Effective Repulsive Action of Gravitational Quantum Superpositions Under Postselection

Abstract

A classic feature of gravity is that it is an attractive force. If a source mass is prepared in a localized (classical- like) state, it will cause another probe mass to move towards it. Here we consider the situation in which a source mass is prepared in a quantum superposition of distinct spatial states while a probe mass interacts with it. Conditional on the detection of the source mass in a specific state, the probe mass will be found to move away from the source mass (repulsion). This signifies the quantum superposition of gravitational forces acting on the probe mass and thereby the fact that spacetime can exist in quantum superpositions. The technique used is the repulsive effect arising from an anomalous negative weak value. A potential experimental implementation with spin bearing nanocrystals is outlined.

Figures (2)

• Figure 1: Schematic idea of the repulsive effect of a quantum superposition of gravitational fields under postselection. (a) the usual gravitational attractive effect of mass-1 in a localized state $|R\rangle_1$ on mass-2 in an initial gaussian (localized) state. This attraction leads to mass-2 gaining a momentum $\delta_p$ towards mass-1. (b) mass-1 in a superposition of two localized states $|L\rangle_1$ and $|R\rangle_1$ (given by Eq.(\ref{['initial']})) and further subjected to postselection (given by Eq.(\ref{['final']})). Under postselection, mass-2 appears to acquire a momentum $\delta_p/\epsilon$ away from mass-1.
• Figure 2: Mass-1 undergoing a Stern-Gerlach interferometry is outlined. The procedure uses an inhomogeneous magnetic field to accomplish spin-dependent splitting of paths. Two spin flipping pulses (also called $\pi$-pulses) are used to complete the interferometry as shown in the figure. The time axis is shown on the left. At the end of the interferometry, at time $\tau$, the spin is postselected in the $(|\uparrow\rangle_Q-|\downarrow\rangle_Q)/\sqrt{2}$ state, for which mass-2 has acquires a momentum away from mass-1.