Quantum interest in ($3+1$)-dimensional Minkowski space

The so-called “quantum inequalities,” and the “quantum interest conjecture,” use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a timelike observer, potentially preventing the existence of exotic phenomena such as “Alcubierre warp drives” or “traversable wormholes.” Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or nonexistence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple variational proof of one version of the quantum interest conjecture in ($3+1$)-dimensional Minkowski space.