Random Thought #1 (I expect to have a lot of these)

Here's an interesting puzzle for you sci-fi nerds out there; is there a way to break the speed of light as far as communications technology is concerned? I'm not talking about transporting things faster than the speed of light. I'm talking about communicating over distances of light years. The reason that makes a difference is because someone who's trying to come up with communication technology has a clear advantage over someone who's trying to come up with transportation technology. Specifically, if you replicate an object, it's a different object, but if you replicate a message, it's the same message, so all the problems you have with nanotech teleporters could be escaped completely when it comes to communication- if you walk through a teleporter that disassembles your body and reassembles it at another location, you don't know whether or not the other person constitutes your identity and may have your consciousness phased out in the process. You don't have that issue with communicated messages.

So if you managed to develop a computer that was sophisticated enough to store the location and momentum of every particle in, oh, let's say a solar system, and powerful enough to calculate the trajectory and motion of all those particles at the same rate that those particles themselves changed, then placed that computer about a light year or so away from the solar system whose events its gradually plotting out, then you could actually have that computer predict what messages the denizens of its designated solar system are sending and print them out as they were being, oh, let's say dropped in a certain mailbox in said solar system.

Let's set aside for a second the fact that creating a computer of this complexity would be ridiculously and impossibly difficult. And let's assume that the messages printed out on the other side would be reasonably accurate if you made the appropriate modifications to the computer's predictions to account for quantum probability. Here are my questions-

Would you be able to make this computer without actually replicating the solar system that it was designed to keep track of? Is it possible for a computer to keep track of the relative position and momentum of a system of particles if it's less complex than that system? And if not, do you think it would be possible to omit enough irrelevant details about that solar system to make it possible to keep track of it without being as complex as it? For example, I'm guessing the computer would need less detailed data about uninhabited planets than about inhabited ones, less about inanimate objects than about animate ones, and could probably omit a lot of data about vestigial biological and psychological functions. But even omitting minute details about all those things (and for that matter, limiting the computer's calculations to just one solar system out of all the kajillions out there) might make a huge difference to the computer's calculations.