Conservation laws and temporal witnesses of non-classicality

The problem of the universality of Quantum Mechanics has been debated for a long time, with some physicists in favour of it and others instead who consider Classical Physics to be more fundamental, to the extent that it is not necessary to quantise all physical systems. One of the most challenging topics emerging from this debate in contemporary physics is Quantum Gravity, whose goal is to unify the most fundamental theories known so far: General Relativity and Quantum Physics. Recently, promising laboratory-scale tests of quantum gravity effects have been proposed. They are based on the so-called “Bose-Marletto-Vedral effect”, which exploits entanglement generation between two masses interacting only with a gravitational field and acting as a generalised Bell’s theorem for models of matter-gravity coupling. Variants of this scheme include detection of gravity-induced non-Gaussianity generation in a single mass’ dynamical evolution. Here we provide a radical generalisation of this single-mass argument, removing the underlying assumption of a specific interaction model: we show that if a system M (e.g. gravity) can induce the dynamical evolution of another system Q (e.g. a mass) from a state where one of its observables is sharp to another state where a different, non-commuting observable is sharp, then M must be non-classical provided that an additive quantity of the total system Q+M is conserved. The argument qualifies as a general temporal equivalent of the Bose-Marletto-Vedral effect using the formalism of quantum theory: provided the possibility of the task and the actual conservation of the additive observable, the non-trivial “rotation” of the physical system Q will automatically rule out all possible classical models for the mediator M. The equivalence between the spatial and temporal arguments clarifies the role of time in nature, expanding on the so-called temporal locality and entanglement. The result leads to new perspectives on the design of an experiment able to assess the non-classical nature of whatever physical systems, from gravity to biological entities, suggesting new answers to fundamental questions about the universality of Quantum Physics and its compatibility with life.