A realist interpretation of unitarity in quantum gravity
Abstract
Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalisability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler-DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in Alexander et al (2022 Phys. Rev. D 106 106012), by parameterising a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalisable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalisable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- June 2024
- DOI:
- 10.1088/1361-6382/ad3eda
- arXiv:
- arXiv:2310.15157
- Bibcode:
- 2024CQGra..41k5005S
- Keywords:
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- problem of time;
- normalisability;
- unitarity;
- pilot-wave theory;
- de Broglie–Bohm;
- Ashtekar variables;
- General Relativity and Quantum Cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- Matches published version