Are we living in a computer simulation?

Let's figure out a testable hypothesis for whether we are not living in a computer simulation. The Turing machine is a model for all computers. The memory of a Turing machine is countably infinite. If we can show that the universe that we live in has uncountably infinite objects or positions or time divisions then that would imply we are not living in a computer simulation because a computer can only have countably infinite states.