(Abridged) Using a 100 ks XMM-Newton exposure of NGC 4051, we show that the time evolution of the ionization state of the X-ray absorbers in response to the rapid and highly variable X-ray continuum constrains all the main physical and geometrical properties of an AGN Warm Absorber wind. The absorber consists of two different ionization components. By tracking the response in the opacity of the gas in each component to changes in the ionizing continuum, we were able to constrain the electron density of the system. The measured densities require that the high and low ionization absorbing components of NGC 4051 must be compact, at distances 0.5-1.0 l-d (2200 - 4400Rs) and < 3.5 l-d (< 15800Rs) from the continuum source, respectively. This rules out an origin in the dusty obscuring torus, as the dust sublimation radius is at least an order of magnitude larger (>12 l-d). An accretion disk origin for the warm absorber wind is strongly suggested, and an association with the high ionization, HeII emitting, broad emission line region (radius <2 l-d) is possible. The two detected phases are consistent with pressure equilibrium, which suggests that the absorber consists of a two phase medium. A radial flow in a spherical geometry is unlikely, and a conical wind geometry is preferred. The implied mass outflow rate from this wind, can be well constrained, and is 2-5% of the mass accretion rate. If the mass outflow rate scaling with accretion rate is representative of all quasars, our results imply that warm absorbers in powerful quasars are unlikely to produce important evolutionary effects on their larger environment, unless we are observing the winds before they get fully accelerated. Only in such a scenario can AGN winds be important for cosmic feedback.
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