Structure of the World Crystal

Abstract

Identifying space with a superconducting cosmic dust, the structure of the ‘world crystal’ is built. Particles moving on open geodesics are assimilated with the ‘electron gas’ in a lattice, and those moving on closed geodesics with nodes of the same lattice. By considering that this kind of structure may be achieved by pinning on a background gravitomagnetic field, the properties of such fields are studied. From this analysis and computing the background energy we are lead to a Cantorian-fractal structure of space–time, which allows one to interpret the gravitational interaction in terms of a mechanism similar to the composite fermions mechanism.

Some properties of the world crystal in fractal spacetime theory.

“…where we considered that k = 2m 0 Dω (Nottale 1996;Agop et al . 1998a), it results that the mean speed of a particle in the spatial crystal (equation 9) may be understood as the group speed of the Bloch waves (equation 10).…”

“…Using this theory it was proved that motions in the solar system, in double galaxies and in the universe are quantised (Agop et al . 1998a;Nottale 1998).…”

“…1998a;Nottale 1998). In the same context, by identifying space with a superconducting cosmic dust and by supposing that in the presence of a background gravitomagnetic field this 'matter' orders itself as a crystal, called the 'world crystal', we have shown that the physical spacetime is fractal (Agop et al . 1998b(Agop et al .…”

“…In the present work we suppose that the physical spacetime is fractal and that it orders itself as a crystal in the presence of a background gravitomagnetic field (Ciubotariu and Agop 1996;Agop et al . 1998bAgop et al .…”