Energy Condition - Attempts at Falsifying The Strong Energy Condition

Attempts At Falsifying The Strong Energy Condition

While the intent of the energy conditions is to provide simple criteria which rule out many unphysical situations while admitting any physically reasonable situation, in fact, at least when one introduces an effective field modeling some quantum mechanical effects, some possible matter tensors which are known to be physically reasonable and even realistic because they have been experimentally verified to actually fail various energy conditions. In particular, in the Casimir effect, in the region between two conducting plates held parallel at a very small separation d, there is a negative energy density

between the plates. (Be mindful, though, that the Casimir effect is topological, in that the sign of the vacuum energy depends on both the geometry and topology of the configuration. Being negative for parallel plates, the vacuum energy is positive for a conducting sphere.) Fortunately, various quantum inequalities suggest that a suitable averaged energy condition may be satisfied in such cases. In particular, the averaged null energy condition is satisfied in the Casimir effect. Indeed, for energy-momentum tensors arising from effective field theories on Minkowski spacetime, the averaged null energy condition holds for everyday quantum fields. Extending these results is an open problem.

The strong energy condition is obeyed by all normal/Newtonian matter, but a false vacuum can violate it. Consider the linear barotropic equation state

,

where is the matter energy density, is the matter pressure, and is a constant. In the case where, which is known as the false vacuum, the strong energy condition is violated. However, this equation of state only becomes relevant above temperatures of at least Kelvin. This would only happen under highly extreme conditions when quantum effects become dominant, and where classical general relativity would not apply. The main reason for wanting to falsify the strong energy condition is to avoid the initial singularity in the universe. The aforementioned suggests that a non-singular universe model would not obey the laws of classical physics at all times in the past.