  In this paper we consider the question of the degree to which negative and
positive energy are intertwined. We examine in more detail a previously studied
quantum state of the massless minimally coupled scalar field, which we call a
``Helfer state''. This is a state in which the energy density can be made
arbitrarily negative over an arbitrarily large region of space, but only at one
instant in time. In the Helfer state, the negative energy density is
accompanied by rapidly time-varying energy fluxes. It is the latter feature
which allows the quantum inequalities, bounds which restrict the magnitude and
duration of negative energy, to hold for this class of states. An observer who
initially passes through the negative energy region will quickly encounter
fluxes of positive energy which subsequently enter the region. We examine in
detail the correlation between the energy density and flux in the Helfer state
in terms of their expectation values. We then study the correlation function
between energy density and flux in the Minkowski vacuum state, for a massless
minimally coupled scalar field in both two and four dimensions. In this latter
analysis we examine correlation functions rather than expectation values.
Remarkably, we see qualitatively similar behavior to that in the Helfer state.
More specifically, an initial negative energy vacuum fluctuation in some region
of space is correlated with a subsequent flux fluctuation of positive energy
into the region. We speculate that the mechanism which ensures that the quantum
inequalities hold in the Helfer state, as well as in other quantum states
associated with negative energy, is, at least in some sense, already
``encoded'' in the fluctuations of the vacuum.
