Historical research guide · 0838 · 2018
Traversable wormholes in four dimensions
Juan Maldacena · Alexey Milekhin · Fedor Popov
In one minute
Wormholes have been a physicist’s daydream since John Wheeler sketched one in 1966 — the paper reproduces his drawing on its first page. The obstacle has always been the energy bill. A short wormhole joining distant points would break causality, and a long one needs a negative energy that classical matter cannot supply. Juan Maldacena, Alexey Milekhin and Fedor Popov, at the Institute for Advanced Study and Princeton, build one anyway, out of parts nobody would call exotic. Take two nearly extremal black holes carrying large opposite magnetic charges. A massless charged fermion moving in that magnetic field drops into a lowest Landau level whose states each ride a single magnetic field line, and in this configuration those field lines close into circles. A massless fermion on a circle carries a negative Casimir energy — the same effect measured between Casimir plates — and that is precisely what holds the throat open. Their own emphasis: no exotic matter is required, and the ordinary matter of the Standard Model is enough.
Connection
Chapter 4 is the metric-engineering chapter, and this paper moves the traversable wormhole from needing matter nobody has ever seen to needing a Casimir energy that is measured in laboratories, arranged in the right geometry. Chapter 13 gains the other half: the same solution reads as a pair of entangled black holes, so a spacetime connection and an entangled state turn out to be two descriptions of one object.
From the source
A traversable wormhole solution exists in four dimensions in a theory of Einstein gravity plus a U(1) gauge field plus massless charged fermions. The authors emphasise that it requires no exotic matter, and that the ordinary matter of the Standard Model is enough — taking the U(1) to be weak hypercharge and the whole configuration to be smaller than the electroweak scale.Abstract; Sect. 8; Sect. 9.1, Summary
The negative energy that makes the solution possible is Casimir energy, generated rather than assumed. In a large quantised magnetic flux q, a single four-dimensional charged fermion field becomes of order q massless two-dimensional fields, each localised along one magnetic field line; in this geometry those field lines close into circles, and a massless two-dimensional fermion on a circle develops a negative Casimir-like vacuum energy with a negative null-null stress component.Sect. 1, Introduction, paragraph 2; Sect. 5.2, Negative energy; Sect. 9.1
Feeding that negative energy into the Einstein equations in the throat region does not merely permit the wormhole, it fixes the length of the throat. The classical action scales as q squared while the fermion effect scales as q, and the resulting throat is longer than q squared Planck lengths.Sect. 5.3, Stabilizing the wormhole; Sect. 9.1, paragraph beginning ‘It might seem surprising’
It is a long wormhole rather than a short one, so it does not lead to causality violations in the ambient space: passage through it takes longer than the trip outside. The traveller’s own proper time through the throat is of order the light-crossing time of the black hole, scaling as q, while the time measured outside scales as q squared.Sect. 1, Introduction, paragraph 1; Sect. 9.1, final paragraph
The solution has no horizon and no entropy, and can be viewed as a pair of entangled near-extremal black holes in a state close to the thermofield double. The interaction that makes that state the ground state is generated automatically by the exchange of massless fermion fields between the two mouths, rather than being postulated — the authors draw the analogy with the Van der Waals force between two neutral atoms.Abstract; Sect. 9.1; Sect. 9.2, Van der Waals analogy
The configuration is metastable and the authors name what remains open. The two mouths are kept apart by orbiting each other, which radiates gravitationally and electromagnetically until they merge; sending too much energy through develops a pair of horizons, though low-energy waves probe it safely; and no simple procedure is yet known for steering a real system into the wormhole rather than into two separate black holes. Answering that would say how a spacetime connection is generated from entanglement, and might, they write, lead to a futuristic experiment that checks it.Sect. 6.1; Sect. 1, paragraph 3; Sect. 9.3, Open questions
The way in
https://arxiv.org/abs/1807.04726How to cite it
Juan Maldacena, Alexey Milekhin, Fedor Popov (2018) Traversable wormholes in four dimensions doi:10.1088/1361-6382/acde30