[warning: Clickbait title of the video: The answer is: “probably not”. He goes into great detail about that I think; watching now]
I found this nice answer on Quora:
Is it possible to simulate all of the laws of physics on a computer?
So a few months ago I would have said yes, but since then I have been to an online seminar given by Prof David Tong where he argued to the contrary. I would like to emphasise, David Tong is a Professor of theoretical physics at Cambridge, and has made a huge number of contributions to theoretical physics especially regarding Quantum Field Theory. In other words, he is a very good source!
He had two main arguments:
- The numerical sign problem – In short you can describe quantum mechanics in terms of something called path integrals, and there are significant problems with recreating these on a computer.
- Chiral Fermions (This is actually the main topic of the talk) – You say in your question give a “certain level of granularity”, you’re correct that this seems a natural suggesting if you want simulate the universe. However it turns out that there is something called Chrial fermions in our universe, and there are significant problems with putting these on this kind of lattice structure.
I have found a version of the same talk David gave elsewhere. He discusses both of the above in much more detail than I can give here (Only the first ~15 mins will probably be of interest to you, it turns quite technical after that): https://youtu.be/QPMn7SuiHP8