Say I have a theory with only one (energy) scale, e.g. one given by the fundamental constants

$$\epsilon=\sqrt{\dfrac{\hbar c^5}{G}}.$$

In this case, where I can't compare to something else, is there a way to argue that

$$\epsilon<\epsilon^2<\epsilon^3<\dots\ ?$$

By that reasoning, can there be a (field?) theory, where values are obtained from some expansion like in a path integral (which needs a hierarchy of that sort)?

If you really only need/have a theory with $\hbar, c, G$, how can energies like particle masses be *deduced* from the theory (instead of being experimental input)? And then if, at best, the theory predicts some mass of a particle $\phi$ to be $m_\phi=a_\phi\dfrac{\epsilon\ }{\ c^2}$, then the number $a_\phi$ must have some geometrical meaning, right?

This post imported from StackExchange Physics at 2014-04-05 04:28 (UCT), posted by SE-user NiftyKitty95