  The cosmological constant (lambda) of general relativity is a natural
consequence of embedding Einstein's theory in a five-dimensional theory of the
type needed for unification. The exact 5D solution for lambda less than 0 shows
waves in ordinary 3D space with properties similar to those of de Broglie or
matter waves. Here the dispersion relation is derived for matter waves in a toy
two-phase model, where regions with lambda less than 0 and lambda greater than
0 average on the large scale to lambda = 0, thus providing in principle a
resolution of the cosmological-constant problem. A striking result of the
analysis is that the dispersion relation is bimodal, with a well-defined window
of high-frequency transmission which effectively defines the speed of light.
