[semi-extrinsic]

I suppose you meant 6*N? Which is a lot better, but still intractable. And anyway, we don't exactly resolve molecules in e.g. turbulent flow simulations, yet they still take tens, even hundreds of millions of CPU-hours.

[noobermin]

6*N, yes. Pretty bad mistake there. But yes, even if you don't model every particle and restrict yourself to "parcels" of fluid like in most simulations, you still have a very difficult problem.

[igravious]

Okay, this is really showing my ignorance but why 6?

You start off with 4 (3 space plus one time (ignoring 11-dimensional space-time)) and add which dimensions exactly? Can the individual interactions between wave/particles be reduced to 2 dimensions? Aren't they going to interact along the whole range of forces they exert: gravitational, weak, electromagnetic, strong?

[kilotaras]

3 dimensions for position + 3 dimensions for speed

[igravious]

3 dimensions for momentum in other words? Surely it cannot be that simple. That's astounding.

[etatoby]

Unless you consider quantum effects, which are probably relevant in this situation, then it's an exponentially larger problem space.