Well since we know the laws of physics can be used to implement a Turing machine, we therefore know the laws of physics support computation.

If I remember my college computability course correctly, any system that can be used to implement a Turing machine is itself Turing complete. Even if by no other means than to implement a Turing machine.

Besides you really don't need much: Branching, jumps, and a way to read/write. Voila, turing complete.

Infinite memory is helpful, but we consider computers Turing complete despite not having infinite memory. If you take infinite memory as a hard requirement then the entire universe together is not Turing complete. But that isn't useful so we often waive that part.