Quantum Interest in (3+1) dimensional Minkowski space

TL;DR

This paper proves a version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space, showing how quantum field theory constrains exotic spacetime phenomena through energy density restrictions.

Contribution

It provides a simple proof of a version of the Quantum Interest Conjecture in (3+1)D Minkowski space using quantum mechanical pseudo-Hamiltonian techniques.

Findings

Quantum inequalities restrict energy density distributions.

The Quantum Interest Conjecture is validated in (3+1)D Minkowski space.

Constraints on exotic phenomena like warp drives are supported.

Abstract

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 time-like 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 non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.