Quantum reference frames for an indefinite metric

Abstract

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.

18+7 pages, 7 figures. Comments are welcome. v2: published version with general minor modifications and additional Supplementary Note 4

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• Quantum generalisation of Einstein's Equivalence Principle can be verified with entangled clocks as quantum reference frames
• Quantum Reference Frames for Lorentz Symmetry
• Quantum conformal symmetries for spacetimes in superposition
• Indefinite causal order and quantum coordinates
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Universality of quantum time dilation
• Quantum Time and the Time-Dilation induced Interaction Transfer mechanism
• Superpositions of thermalisations in relativistic quantum field theory
• Quantum Galilei group as quantum reference frame transformations
• A spacetime-covariant approach to inertial and accelerated quantum clocks in first-quantization
• Space-time superpositions as fluctuating geometries
• Quantum Mechanics Relative to a Quantum Reference System: a Relative State Approach
• Knot invariants and indefinite causal order