Speaker
Description
The Schrödinger–Newton equation aims at describing the dynamics of massive quantum systems subject to the gravitational self-interaction. As a deterministic nonlinear quantum wave equation, it is generally believed to conflict with the relativistic no-signalling principle. Here I challenge this viewpoint and show that it is of a key importance to study the quantitative and operational character of the superluminal effects. To this end, a rigorous formalism of probability measures on spacetime was employed to quantify the probability of a successful superluminal bit transfer via the single-particle Schrödinger–Newton equation. Here it is demonstrated that such a quantity decreases with the increasing size and mass of the system. Furthermore, I prove that the Einstein–Dirac system, which yields the Schrödinger–Newton equation in the non-relativistic limit, is perfectly compatible with the relativistic causal structure. The presented study demonstrates that the Schrödinger–Newton equation, which is by construction non-relativistic, is in fact ‘more compatible’ with the no-signalling principle than the ordinary free Schrödinger equation.