  We study the three dimensional many-particle quantum dynamics in mean-field
setting. We forge together the hierarchy method and the modulated energy
method. We prove rigorously that the compressible Euler equation is the limit
as the particle number tends to infinity and the Planck's constant tends to
zero. We establish strong and quantitative microscopic to macroscopic
convergence of mass and momentum densities up to the 1st blow up time of the
limiting Euler equation. We justify that the macroscopic pressure emerges from
the space-time averages of microscopic interactions, which are in fact,
Strichartz-type bounds. We have hence found a physical meaning for Strichartz
type bounds which were first raised by Klainerman and Machedon in this context.
