Why does the speed of light totally prevent instantaneous information exchange? Based on the classical light-cone approach it's easy to see you can't transmit information faster than $c$ but why does the speed of light (as far as I know) treat information transmission in this way formally?
For instance going the Sci-Fi route, in Orson Scott Card's Ender universe there is a device called an ansible which seems to be described as some sort of coupled state device - pair two devices and as they move apart they remain linked. The details probably don't matter since this is a hypothetical question.
With ansibles, you obviously can only move the devices subject to normal physics so if you found a colony 100 light-years away, it takes (at least) 100 years to get the ansible there. But then, you have communication.
Is it possible in reasonably simple (say degree but not post-graduate level) terms to explain why this is fundamentally impossible, why information cannot by any means violate the light-speed limit, rather than that we just can't think of a way to do it?
 A: Faster than light communication would violate causality. If FTL communication was somehow allowed by nature, then you could kill someone before firing the gun which just doesn't make any sense. You simply cannot have something that is caused by some event happen before the event occurs. Put simply, FTL communication gives rise to paradoxes.
A: One principal that would be violated is causality.  Just looking at things from a single frame (such as here on earth), there is no apparent problem.  But as soon as you examine things in other frames it gets tricky.  
Once you allow for travel faster than $c$ in one frame, it becomes possible to construct a series of messages, each of which travels forward in time in some particular frame, but where the final message arrives at the transmitter before the time when it sends the message.  
Here's a site with some good Minkowski diagrams for it.
http://www.theculture.org/rich/sharpblue/archives/000089.html
A: The thing about the speed of light $c$ is that it's not just a number associated with a certain type of particle. While we could talk about the mass of the proton, and there would be no problem assuming non-protons had greater or lesser masses, the value $c$ is an entirely different beast.
$c$ is an intrinsic property of spacetime itself, not of the particles in spacetime. You wouldn't expect there to exist anything (particle, signal, information) that you could insert into spacetime with the property "changes the nature of spacetime for itself."
The above is meant to undermine the "if it's just a property of everything we've found so far, we haven't ruled out finding things without this property" line of thought.

For a more concrete demonstration of what goes wrong when you alter the structure of spacetime as we know it, take a look at the "tachyonic antitelephone". This demonstrates how any abstract communication faster than light leads to causality violations as observed by even not-faster-than-light observers.
There are many variations on the thought experiment; here's one of them (with the math worked out in the linked article): $A$ is moving away from $B$ with speed $v < c$ in $B$'s reference frame. $A$ sends a faster-than-light message to $B$, who responds in kind with a reply. The problem is for sufficiently fast (but not faster than $c$!) speeds $v$, $A$ will receive the reply before sending the message. Faster-than-light anything begets time travel.

Since it gets repeated far, far too often, I'll also counter quantum entanglement arguments here. Quantum entanglement does nothing in the hypothetical "why can't this communicate faster than light?" scenarios other than guarantee that the two particles will "collapse" to the same (or opposite, or orthogonal, or whatever) states when either is observed. The only quantum mechanical aspect of the whole thing is the fact that the eventual collapsed state can't even exist before the measurement (it's not a hidden variable).
But the correlation -- the thing you want to rely on to communicate faster than light -- could be achieved entirely classically. Take a red marble and a blue marble, put them in a bag, and draw one out randomly without looking. Lock your marble in a box, and hand the bag to someone else, who also doesn't peak. Send the person far away. Then, look at your marble. If it's blue, you instantly know the other person has red. But you transmitted nothing. All quantum mechanics does is make it so who has which marble isn't pre-determined.
This shouldn't come as a surprise, because the only notions of space and time in quantum mechanics are the ones from spacetime itself. Quantum mechanics doesn't come equipped with some independent notion of distances. So whatever structure spacetime has applies to quantum things just as much as marbles and people and signals.

Everything said here stays true even in general relativity, by the way. Enabling things to move faster than $c$ still leads to causality violations. Even wrapping things in a "warp bubble" and moving that faster than $c$ leads to causality violations.
A: Information has to be transmitted by something.  The laws of Physics state that the maximum speed that anything can move at is the speed of light, which seems to be a fundamental property of the universe.  So, if we can find something that can travel faster than light then it would be possible to transmit information faster, but until then we are limited to light speed. [edited to remove dubious suggestion that quantum entanglement might enable faster-than-light information transmission].
A: A good approach to understand is the consideration of the two components of c, permittivity and permeability of vacuum. They are two constants of space, and already by their name we understand that it is a physical property/ a physical limit of space not to transmit any radiation faster than with light speed.
The hypothetical proper time of photons is zero, because from their hypothetical point of view they are not taking part in spacetime, their Minkowski diagram would be reduced to a dimensionless point. In this sense it could be said that information is transmitted immediately - but this is a consideration which does not take into account the spacetime where we are living in as observers. In the same way as there is a fundamental law (the second SR postulate) that light speed cannot be observed faster than c, there is no mean for spacetime observers to get information faster than at light speed. 
