Energophilia

In pilitron physics, energophilia is a force that causes energy to attract energy, and on large scales is the cause of gravity.

Tension
The tension factor, or tension function, as described in vacuum lagrangian, describes the curvature of space which causes energophilia. For 2 arbitrarily small regions of space containing energy that are immediately next to each other, the tension is:


 * $$\tau = \frac{\mathcal{L}_1 + E_1}{\mathcal{L}_2 + E_2}$$

Field
The energophillic field fills the entire Universe, and does not "expand" at any rate, in the way that the electromagnetic field expands away from the source at the speed of light. Instead, the energophillic field has an infinetessimal range. It can be described with the following equation:


 * $$\frac{\partial \mathbf{\Phi}(E, \mathbf{x})}{\partial \mathbf{x}} = \frac{d\tau\left(V\right)}{dV}$$

We can also take the derivative relative to energy - this will tell us how space changes when energy contained in it changes. Just like for when we take an infinitessimly small distance the Lagrangian and therefore the tension changes infinitessimly, if we change the energy infinitessimly, the tension will also change infinitessimly, so we have:


 * $$\frac{\partial \mathbf{\Phi}(E, \mathbf{x})}{\partial E} = \frac{d\tau\left(V\right)}{dV}$$

Which relates energy and space:


 * $$\frac{\partial \mathbf{\Phi}(E, \mathbf{x})}{\partial \mathbf{x}} = \frac{\partial \mathbf{\Phi}(E, \mathbf{x})}{\partial E}$$

Let's take an arbitrary value of $$E$$ and $$\mathbf{x}$$, and say that the field function solves to $$\mathbf{A}$$. The equation then tells us that:


 * $$\frac{\mathbf{A}}{E} \propto \frac{\mathbf{A}}{\mathbf{x}}$$

Which implies that:


 * $$E \propto \mathbf{x}$$

Which means that there is a factor which converts distance to some energy - we call this the energetic factor, $$\bar{\omega}$$:


 * $$E = \bar{\omega}\mathbf{x}$$