# How Much Computing Power would be Required to Fully Simulate a Cubic Meter?

Imagine you want to simulate a cubic meter down to the particle. By following the Standard Model and other basic physical equations, how much computing power would be required to do this, in say, a day?

Thanks

• Seems like a question for what-if.xkcd.com – Denis Sep 17 '15 at 12:48
• while currently nonmainstream/ sideline think this is a valid research question/ problem crossing physics & CS & relates to questions about the intrinsic computational aspects of universe/ physics laws/ reality associated with digital physics. fyi this question is somewhat related, what is the volume of information – vzn Sep 18 '15 at 5:34
• This article touches on the issue, if anyone's interested pbs.org/wgbh/nova/blogs/physics/2014/04/… – APCoding Sep 19 '15 at 0:32
• A wiki article en.wikipedia.org/wiki/Quantum_simulator – APCoding Sep 19 '15 at 0:36
• The answers at Physics.SE are fairly complete. In short: it is not likely to be feasible in the foreseeable future, no, and no. – András Salamon Sep 20 '15 at 14:21

tricky question! there is some diverse crosscutting research into this question, and will attempt to outline it, but will in the end take the position here that the question is contradictory/ impossible at heart (and anticipating some this may be a controversial conclusion). here are two key recent references from a physics pov addressing your question.

a rough complexity theory estimate of "simulating particle physics" is to count the number of particles, and there are about $O(n^2)$ interactions between particles, and many supercomputer simulations of particle dynamics fit this. so as a rough bound, one would pick the smallest particles, but, wait! the standard model has many subatomic particles! so one might use neutrinos, one of the smallest known stable particles, as an estimate... but then what about unstable particles such as quarks/ leptons?

there is also the whole other problematic accuracy/ precision problem of the butterfly effect long known in computational physics aka "sensitive dependence on initial conditions".

Aaronson write in his essay Is There Anything Beyond Quantum Computing?:

Is there any such problem that couldn’t be solved efficiently by a quantum computer, but could be solved efficiently by some other computer allowed by the laws of physics?

so he sketches out weird physics such as black holes or quantum gravity that might not be simulable by a quantum computer. but flipping this whole essay on its head (in a manner it which it was unintended), what he is describing are frontier areas of physics that currently do not have complete/ definite physical theories known by humans (at best, only plausible candidates/ approximations floating around.) eg:

• black holes
• time curves
• quantum gravity