The most popular ‘brane world’ scenario is probably the so-called Randall-Sundrum model, which is built upon a warped five-dimensional geometry that is bounded by two four dimensional branes (actually, that is more specifically the RS1 model, there’s also a RS2 model which, confusingly, has only one brane).
The two branes differ in terms of their energy scale: one, the gravity- or Planckbrane, is characteristically at the Planck scale, while the other, the weak- or Tevbrane is at the scale of about one TeV, as the name implies, which is considerably lower than the Planck scale. The fields of the standard model, i.e. the matter particles, the electromagnetic force and the two nuclear forces, are confined to the Tevbrane, while gravity can propagate in the bulk – however, it’s strong on the Planckbrane, i.e. the graviton’s probability function is highest there, and drops of exponentially towards the Tevbrane, explaining its relative weakness. This exponential drop is related to the warping of the (five dimensional) bulk along the fifth dimension.
In this scenario, there wouldn’t be much of a point in trying to communicate with the other brane, as all that exists there would be (strong) gravity; I’m not sure you could build any structures out of just that which could acquire the necessary complexity for sentience. Although, I suppose one could add matter (and other) fields to the Planckbrane, but I’m not aware of any research in that direction.
As for the quantum tunnelling/speed of light experiment, there was a bit of a buzz generated by that a couple of years ago, and I think it was a Mozart symphony that has been transmitted. However, as far as I can tell, the consensus seems to be that the violation of the speed of light barrier is only an apparent one, that in fact, no information is being transmitted faster than c. Effectively, it took as long as it would usually take to send, receive, and interpret the information.
In fact, it’s similar to how one can achieve (apparent) faster than light speeds using classical effects in electromagnetism, by manipulating the ‘shape’ of the signal sent. Consider a propagating signal pulse:
* * * *
* * * *
* * ---> * *
* * * *
* * * *
* * * *
p q
The whole thing moves at the speed of light, and so does the maximum, moving from point p to point q, such that p = q + ct, if t is the time the whole thing took.
But now consider a signal that gets narrower as it propagates:
* * *
* * * *
* * ---> * *
* * * *
* * * *
* * * *
p q r
The maximum now travelled farther than in the previous case in the same time, moving not only to q, but to r – it has travelled faster than light!
But, even though it’s tempting to see a violation of relativity here, again, there is no way to use this to transmit information FTL – since before the maximum arrives, the wave front does, which sets the signal speed (you don’t need to wait for the maximum to arrive in order to register a signal, once the wave front hits, you know one’s coming); and you’ll notice that, thanks to me spending way too much time counting spaces, the front of the wave packet travels the same distance in both cases – meaning the signal speed is again exactly c.
This is a bit like the flashlight-shone-onto-the-moon thought experiment: I shine a sufficiently strong light at the moon, and just a small flick of my wrist will send the light spot across the moon’s complete surface, at speeds far greater than that of light. But again, no information is transmitted in this case, as there is no way for somebody on the moon’s surface to modulate the light spot in such a way as to send somebody else a message.
