ON SOME POSSIBLE PHYSICAL CONSEQUENCES OF THE EMBEDDING OF SUPERCRYSTALS INTO THE SPACES WITH HIGHER AND HIGHER DIMENSIONS AND OF THE COMPACTION OF THESE SPACES
Jerzy Warczewski & Pawel Gusin
University of Silesia, Institute of Physics,
ul. Uniwersytecka 4, Pl-40007 Katowice, Poland,
e-mail: warcz@us.edu.pl
Keywords: Aperiodic crystals,
embedding procedure, atomic surfaces, compaction procedure,
d-dimensional torus, group of the automorphisms, real matter,
dark matter
The de Wolff's embedding procedure of the aperiodic structures is extended up to the higher dimensional spaces. The assumption is made about the dimension limit of these spaces. In this procedure the real atoms transform into atomic surfaces. The compaction of the primary space (the space with the highest dimension under consideration) is discussed.
The existence of the general relation between the aperiodic crystal structure and the invariants of the group of the automorphisms of the d-dimensional torus (being the result of the compaction of the atomic surface) is pointed out and proved for d = 1 and 2 [1].
The hypotheses are put forward about the
behaviour of the atomic surfaces in higher dimensions, about the
interpretation of the aperiodic structures as an analogy to the
background radiation as well as about the creation of both the
real matter and the dark matter [2] .