*a b / a*

**≠**

*b*. In this multiplication, the imaginary part of

*b*that is perpendicular to the imaginary part of

*a*is rotated over an angle that is twice the complex phase

**φ**of

*a*.This fact means that if φ

**=**π/4, then the rotation

*a b / a*

*shifts*

*b*

_{⊥}

*to another dimension*. This result puts quaternions for which the size of the real part equals the size of the imaginary part in a special category. A rotation over π/2 radians can implement switches between tri-states. In fact the color switch of a quark represents such a switch.

The symmetry flavor of quarks is anisotropic. The members of the hop landing location swarm of a quark belong to a discrepant parameter space. The special quaternion pairs can switch the symmetry flavor of these members. Thus the pair can switch the color charge of quarks. This means that in such pairs, the quaternions behave like

*. This does not explain how these pairs can implement the full activity of gluons. The quaternion pair must be enabled to rotate each member of the swarm.*

**gluons**Quaternionic number systems exist in versions that differ in the way that they are ordered. This ordering can be achieved by a Cartesian coordinate system and that can be followed by ordering via a polar coordinate system. If one dimension is ordered differently, then the two number systems differ in the handedness of the external product of the imaginary parts. Thus members of these discrepant number systems cannot be multiplied. Rotating with an imaginary quaternion such that the discrepant direction is reversed can unblock the condition.

It is possible that reality implements such rotations. This may happen at the reflection instants of the zigzag of elementary particles. Observers perceive these events as creation and annihilation events of pairs of particles that are each others antiparticle.

The gluon activity affects anisotropic particles, such as quarks. It does not affect isotropic particles, such as electrons, positrons and neutrinos.

How reality implements such phenomena is still unclear. But a good chance exist that reality exploits quaternions for such purposes.