![]() ![]() If you could simulate a large number of Standard Model particles, with sufficient temporal and spatial resolution to capture all the interactions, and enough temporal and spatial range to be able to measure fluid effects, there's no reason to expect you could not, say, calculate the viscosity of water from the Standard Model. There are, indeed, papers that try to do calculations like this, such as, although not starting from the Standard Model, but from "one level down" (interactions between molecules). ![]() In principle, you could try to compute these quantities from a deeper theory. The effect of the layers of physics below the fluid description, which nest like Russian dolls at least until you reach the Standard Model, is wrapped up in parameters like the viscosity of water, which are measured. What matters are the symmetries of the underlying processes, and the fact that the interactions are local. In an important sense, the details of what lies underneath do not matter. You would still get an identical long-distance fluid mechanical set of equations, even if the Standard Model were replaced by another local theory of physics obeying the same symmetries. ![]() In this sense, a lot of the details of the interactions between particles is actually irrelevant in fluid mechanics, by design. Then, one makes the approximation that the evolution of the average quantities will not depend on higher order statistics of the distribution, which describe complicated interactions between particles (so-called collision terms). One way to derive fluid dynamics is to start from the equations of motion for $N$ particles, and use these to compute the evolution of average quantities (like the density) of the distribution of particles. ![]()
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