A Conservative Theory of Semiclassical Gravity

TL;DR

The paper introduces a conservative semiclassical gravity framework in which quantum systems source gravity only when they undergo environment-induced decoherence via Stable Determination Chains (SDCs), allowing flat spacetime in decohered-free regions. It develops a quantum-theory basis (EnDQT) with local test-function interactions to model determinate outcomes and the spread of determination capacity, and formalizes three postulates tying SDCs to gravity, default spacetime, and Hadamard-state sourcing. In curved spacetime, decoherence drives states that are Hadamard and amenable to semiclassical equations, enabling a practical program to solve the semiclassical dynamics without modifying quantum mechanics. A central claim is that the cosmological constant $\Lambda$ can be estimated from four-volume fluctuations associated with SDCs, predicting a time-varying $\Lambda$ and offering a potential link to dark energy and dark matter, while yielding testable predictions for gravcats and the BMV experiment that distinguish it from quantum-gravity and spontaneous-collapse theories. Overall, the work articulates a testable, conservative route to gravity emerging from QFT via causal SDCs, with wide-ranging implications for cosmology and black-hole physics.

Abstract

We argue that semiclassical gravity can be made consistent by assuming that quantum systems source or are classically affected by a gravitational field only when they undergo certain non-gravitational interactions that give rise to environment-induced decoherence. When systems are not affected by this decoherence-inducing process, they do not source a gravitational field, and the expectation value of their stress-energy tensor does not enter the semiclassical equations describing the gravitational field in a region. In the absence of these interactions in a region, spacetime may be flat. We argue that this can be tested by investigating the gravitational field sourced by quasi-isolated systems and the absence of gravity-mediated entanglement in the Bose-Marletto-Vedral (BMV) experiment, providing distinct predictions. We propose a possible kind of decoherence-inducing interaction that gives rise to gravity, involving chains of causally ordered non-gravitational localized interactions between quantum systems modeled via decoherence and test functions that we call Stable Determination Chains (SDCs). SDCs obey conditions that aim to address the measurement problem and allow for a conservative theory of gravity. It is conservative because it does not need to modify the fundamental equations of quantum theory, unlike spontaneous and gravity-induced collapse approaches to semiclassical gravity, and it does not invoke relationalism. Furthermore, it does not appeal to nonlocal, retrocausal, or superdeterministic hidden variables. SDCs might provide additional benefits, such as a semiclassical prediction of the magnitude of the cosmological constant, a justification for why the vacuum does not source gravity, the prediction of a time-varying cosmological constant weakening over time in agreement with some evidence, certain dark matter effects, and a proposal about how gravity arises from QFT.

Figures (6)

• Figure 1: If there is a quantum gravitational interaction between the particles, the interaction distinguishes three paths as there are three distinct particle separations, $d_{ee} = d_{gg} = d$ and $d_{eg}$ > $d$, $d_{ge} < d$. This will entangle the two-particle center of momentum motion in a way that depends on the mass of each particle. If we repeat the experiment with two particles of different masses, the entanglement will be different. Measurements made in a free-falling frame could distinguish the three paths.
• Figure 2: An SDC with systems $A$, $B$, and $C$ in QFT interacting in overlapping regions of spacetime. In this image, we are representing the systems in the Schrödinger picture.
• Figure 3: The order of the following SDC goes from the top to the bottom. Multiple systems $A_{00},A_{01} ...$, or modes of a field $A$, belonging to SDCs, and interacting with systems $B_{0},B_{1} ...$ or modes of a field $B$ in a spacetime region. They give rise to these modes having a determinate value of some of their observables, and to sourcing a gravitational field in that region. $A_{11},A_{12} ...$ will also end up having determinate values of their observables and source the gravitational field together with $B_{1},B_{2} ...$ in that region. Then, $B_{1},B_{2}, ...$ interact with systems $C_i$ for different $i$, or modes of the field $C$, giving rise to the systems involved having determinate values and sourcing a gravitational field in a spacetime region. The inference regarding how these interactions occur, and the possible values of systems, is made using decoherence models. We omit system $D$ with some of its modes, which emit the test functions that localize these interactions in spacetime regions. Note that the labels above do not aim to be realistic, and just aim to make the structure of SDCs manifest.
• Figure 4: Two-dimensional spatial hypersurface of members of an SDC probing a scalar field at separate points of what can be illustrated as an array of detectors, giving rise to that field sourcing a gravitational field in a certain region. A realistic picture would not involve points, but regions.
• Figure 5: Strength and Overlap obtained by numerical simulations for a $t_{AB}=0.5$ and $\sigma_{AB}=0.13$, and for multiple values of $t_{BC}$ and $\sigma_{BC}$ within the interval $[0,3]$ and within the common support of $f_{AB}$ and $f_{BC}$. To calculate these quantities, the Schrödinger equation with the Hamiltonian in (\ref{['InteractionABC']}) was solved to yield the state $|\psi(1)_{\text{Num}} \rangle$.