So how close would we have to be to a twin Earth before we could hear it, i.e. hear ourselves? If twin Earth were orbiting Alpha Centauri, could we hear it with our own technology? How about fifty years from now?
In a post at David Brin's blog, he rounds up arguments about our own relative silence by stating "even military radars and television signals appear to dissipate below interstellar noise levels within just a few light years. Certainly they are far less visible -- by many orders of magnitude -- than a directed beam from any of Earth's large, or even intermediate, radio telescopes." (Interestingly, none other than Seth Shostak of SETI is credited with this observation.)
So right now it looks like our C-Index is ~3 light years. If you're interested in this kind of thing you probably already know this isn't even as far as the next closest star, which is 4.3 light years away. They could be right there, chattering just as loud as us, and we still wouldn't know.