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Space-Time Events

Space-Time Events
 k\delta_{\hat{m}}\delta_{\hat{e}}\delta_{\theta}
1+10+1
20-1+1
3-10+1
40+1+1
5+10-1
60-1-1
7-10-1
80+1-1

Consider a particle P described by a repetitive chain of events that are written as

\Psi^{\mathsf{P}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\Omega}_{3}  \, \ldots    \, \right)

where each cycle can be parsed into eight sub-orbital components

\mathsf{\Omega}^{\mathsf{P}} = \left( \mathsf{P}_{1}, \, \mathsf{P}_{2} \, \ldots \, \mathsf{P}_{k} \, \ldots \, \mathsf{P}_{8} \right)

so that there is one component  \mathsf{P}_{k} for each combination of the phase  \delta_{\theta}, the magnetic polarity  \delta_{\hat{m}} and the electric polarity  \delta_{\hat{e}} as shown in the accompanying table. This arrangement ensures that P has a fixed relationship with the electric, magnetic and polar axes. It provides a logically sufficient array of sensation to make an account of events that is fully three-dimensional. We can assign  \bar{r}, a well-defined position, and  t, the time of occurrence to these events without making further assumptions. Compound events like \mathsf{\Omega} are called space-time events. Chains of space-time events like  \Psi are called trajectories. Particle trajectories are generically written as  \Psi \!  \left( \bar{r}, t \right) to emphasize that their events have space-time coordinates.

Orientation of a space-time event in quark space. Red numbers indicate values of k.

This image shows the relationship between spatial axes and P’s sub-orbital components. The eight components may be composed from some miscellaneous collection of quarks beyond the bare minimum required to establish a spatial orientation. So sub-orbital events are shown as different pie-shaped wedges. Events  \mathsf{P}_{5} through  \mathsf{P}_{8} are out-of-phase with events  \mathsf{P}_{1} through  \mathsf{P}_{4} so they are depicted in a lower tier on the polar axis. Click here for a movie showing all eight sub-orbital events in an atomic-cycle.

Coherent Interactions

Consider some generic particles \mathbb{X}, \mathbb{Y} and \mathbb{Z} that are objectified from space-time events like the ones defined above. And let these particles interact with each other as \mathbb{X} + \mathbb{Y} \leftrightarrow \mathbb{Z}. If this process preserves relationships between sub-orbital events such that

\mathsf{P}_{1}^{ \, \mathbb{X}} + \mathsf{P}_{1}^{ \, \mathbb{Y}} \leftrightarrow  \mathsf{P}_{1}^{ \, \mathbb{Z}}

\mathsf{P}_{2}^{ \, \mathbb{X}} + \mathsf{P}_{2}^{ \, \mathbb{Y}} \leftrightarrow  \mathsf{P}_{2}^{ \, \mathbb{Z}}

\mathsf{P}_{3}^{ \, \mathbb{X}} + \mathsf{P}_{3}^{ \, \mathbb{Y}} \leftrightarrow  \mathsf{P}_{3}^{ \, \mathbb{Z}}

. . .

\mathsf{P}_{8}^{ \, \mathbb{X}} + \mathsf{P}_{8}^{ \, \mathbb{Y}} \leftrightarrow  \mathsf{P}_{8}^{ \, \mathbb{Z}}

then we say that the interaction is coherent. That is, relationships that determine the phase and orientation do not get mixed-up when a particle is formed or decomposed. Alternatively, we say that an interaction is incoherent if information about phase and orientation gets scrambled during the process.