as an operator (density). This can be seen as follows. If the quantized energy density were still positive, one can take the square root (via the spectral theorem) of e.g. the positive operator $H_V$ and get: $$0= (\Omega|H_V\Omega)= (H_V^{1/2}\Omega|H_V^{1/2}\Omega)$$ hence $$H_V^{1/2}\Omega=0$$ As $H_V^{1/2}$ is also a local observable this is a contradiction due to the Reeh-Schlieder theorem.

$H_V$ is not a positive operator, hence its spectrum contains negative spectral values. It is then easy to construct Hilbert-space vectors, $\psi$, so that the measurement of $H_V$ in $\psi$ yields negative values for the local energy.

Remark: We recently learned that this argument is originally attributed to Epstein (unpublished;[@Reeh] or see [@Summers1]), while the derivation which can be found in [@Gla] is a completely different one.

The important message (in our view) of all this is that, perhaps in contrast to naive expectation, the quantum vacuum contains a lot of negative energy excitations which globally exactly balance the positive excitations. One may now speculate about the possibility of making use of this observation.

\[worm\]Wormhole Spaces
=======================

In this section we want to describe (very) briefly and sketchily the three different lines of reasoning which lead us to the concept of [wormhole spaces]{}. 