Interaction potential

The interaction potential is the potential of transmitting energy between 2 pilitrons next to each other. The interaction potential is related to energy $$E$$ and spin potential $$S$$ of two pilitrons by:


 * $$\iota = \frac{S_1 + S_2\sqrt{E_1 E_2}}{2\eta}$$

Conservation of Interaction
There is a limited number of states in a given volume due to the conservation of interaction. When interaction potentials of a pilitron in the three dimensions ($$x$$, $$y$$ and $$z$$) times the two directions ($$+$$ and $$-$$) are added up:


 * $$\iota_x^+ + \iota_x^- + \iota_y^+ + \iota_y^- + \iota_z^+ + \iota_z^- = T \,\!$$

The total $$T$$ is conserved, ie. when measured at any given moment, it will always remain constant, and since interaction is quantized, there is a limited number of possible interaction potentials.

Geometrical Notation
Since each pilitron has 6 connections, which is 2 directions times 3 dimensions, a "geometry table" can be used to describe its interaction potentials in each direction. The rows are dimensions, labelled x, y, and z, and the columns are directions, labelled - and +. So, if we denote the interaction potentials as in the above equation, and put them onto a geometry table, it would look as follows:



\begin{vmatrix} \iota_{x}^{-} & \iota_{x}^{+} \\ \iota_{y}^{-} & \iota_{y}^{+} \\ \iota_{z}^{-} & \iota_{z}^{+} \end{vmatrix} $$

So the sum of all the numbers in the table is $$T$$, the conserved total.

Equations
Interaction potential over a certain distance and time can be given by:


 * $$\frac{\iota_1 \times \iota_2 \times \iota_3 \times \iota_4 \times ...}{t}$$

Which is the product of all interactions along a path, divided by time.