Localisation and Nonlocality in Compound Energy-Momentum Eigenstates

Abstract

A thought experiment considering conservation of energy and momentum for a pair of free bodies together with their internal energy is used to show the existence of states that have localised position while being eigenstates of energy and momentum. These states are applicable to all varieties of physical bodies, including planets and stars in free motion in the universe. The states are compound entanglements of multiple free bodies in which the momenta of the bodies are anticorrelated so that they always sum to zero, while their total kinetic energy is anticorrelated with their internal energies, so the total is a constant, E. The bodies are relatively localised while the total state has well-defined energy and momentum. These states do not violate Heisenberg uncertainty because the total centre of mass is not localised, hence the states naturally describe whole universes rather than isolated systems within a universe. A further property of these states, resulting from the form of the entanglement, is that they display nonlocality in the full sense of signal transmission rather than the more restricted Bell sense.