Sir Roger Penrose came to speak at my university today; in between the informal Q&A session and my preparatory reading up on his work, my mind wandered and I had an interesting thought. I'm not well acquainted with the topics relevant to this thought, so I welcome corrections. In any case, I'd be interested to hear opinions.

Suppose that the entire state of the universe can be described at any point in time (this must be true; the universe itself is that description). Suppose that there is some system of rules or laws P (a "theory of everything") according to which the universe's state evolves. Suppose that we know P. A natural question would be, "according to P, will the universe end?"

P could not possibly conclude that the universe will end; the end of the universe implies the end of any evolving state/program/&c and therefore P will be able to tell whether any evolving state would halt, and this would contradict the uncomputability of the halting problem.

Therefore, either P will conclude that the universe will never end, or there is no such P, in which case we can't know whether the universe will end.

I'm sure that I have an incomplete understanding of some of what I'm talking about and/or I have misformulated something. I haven't even really thought this through; I'm in a lecture right now.

Thoughts?