In one minute

L. H. Ford and Thomas Roman connect the averaged weak and averaged null energy conditions with quantum inequalities, uncertainty-principle-type limits on negative energy. They study a quantised free massless scalar field in flat spacetime in two and four dimensions. In a two-dimensional universe with a compact spatial direction, they bound the difference between the energy density of any quantum state and that of the Casimir vacuum. That difference obeys averaged energy conditions, which is surprising because the Casimir vacuum alone satisfies neither quantum inequalities nor averaged conditions. Such difference inequalities may limit how far energy conditions can be violated beyond a background such as the Casimir vacuum.

Averaged Energy Conditions and Quantum Inequalities