# Simulating a proton

How much computing power would it take to simulate a single proton from the bottom up, without taking any shortcuts whatsoever?

My current understanding is that:

1. A proton is basically a seething ball of virtual particles and antiparticles, all of which would have to be simulated.

2. The number of these is difficult to exactly determine or even define, but roughly speaking, depends on the minimum wavelength (maximum energy) at which things cut off (assuming there is such a cutoff, otherwise it's infinite).

3. It is conjectured (though as yet without hard evidence) that there is a cutoff at the Planck wavelength 10^-35 meters, which divided into the proton diameter 10^-15 meters would give on the order of 10^60 virtual particles.

4. Perfectly simulating a quantum system (to infinite precision) would as far as we currently know take infinite computing power, but simulating it to high enough precision that you can't tell the difference takes computation exponential in the number of particles, so the required computing power would be on the order of 10^10^60.

Is this more or less correct? (I'm aware that actually carrying out a computation of that size is physically impossible.)

• Related: physics.stackexchange.com/q/10262/520. While I am not conversant with the state of the art of lQCD in 2012, my take is that protons are light quark states, so you can expect this to be computational demanding. Note that lQCD is a well developed field already. – dmckee --- ex-moderator kitten Nov 14 '12 at 0:13
• I'd be surprised if you had to discretize down to the Planck length - some virtual particles are far more important than others, and the anomalous electron moment, e.g., gets to around double precision with ~$10^4$ or so contributions, iirc. Also, the cutoff isn't a physical thing - it's the point where physicists would stop placing money on the theory holding true. – user10851 Nov 14 '12 at 2:49