Affiliation:
1. Institute of Physics, University of Amsterdam
2. Stanford University
3. Institute for Advanced Study, Princeton University
Abstract
We study density matrices in quantum gravity, focusing on topology change.
We argue that the inclusion of bra-ket wormholes in the gravity path integral is not a free choice, but is dictated by the specification of a global state in the multi-universe Hilbert space.
Specifically, the Hartle-Hawking (HH) state does not contain bra-ket wormholes.
It has recently been pointed out that bra-ket wormholes are needed to avoid potential bags-of-gold and strong subadditivity paradoxes, suggesting a problem with the HH state.
Nevertheless, in regimes with a single large connected universe, approximate bra-ket wormholes can emerge by tracing over the unobserved universes.
More drastic possibilities are that the HH state is non-perturbatively gauge equivalent to a state with bra-ket wormholes, or that the third-quantized Hilbert space is one-dimensional.
Along the way we draw some helpful lessons from the well-known relation between worldline gravity and Klein-Gordon theory.
In particular, the commutativity of boundary-creating operators, which is necessary for constructing the alpha states and having a dual ensemble interpretation, is subtle.
For instance, in the worldline gravity example, the Klein-Gordon field operators do not commute at timelike separation.
Funder
Ministerie van Onderwijs, Cultuur en Wetenschap
National Science Foundation
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Simons Foundation
Subject
General Physics and Astronomy
Cited by
32 articles.
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