The dispersion relation for matter waves in a twophase vacuum
Abstract
The cosmological constant Λ of general relativity is a natural consequence of embedding Einstein's theory in a fivedimensional (5D) theory of the type needed for unification. The exact 5D solution for Λ<0 shows waves in ordinary threedimensional (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 twophase model, where regions with Λ<0 and Λ>0 average on the large scale to Λ≃0, thus providing in principle a resolution of the cosmologicalconstant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a welldefined window of highfrequency transmission which effectively defines the speed of light.
 Publication:

Modern Physics Letters A
 Pub Date:
 October 2014
 DOI:
 10.1142/S0217732314501685
 arXiv:
 arXiv:1411.0046
 Bibcode:
 2014MPLA...2950168W
 Keywords:

 Cosmologicalconstant problem;
 waveparticle duality;
 extra dimensions;
 11.10.Kk;
 04.50.+h;
 04.90+3;
 Field theories in dimensions other than four;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 General Relativity and Quantum Cosmology
 EPrint:
 Mod. Phys. Lett. A v.29, No. 31 (2014), 9 pp