Path principle

In pilitron physics, the path principle is a principle that controls how objects move in space and time.

The principle
The path principle says that any fundamental particle without mass will try to move in all directions possible, but will only actually move across the path that takes the most action (most energy and most time). If there are 2 possible paths with the same action required, the particle will split into 2 entangled pieces.

The reason for this principle is that a particle will always move towards the direction of the highest Lagrangian, because the other Lagrangians cannot cancel it out.

Action
Action, $$\mathcal{A}$$ (sometimes $$\mathcal{S}$$) is the integral over time of a particle's Lagrangian:


 * $$\mathcal{A} = \int_{t=A}^{t=B} \mathcal{L} dt$$

The Lagrangian, therefore, is the derivative of action in relation to time:


 * $$\mathcal{A}^\prime(t) = \mathcal{L}(t)$$

Therefore the immediate change in path is determined by the highest Lagrangian for each possible path.