Lets define $P$ a physics over a set $X={particles,waves,...}$ endowed with the equivalence relation $E:X \rightarrow X \times X$, where $E$ being the associated energy function.
>Theorem
$\forall x,y \in X$, $xEy$ is an equivalence relationship.
>Proof
i) $xEx$
We know that $x = x /Rightarrow E(x)=E(x)$
ii) $xEy /Rightarrow yEx$
We also know that if two elements of $E$ are such that $E(x)=E(y)$ then $E(y)=E(x)$
iii) $xEy$ and $yEz /Rightarrow xEz$
It follows from ii) that $E(x)=E(z)$