Fisher order measure and Petri’s universe

Given a closed system described via an amplitude function ψ ( x ) , what is its level of order? We consider here a quantity R defined by the property that it decreases (or stays constant) after the system is coarse grained. It was recently found that (i) this quantity exhibits a series of properties that make it a good order-quantifier and (ii) for a very simple model of the universe the Hubble expansion does not in itself lead to changes in the value of R . Here we determine the value of the concomitant invariant for a somewhat more involved universe-model recently advanced by Petri. The answer is simply R = 2 ( r H r 0 − r 0 r H ) , where r H is a model’s parameter and r 0 is the Planck length. Thus, curiously, the Petri-order seems to be a geometric property and not one of its mass-energy levels. Numerically, R = 26.0 × 10 60 . This is a colossal number, which approximates other important cosmological constants such as the ratio of the mass of a typical star to that of the electron ∼ 1060, and microlevel constants such as exp ( 1 / α ) , where α is the fine structure constant.