[@Susskind2]). But we see that this is only a necessary but not a sufficient property for an entropy-area law to hold. We hence arrive at the preliminary conclusion:

From our preceding arguments and observations we conclude that the holographic principle implies that the fluctuation patterns in $V$ are long-range anticorrelated in a fine-tuned way on a microscopic scale and are essentially fixed by the state of the fluctuations on the bounding surface. The dynamical mechanism, which generates these long-range correlations must however, by necessity, have quite unusual properties (cf. subsection \[bulkboundary\]).

Before we derive the wormhole structure of the quantum vacuum on a primordial scale in the next sections, we continue with the general analysis of the pattern of vacuum fluctuations and derive some useful properties of it.

A particular role is usually played by the energy and its fluctuations. Furthermore, vacuum fluctuations are frequently discussed together with the so-called [zero-point energies]{}. While they are not exactly the same, they are closely related. Both occur also in connection with the [cosmological constant problem]{} (to mention only a few sources see e.g. [@Zinkernagel1],[@Zinkernagel2],[@Nernst],[@Enz],[@Boyer],[@Weinberg],[@Straumann]).

In the simplest examples like e.g. the quantized harmonic oscillator or the electromagnetic field we have $$H=P^2/2m+m\omega/2\cdot Q^2$$ 