As such large integrated fluctuations in a macroscopic region of the physical vacuum are not observed (they are in fact microscopic on macroscopic scales), we conclude:

The individual grains or supposed elementary DoF do not fluctuate approximately independently.

Remark: We note that this fact is also corroborated by other, independent observations.

We can refine the result further (cf. [@Requ1]) by assuming that the fluctuations in the individual grains are in fact not independent but correlated over a certain distance or, more precisely, are [short-range correlated]{}. In mathematical form this is expressed as [integrable correlations]{}. This allows that “positive” and “negative” deviations from the mean value can compensate each other more effectively. Letting e.g. $q(x)$ be the density of a certain physical observable and $Q_V:=\int_V q(x)\,d^n\!x$ the integral over $V$. In order that $$\langle Q_VQ_V\rangle^{1/2}\ll V^{1/2}$$ we proved in [@Requ1] that it is necessary that $$\int_V \!d^n\!y\,\langle q(x)q(y)\rangle\approx 0 \label{fluc}$$

We made a more detailed analysis in [@Requ1] under what physical conditions property (\[fluc\]) can be achieved, arriving at the result:

Nearly vanishing fluctuations in a macroscopic volume, $V$, together with short-range correlations imply that the fluctuations in the individual grains are anticorrelated in a fine-tuned and non-trivial way, i.e. positive 