I guess we could try to see this as a modelling problem: how can we re-phrase the question so that it becomes computer science and not physics? I'll try to give a simple, concrete example of how we might try to do this, to get things started...
Let's replace the "universe" by something that is very discrete and simple (and finite!). Let's say that our universe is a finite cellular automaton. In particular, the whole world $W$ is an $n \times n$ grid.
Assume that the initial configuration of the world $W$ is arbitrary. Now the question seems to be the following: Can we choose a strict subset $C$ of $W$ ("computer"), and an initial state of $C$, that satisfies the following conditions:
We do not change the initial state of $W \setminus C$. (That is, we just "build our computer $C$", without tampering the world outside it.)
Then we can run any number of steps of the cellular automaton (the whole world $W$, including $C$ and any interactions between $W \setminus C$ and $C$).
We can read the current state of the world $W$ by merely inspecting $C$. (That is, $C$ must be a "simulation" of $W$. Note that we must be able to read the state of whole $W$, not only $W \setminus C$. In a sense, $C$ must be able to simulate both its outside and its inside!)
Now, is this doable? It might be tempting to use a counting argument (there are more states in $W$ than in $C$) and say that it is impossible. But this is not necessarily the case!
Let's assume that our cellular automaton is totalistic. Then what we can do is we simply let $C$ be the right half of our grid $W$, and let the initial configuration of $C$ be a mirror image of $W \setminus C$, so that everything is symmetric. That's it.
Start the automaton and see what happens. The current state of $W$ will always be equal to the state of $C$ + its mirror image. That is, merely inspecting $C$ is enough to tell what is the state of whole $W$.
(Of course here the computer interacts with $W$, and affects the future state of $W \setminus C$. But that's what happens in the real world, too.)
Now it might be interesting to see if there is a non-trivial answer to this question. For example, which CAs admit computers that have size smaller than half of $W$?