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A quantum vacuum corresponds to closed loops of particle-antiparticle pairs, in the language of Feynman diagrams. There is no relation between $E$ and $p$ for these particles, i.e., they are not on their mass shell. It is suggested that the QV is insensitive to the direction of time (seen as an irreversable thermodynamic process), but I'm not sure what this means. On top of that it is said that we can't make a mental picture of a QV, and it's purely a mathematical construct (which means we can make a time reversal operation on the QV). But it has to correspond something physical. So suppose we could make a film of the process (which involves time), could we see a difference between the film running forwards or backwards. That is, is the QFT vacuum $T$-invariant?

Qmechanic
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Deschele Schilder
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A quantum vacuum is an eigenstate of the Hamiltonian, so the energy is certain and the occupation numbers are certain too. "Fluctuations" of some variables (like $x$ and $p$) do not change this fact. So it is a T-invariant state.

Vladimir Kalitvianski
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