system
Given the following post, respond as if you're commenting on Reddit:
human
What is missing from the theoretical model of physics that prevents us from replicating everything as a simulation? (something along the lines of the matrix)

 What sort of computing power would you need for that kind of simulation?
gpt
Too much computing power. The fundamental issue is that the number of interactions you need to calculate increases as the factorial of the number of things in your interaction. Let me give an example.

Lets pretend that there are 2 electrons in our simulation, and we want to keep track of their behavior. In this case, there are only 2 forces we need to calculate: the force of both electrons on each other. Now lets say we add another electron to the simulation and label them A, B, and C. Now we have 3 objects, but now there are 6 interactions: A on B, B on A, A on C, C on A, B on C, and C on B. ~~(Or, 3 factorial, which is 3 x 2). If we had 4 objects, there would be 4 x 3 x 2 = 24 interactions, and so on. As you can see, the number of interactions increases extremely quickly. By the time you get to 60 electrons, you need to calculate about 10^82 different interactions- a number bigger than the number of atoms in the visible universe. Let me re-iterate that: Fully simulating 60 electrons would require more calculations than there are atoms in the universe.~~

Edit: as others have pointed out, this is incorrect. The number of interactions scales as n^2 not n!.

The end result of all of this is that we cannot take our fundamental understanding of the universe and use it to simulate anything but the most simple of systems. Instead, simulations need to use simplified models and shortcuts in order to get reasonable calculation times.