If space-time is finitely quantified, then we end up in Nietche's universe which must eventually simply repeat itself. There are finitely many ultimate positions, and as soon as you get back into one you have already been in, you are looping. Any computation about a finite system can be described by the Turing machine that just considers every available position in the system and checks whether each one happens or not.
But we generally do not believe that. If space (and therefore time) is continuous or otherwise admits infinite potential variation, and if arithmetic of any sort describes how space can be divided, then given Goedel, its ultimate behavior cannot be described by Turing machines.
According to Goedel's Theorem there have to be truths that cannot be verified by first order logic in any infinite system that is consistent and handles arithmetic, no matter how complete the information available about the system. (Flipping it over, if you gave complete information about a system that handles arithmetic, it would turn out to be logically inconsistent.)
The universal Turing machine is just a very clear formulation of the exact system of first-order logic that Goedel was investigating.
In the end, there are strictly more potentially relevant facts in the universe described by any language than there are Turing machines processing that language available to model them. And that does not even consider potential truths that might remain inexpressible in the language itself.