The Baby Universe Hypothesis

I've been thinking of starting a blog for a while, but the real catalyst was some recent discussions about my paper "Baby Universes, Holography, and the Swampland" with Cumrun Vafa. Based on these discussions, I think some less-directed rambling might help to clarify our perspective, and so I've decided to start this blog! With no real plans for how frequently I'm going to post, keep your expectations low, but I feel like there are ideas about physics that don't fit neatly into a paper, so I hope to continue sharing them here.

To get into it, what, exactly, are we claiming in this paper? The central physical claim is the following hypothesis:

In a consistent and complete theory of quantum gravity,

the Hilbert space of baby universe states is one-dimensional.

As an aside, I prefer the word "hypothesis" to "conjecture" for most Swampland conditions; to me, a conjecture is a precise claim about a well-defined mathematical structure, which is either true or false. While some Swampland conditions are precise enough to be conjectures (such as in the context of Calabi-Yau threefolds or AdS/CFT), in general we do not know the complete mathematical formalism to describe quantum gravity, and so I view them more as physical hypotheses, to be verified or falsified by experiments in the potentially distant future. Alternatively, you can view them as conditions that must be satisfied by whatever future formalism we invent, in a similar sense as the Cobordism Hypothesis of Baez and Dolan, which must hold for any sensible definition of infinity category. In this way, they are tools for discovering the right axioms, rather than claims about existing ones.

With semantics out of the way, what does this hypothesis mean? I like Geoff Pennington's characterization of it as "radical holographism," in that it is a radically strict reading of the holographic principle. If quantum gravity in any bulk region is dual to a local quantum system on the boundary, then in the case of an empty boundary we should expect quantum gravity to be dual to a trivial quantum system. In this way, we can read the Baby Universe Hypothesis as a version of Gauss's law for entropy in quantum gravity, saying that there can be no net entropy in a closed universe.

The first objection I keep getting is that this hypothesis is clearly false, simply because of our lived experience of a nontrivial quantum system, with nontrivial dynamics occurring in our everyday life. Though this is a reasonable objection, it is actually a logical pitfall, and arises from a misapplication of textbook quantum mechanics. In order to define a Hilbert space and a set of quantum observables, we must first make a Heisenberg cut, and divide the universe into a system under study and an observer doing the studying. Once this cut is made, the wavefunction is simply a description of the mind of the observer: it allows them to calculate the probabilities of observing different outcomes, which are subjective measures of the observer's surprise at seeing various events.

To address this complaint, then, we need to identify the Heisenberg cut for the baby universe Hilbert space. This cut is outside the whole system, and thus the baby universe Hilbert space describes the quantum observables that can be measured by an observer external to the universe (G-d, if you like). In particular, this is not the Hilbert space that describes our lived experience, since that Hilbert space requires a cut between our own degrees of freedom and those of the rest of the universe. Thus, the Baby Universe Hypothesis only says that there are no measurements to make on quantum gravity from outside the system, and is a strong form of background independence!

How can we reconcile a nontrivial quantum system describing our lived experience with a trivial quantum system describing the universe as a whole? In a quantum field theory, which is not background independent, this would be impossible, as the renormalization group keeps careful track of the number of degrees of freedom, ensuring that there are no more degrees of freedom in the IR than in the UV. However, this is not true in quantum gravity; indeed, it's not clear that the renormalization group makes any sense in quantum gravity, as the IR and UV are inextricably linked.

In particular, we are claiming that realistic quantum theories of gravity have fewer degrees of freedom in the UV than in the IR,¹ as is required by the holographic principle! The only way this can be possible is if there are new gauge redundancies in quantum gravity which have not been taken into account in the effective field theory. Luckily, exactly this type of gauge redundancy has been proposed recently by Jafferis and by Marolf and Maxfield! Taking these into account, the proposal, then, is that the exact state of the entire closed universe is forced by the gauge constraints to be a specific, maximally entangled state between different subregions, with the rest of the naive tensor product Hilbert space consisting of null states. This proposal reveals a key connection between topology and entanglement: in order to have a closed universe, we must choose a specific entangled state, in order to reduce the net entropy of the whole universe to zero. In fact, this paper was heavily influenced by my attempts to understand the meaning of ER = EPR!

As a final comment, I want to note how cleanly this hypothesis resolves a number of tensions and confusions about the proper conceptual framework for quantum gravity. There has been much recent discussion on the role of Euclidean wormholes, as well as the potential for an ensemble of alpha-eigenstates and a formal breakdown of unitarity and factorization. A naive refutation would be to say that we simply shouldn't include Euclidean wormholes in our path integral. However, this seems unnatural, and indeed, I see no good reason to exclude them. What we propose is that, if by some miracle of non-perturbative quantum gravity, the contributions from wormholes and new UV degrees of freedom (such as strings and branes) arrange themselves to produce a one-dimensional baby universe Hilbert space, you can still have unitarity and factorization without excluding wormholes or baby universes by fiat.

Another conceptual confusion about quantum gravity which is resolved by this hypothesis is the question of interpretation of the wavefunction of the universe. Such a wavefunction has always seemed a bit odd to me, for the reasons discussed above. Related to this, there are old questions and debates about how to understand quantum mechanics in a truly background-independent theory, including the so-called "problem of time." The Baby Universe Hypothesis resolves these questions, at least at a formal level, by positing that there is nothing to say! The universe as a whole indeed has no dynamics, as demanded by the Wheeler-DeWitt equation, and time evolution (including topology change) is pure gauge. There is still a key question which we do not attempt to answer, namely how to separate out the relational degrees of freedom experienced by an observer living inside the universe. The phrase "derived quantum error correction" has been floating around in my head, but let's save that for another time.

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1 Of course, as one increases the energy scale from the deep IR, the number of effective degrees of freedom will initially increase, due to the renormalization group flow in the effective field theory. However, once energy scales are reached where quantum gravity effects are relevant, the number of degrees of freedom will presumably turn around and decrease back down to zero in the deep UV. This effect goes by different names in different contexts: in the Swampland Program, it's part of the emergence proposal, and in evaporating black holes, it's the Page curve!^↩