  Einstein theory can be embedded in Kaluza-Klein theory, and in particular all
4D vacuum solutions can be embedded in 5D (pure) canonical space where
spacetime is independent of the extra coordinate. The uniqueness of 5D
canonical space is quickly reproven, and its history and implications briefly
reviewed. For 4D anti-deSitter space, the 5D space involves a wave running
around spacetime, with an associated particle that has a local value of the
cosmological 'constant' proportional to the square of the mass.

General Relativity and Quantum Cosmology