Schrödinger’s cat for de Sitter spacetime

Abstract

Quantum gravity is expected to contain descriptions of semiclassical spacetime geometries in quantum superpositions. To date, no framework for modelling such superpositions has been devised. Here, we provide a new phenomenological description for the response of quantum probes (i.e. Unruh–deWitt detectors) on a spacetime manifold in quantum superposition. By introducing an additional control degree of freedom, one can assign a Hilbert space to the spacetime, allowing it to exist in a superposition of spatial or curvature states. Applying this approach to static de Sitter space, we discover scenarios in which the effects produced by the quantum spacetime are operationally indistinguishable from those induced by superpositions of Rindler trajectories in Minkowski spacetime. The distinguishability of such quantum spacetimes from superpositions of trajectories in flat space reduces to the equivalence or non-equivalence of the field correlations between the superposed amplitudes.

Quantum signatures of black hole mass superpositions

“…The notion of spacetime superpositions has attracted significant recent interest, and has been analyzed in the context of indefinite causal order [21], quantum reference frames and the equivalence principle [22][23][24], analog gravity [25], and tabletop experiments aimed at testing the quantum nature of gravity [26][27][28]. A recent investigation by the present authors developed an operational approach where a particle detector (modelled as the Unruh-deWitt detector [29]) evolves in a de Sitter spacetime which is in superpositions of spatial translations and curvature, to study the quantum effects arising in such a background [30]. However, the conformal equivalence of de Sitter and Rindler spacetime (a uniformly accelerated reference frame in Minkowski spacetime), meant that many of the effects produced by the spacetime superposition could be directly mapped to those experienced by a detector in a superposition of semiclassical trajectories in flat Minkowski spacetime [31,32].…”

Unruh-DeWitt detector in dimensionally-reduced static spherically symmetric spacetimes

“…Therefore, one may hope to be able to construct some sort of "pseudo-KMS" property just for the derivative coupling model so that the Planckian response can be interpreted as a consequence of the pseudo-KMS property. 13 We will try to see how this can be formulated and under what circumstances it will make sense. For convenience we simply refer this as the KMS condition.…”

“…They are now refined to a point where finite-size effects are included in a covariant manner [3][4][5] and capture the impact of quantized centre-of-mass degrees of freedom of the detector [6]. These models also admit "variants": these include non-linear interactions [7], different spins of both the detector and the field [8], harmonic oscillatorbased detectors [9][10][11][12], spacetime superpositions [13][14][15], quantum causal switches [16], and JHEP03(2022)014 even experimental models using lasers [17] and non-linear optics [18]. Within the subject matter now known as relativistic quantum information (RQI), particle detector models are now developed enough to provide a local measurement theory for QFT that respects causality [19].…”

“…One can potentially include proper-time derivatives into the algebra the same way one can enlarge the algebra by including the stress-energy tensor, but for our purposes it is not necessary to take this step, and we may content ourselves with calling this pseudo-KMS condition if we prefer 13. Alternatively, as mentioned earlier one can view this as enlarging the algebra of observables to include proper-time derivatives of the field.…”

Schrödinger's cat state of optical parallel universes

“…Note that (1) is the superposition of parallel worlds before a measurement is performed. According to quantum mechanics, although it is difficult to observe, such a superposition state does exist in a real world if gravity is quantum [23,24]. Suppose that an ant crawls from point A to point B and no observation is made in this process.…”