Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales

We discuss the phase transition in (3 + 1)-dimensional lambda Phi(4) theory from a very physical perspective. The particles of the symmetric phase (phions) interact Via a hard-core repulsion and an induced, long-range -1/r(3) attraction. If the phion mass is sufficiently small, the lowest-energy state is not the empty state with no phions, but is a state with a nonzero density of phions Bose-Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with [Phi] not equal 0 and its excitations (phonons in atomic physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m(2) passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M-h. This interesting physics coexists with triviality; all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio m/M-h, which goes to zero in the continuum limit, can be viewed as a measure of nonlocality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.