RodrigodLA

In 1983, Hartle and Hawking published a paper called «Wave function of the Universe«. This is an outstanding proposal in the field of quantum gravity with a focus on (quantum) cosmology. It gives a prescription of the wavefunction of the universe… (take a moment to think about it)

That is right, we can study the universe as a physical system and since the physical «world» at small scales is quantum, there must be a quantum description.

By gravity I mean Einstein’s theory of general relativity. To be clear, it is not a theory. It has been tested experimentally in several of its predictions such as black holes, gravitational waves, and classical cosmology. In general relativity, gravity is not a force (as in Newton’s theory of gravity), it is a manifestation of the curvature of spacetime. This does not mean that Newton’s theory is incorrect; it just corresponds to a specific limit of general relativity.

One of the intriguing consequences of general relativity (also classical electrodynamics) is that it indicates its own limit of applicability. That is, the solutions of the equations of motion have singular points. At these points, quantities (one of them being the curvature of space-time) blow up, and therefore we cannot trust the solutions at such points. A black hole solution has this singularity, and also the current model of the universe (the so-called Big-Bang model). For the former, the singularity is in space, and for the latter, it is in time. Therefore, the solutions give physical (tested) predictions far from the singular point.

On the other hand, singularities correspond to very small regions of spacetime. Regions in which quantum effects must be strong. So in quantum gravity, it is expected that these singularities will disappear once we find a correct theory. With the basic knowledge of quantum mechanics and general relativity, this does not happen for all possible regimes. This led to the conclusion, in technical jargon, that general relativity is an effective field theory. This means that the quantum description of general relativity is like the macroscopic description of water. We see the ripples in water but not the molecules.

However, the Hartley-Hawking proposal gives a (technical) resolution to the problem of the singularity in time of the universe¹.

This should be contrasted with the current lines of research in quantum gravity such as superstring theory and loop quantum gravity theory. These theories, if correct, should give us a dynamical resolution to the problem.

Why is this proposal still interesting? Well, in the context of superstring theory, Juan Maldacena proposed in 1998 a holographic duality called AdS/CFT. The duality is capable of relating the physics of a particular quantum field theory (conformal field theory, CFT for short) to the physics of a particular spacetime (Anti-de Sitter, AdS for short). This correspondence has been intensively studied and is now well established (at the theoretical level).

Recently this year, Maldacena wrote some comments about the Hartle-Hawking proposal. You can read it here. He emphasizes that the structure of the proposal mimics the structure of the AdS/CFT correspondence. The major difference is that in the case of the universe, we deal with de Sitter spacetime rather than Anti-de Sitter. On the other hand, the Hartle-Hawking proposal is consistent with the theory of cosmological inflation. This theory is well motivated by theoretical arguments (although it does not say anything about the singularity) but yet has no experimental evidence.

To many assumptions may lead you to think that all of this is extremely sketchy. It is true. But notice that these ideas are in the cusp of theoretical physics research.

In 2023 he discussed this topic at the ICTP-SAFIR and the video of the lecture is

This motivated me to write a manuscript (technical one) to understand in detail the Hartley-Hawking proposal. It is aimed for students in these lines of research and if it interests you, the manuscript is

Use the note with caution!

1. I strongly recommend Sean Carroll’s podcast Mindscape for these topics and more. In particular, listen to the one with Hertog where the Hartle-Hawking proposal is discussed. The link is https://www.youtube.com/watch?v=qMXSrkryfTQ&list=PLrxfgDEc2NxY_fRExpDXr87tzRbPCaA5x&index=62&t=2743s. ↩︎