Do you think, that it would be possible to run a infinite and recursive simulation of the universe on an turing machine?
The concept of the Turing machine is a mathematical concept representing exactly that which can be computed (is 'decidable'). Therefore, the answer to that question depends on your worldview.
In a strict scientific-deterministic worldview, the world could ultimately be modeled in a mathematical model, and iterations of that model would be well-defined. Therefore, by definition, a Turing machine could implement that model.
Other worldviews may not accommodate for such possibilities. Hume comes to mind, claiming causation cannot be proven to exist.