In the successful theory of quantum chromodynamics 8 colored gluons are responsible for holding the quarks together in all hadrons classified as baryons and mesons. These 8 gluons are constructed from 6 color charges: red, green, blue, antired, antigreen, and antiblue taken two at a time such that 8 pairs are made of from a combination of 1 color charge and 1 anticolor charge: (1) red-antiblue, (2) red-antigreen, (3) blue-antired, (4) blue-antigreen, (5) green-antired, (6) green-antiblue. Gluons 7 and 8 are simply selected from the dual combinations of red-antired, green-antigreen, and blue-antiblue. These 8 gluons exactly correspond to the 8 traceless Hermitian 3 by 3 matrices introduced by Gell-Mann as a consequence of the special unitary group SU(3) all with determinant equal to 1 in order to preserve gauge invariance symmetry for all colorless elementary particles.


In the proposed quantum theory of the space-time continuum, these gluons are replaced by 8 directional invariance properties. Each property is represented by one of two distinct Möbius topologies. These are the H-pluses and the H-minuses. One of the other differences is that these two topologies are also represented by matrices called Hadamard matrices. Unlike Hermitian matrices, these have determinant zero but not traceless. The trace of a matrix is defined as the sum of the elements along the main diagonal. Furthermore, Hadamard matrices are not limited by their orders. The second order has a special property not shared by any higher order matrices. They can be extracted from the inverse of any 2 by 2 submatrix of a sieve of Diophantus. A sieve of Diophantus is a mathematical construct of an infinite order matrix whose elements are repeated spanning of the set of whole numbers without the number 1 and each element is found by the Diophantine equation: 2m+3n where m and n are respectively the row and column index taking values from zero to infinity. Hadamard algebra can be formulated such that matrix multiplications indicate the mass property of physical reality while matrix additions indicate the electric charge property of the same physical reality. The two fundamental 2 by 2 Hadamard matrices represent the two Möbius topologies mentioned earlier. Each pair gives a colorless topology, or equivalently a directionless topology.