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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.)

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Related: 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 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. – Chris White Nov 14 '12 at 2:49

Why would you want to do that? Models should be better by some strict margin than the data possibly gathered . This modeling is what is a continuous work at the LHC which is gathering data from the structure of the proton at the smallest scale experimentally available. The only way to probe/model the proton is by interactions, and that is limited by the experimental possibilities of validating the model.

Even this video is more useful than a hypothetical model of the proton at impossible to achieve in experiment accuracies. It gives a feeling of how we understand that nature works by reproducing our current knowledge.

Monte Carlo calculations are used to simulate the reactions happening , see Predictive Monte Carlo Tools for LHC Physics .

If one wants to learn how a watch works one does not need to look at the atoms composing it. The case of the proton, which is not a clock but a quantum mechanical object, is even more experimental accuracy dependent, as, what a proton is depends on the energy of the probe that looks at it.

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It depends on what you mean by taking no shortcuts. The impression I get from the lattice QCD literature is that at the current state of the art they can just about do realistic ab initio calculations of the physical properties of the light hadrons. See for example this recent review.

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