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Density matrices in quantum gravity
by Tarek Anous, Jorrit Kruthoff, Raghu Mahajan
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Submission summary
| Authors (as registered SciPost users): | Tarek Anous · Jorrit Kruthoff · Raghu Mahajan |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2006.17000v1 (pdf) |
| Date submitted: | 2020-07-10 02:00 |
| Submitted by: | Anous, Tarek |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2020-9-12 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2006.17000v1, delivered 2020-09-11, doi: 10.21468/SciPost.Report.1984
Strengths
1. Builds on the earlier work in [17] to help clarify various issued in "third-quantisation" (or, to use the better name introduced in the paper, "universe field theory")
2. Excellent use of the familiar example of Klein-Gordon theory/worldline gravity to understand general phenomena that can show up in this framework.
Weaknesses
1. A couple of minor conceptual distinctions could be emphasized more (see below)
Report
This is a strong paper that builds on recent progress in providing much needed clarity to questions about the quantum mechanics of universe creation and annihilation. The authors start with the example of Klein-Gordon theory/ worldline gravity and then use intuition from this example to conjecture how things should work in higher dimensions. Finally they discuss the distinction between the Page density matrix and the (pure) Hartle-Hawking state. Subject to the minor revisions listed below, I believe that it should be accepted for publication.
Requested changes
1. A central claim of the paper is that the Hartle-Hawking state does not contain bra-ket wormholes. By this, the authors mean that there are no wormholes connecting the bra <HH| (in the baby universe Hilbert space) and the ket | HH> (in the baby universe Hilbert space) if both appear in the calculation. However, it doesn't mean there aren't wormholes connecting a "bra" boundary and a "ket" boundary when evaluating a boundary partition function (e.g. Tr(rho^n) as the expectation of a baby universe Hilbert space operator in the Hartle-Hawking state. This is discussed in section 4.2, but it would be good if it was emphasized much earlier. For example, my interpretation of Section 6 of [12] is that it is discussing the latter, not the former, although that the wording is definitely ambiguous (probably because [12] was published before [17]).
2. Similarly, the paper makes the important point that the commutativity of boundary creation operators is slightly more subtle than was suggested in [17], using the example of time-like separated Klein-Gordon field operators. However there are really two distinct notions of commutativity here. The first is the order in which boundaries are added. The second is the existence of singularities and branch cuts in the correlation functions when two operators are inserted with no Euclidean time separation. It is only in the second sense (which corresponds to operators not commuting in the canonical quantisation of Klein-Gordon theory) that boundary creation operators don't commute. No matter which order we apply boundary creation operators, we always get the Euclidean time ordered correlation functions. So the boundary creation operators commute in the first sense. Again this is clear from a thorough reading of the paper (and is clearly understood by the authors), but could be emphasized more clearly at the beginning.
3. The density matrix rho_Page needs to be proportional to the identity matrix. However, in many/most relevant cases, the baby universe Hilbert space is infinite-dimensional, so no such density matrix exists. Some brief comments on this would be nice.
Report #1 by Anonymous (Referee 2) on 2020-9-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2006.17000v1, delivered 2020-09-08, doi: 10.21468/SciPost.Report.1974
Report
The paper makes several important points regarding recent work on spacetime wormholes and baby universes, connecting previous work from various authors and perspectives. The paper is well organized and written, and the arguments are presented in a clear way. I recommend publication.