1 =         i =         j =         k =


-1 =       -i =       -j =       -k =       Quaternions


s1 =         s2 =         s3 =       Pauli matrices


s1 s2 s3    
s1 1 i -j    
s2 -i 1 k    
s3 j -k 1   s1 * s2 = i, s1 * s3 = -j, and so on.

ijk = s1 * s2 * s3 * s1 * s2 * s3 = -1


DARK       -1 * -1 = 1 * 1 = -1

DARK       -1 * 1 = 1 * -1 = 1


DARK       -i * -i = i * i = 1

DARK       -i * i = i * -i = -1


DARK       1 * i = -1 * -i = -i

DARK       1 * -i = -1 * i = i               Dark multiplication rules


In the fourth line DARK -i * i = i * -i = -1 one recognizes the vacuum marble pair ( i   -i ) yielding -1, the backward time evolving vacuum as observed by us.

DARK = =


      s1 s2 s3
    s1 -1 -i j
    s2 i -1 -k
DARK   s3 -j k -1

See also

paragraph Dark multiplication rules at page 2 of EXPANSION OF THE UNIVERSE

Colors as quaternions as matrices, page 9 of QQD