State

In the pilitron theory, space-time is described as a set of states - for each position and each time, there is a state. It is denoted by $$\mathbf{S}$$ and defined as the vector:


 * $$\mathbf{S} = \left[\mathcal{L}, q, \chi, m, s, \mathbf{D}\right]$$

where:


 * $$\mathcal{L}$$ is the Lagrangian.
 * $$q$$ is the electrical charge.
 * $$\chi$$ is color charge.
 * $$m$$ is the mass.
 * $$s$$ is the spin.
 * $$\mathbf{D}$$ is the direction of motion counterpart.

Based on $$\mathbf{D}$$, we can figure out the true direction of motion, $$\mathbf{D}_R$$, by:


 * $$\mathbf{D}_R = \frac{\mathbf{D}}{|\mathbf{D}|}$$

Vacuum state
The vacuum state is the state of space that contains no matter. It is represented by $$\mathbf{V}$$ and its value is:


 * $$\mathbf{V} = \left[\mathsf{L}_V, 0, 0, 0, 0, \mathsf{D}_V\right]$$

Where:


 * $$\mathsf{L}_V$$ is the distribution of vacuum lagrangians.
 * $$\mathsf{D}_V$$ is the distribution of all possible directions of motion.