Definition
Negative energy density is a region of spacetime where the local energy density is less than that of the quantum vacuum — that is, less than zero by conventional reckoning.
Classical matter has non-negative energy density everywhere, but quantum field theory routinely allows local densities to dip below the vacuum value, provided certain integrated quantum-inequality bounds are satisfied.
Why it matters
How it works
In classical physics, every form of matter and radiation has positive energy density. The various "energy conditions" of general relativity — weak, dominant, strong, null — all encode the assumption that nowhere does the energy density (or appropriate combination of energy and pressure) become negative. From these conditions follow the Hawking-Penrose singularity theorems, the second law of black-hole mechanics, and chronology protection arguments.
Quantum field theory complicates this picture. The Casimir effect — two parallel conducting plates in vacuum experiencing an attractive force — was the first laboratory demonstration that the region between the plates can have an energy density lower than the surrounding vacuum, i.e. effectively negative. Squeezed-vacuum states of light routinely produce local negative-energy fluctuations. Hawking radiation itself involves negative-energy flux into the black hole.
But quantum field theory does not allow arbitrary violations. "Quantum inequalities" derived by Ford and Roman show that any negative-energy excursion of magnitude |ρ| can last at most a time τ such that |ρ| τ⁴ is bounded by a constant of order ℏ — borrow more negative energy and you must give it back faster. For macroscopic engineering — say, holding a wormhole open at human scales — the integrated negative energy required is enormous, and quantum inequalities make it implausible without dramatic new physics. That gap is what gives chronology protection its bite.