Quantum reference frames for an indefinite metric.

The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence of mass configurations in superposition, and hence an indefinite spacetime metric, using quantum reference frame (QRF) transformations. Specifically, we show that, as long as the mass configurations in the different branches are related via relative-distance-preserving transformations, one can use an extension of the current framework of QRFs to change to a frame in which the mass configuration becomes definite. Assuming covariance of dynamical laws under quantum coordinate transformations, this allows to use known physics to determine the dynamics. We apply this procedure to find the motion of a probe particle and the behavior of clocks near the mass configuration, and thus find the time dilation caused by a gravitating object in superposition. Comparison with other models shows that semi-classical gravity and gravitational collapse models do not obey the covariance of dynamical laws under quantum coordinate transformations. Finding a way to combine quantum mechanics and gravity is a longstanding issue in physics. While there are different approaches to quantum gravity, there are many challenges in making concrete predictions for scenarios at the interface of these two theories. Here, the authors propose a first-principles strategy to determine the dynamics of objects in the presence of mass configurations in superposition, which enables predictions where the gravitational source is in a quantum superposition rather than a classical configuration. [ABSTRACT FROM AUTHOR]