How processor speed would be required to render and run (operate) this world? Infinite?

Question

The question is straight & simple and it needs big figures!

Answer 1

It's going to have to be a massively parallel processor, where each CPU would be dedicated to "modeling" the behavior of a single particle.  So something on the order of N processors, where N is the number of particles contained in the world, would be required.  Particles might have to be defined at the sub-atomic level, since nuclear decay processes are important.  So to get a rough idea, take the total mass of the planet and divide by the mass of a proton, then double that number since there have to be as many electrons and protons.  I don't think you have to go below protons/neutrons/electrons, since at typical planetary energy levels you don't protons decaying spontaneously.  Probably you would have to account for cosmic rays, but that's going to be a small number compared to the number of protons, neutrons and electrons.  I get this to be around 10^52 total particles, so 10^52 CPUs.  

As for CPU speed, in order to run in real-time, the clock speed has to be faster than the fastest process being modeled.  That would probably be things like nuclear relaxation times.  Maybe estimate on the order of yocto-seconds (10^-24 s).  So the speed in terms of frequency has to be at least twice the inverse, so on the order of 2 yotto-Hz (2x10^24 Hz), probably a good deal faster.  

But I could be off by several orders of magnitude either way since I didn't sit down and figure out the scales you would have to model carefully.