It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength λ inside a domain of (normalized) size of the order of n, there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information √ channels across these two regions is only of the order of n, so the per-user information capacity must follow an inverse square-root of n law. This result shows that claims of linear capacity scaling, and consequent constant per-node rate, are artifacts of unrealistic channel modeling assumptions. More generally, it shows that information-theoretic limits of wireless communication problems can be obtained without relying on stochastic fading channel models, but studying their physical geometric structure.