than light signalling. No information can travel faster than light, when speed is measured relative to a local frame of reference, with the possible exception of systems that never exist slower than the speed of light. Even in the laws of nature, there is always a loophole...