Only ConnectOnly Connect by Greg Egan   Appearance of the Border | “Only
Connect” | Decoherence | Spin Networks    Schild's Ladder contents    Back to
home page | Site Map | Framed Site Map      It's beginning to look as if E.M.
Forster's famous dictum was superfluous. A theory in which the building
blocks of the universe are mathematical structures, known as graphs, which do
nothing but connect, has just passed its first experimental test. A graph can
be drawn as a set of points, called nodes, and a set of lines joining the
nodes, called edges. Details such as the length and shape of the edges aren't
part of the graph itself, though; the only thing that distinguishes one graph
from another are the connections between the nodes. The number of edges that
meet at any given node is known as its valence. In Quantum Graph Theory, or
QGT, a quantum state describing both the geometry of space and all the matter
fields present is built up from combinations of graphs. The theory reached
its current form in the work of the Javanese mathematician Kusnanto
Sarumpaet, who published a series of six papers from 2035 to 2038 showing
that both General Relativity and the Standard Model of particle physics could
be seen as approximations to QGT. Sarumpaet's graphs have a fascinating
lineage, dating back to Michael Faraday's notion of “lines of force” running
between electric charges, and William Thomson's theory of atoms as knotted
“vortex tubes”. Closer ancestors are Roger Penrose's spin networks, trivalent
graphs with each edge labelled by a half integer, corresponding to a possible
value of the spin of a quantum particle. Penrose invented these networks in
the early 1970s, and showed that the set of all directions in space could be
generated from simple, combinatorial principles by imagining an exchange of
spin between two parts of a large network. Generalisations of spin networks
later appeared in certain kinds of Quantum Field Theory. Just as a wave
function assigns an amplitude to every possible position of a particle, a
spin network embedded in a region of space can be used to assign an amplitude
to every possible configuration of a field. The quantum states defined in
this way consist of lines of flux running along the edges of the network. In
the 1990s, Lee Smolin and Carlo Rovelli discovered an analogous result in
 quantum gravity, where spin network states have a simple geometric
 interpretation: the area of any surface depends entirely on the edges of the
 network that intersect it. These edges can be thought of as quantised “flux
 lines of area”, and in quantum gravity area and other geometric measurements
 take on a discrete spectrum of possible values. It then makes sense to
quantise the topology as well, with the nodes and edges of the network
replacing the usual idea of space as a continuum of points. In the first
decades of the new millennium, John Baez, Fotini Markopoulou, José-Antonio
Zapata and others did ground-breaking work on the possible dynamical laws for
spin networks, assigning quantum amplitudes to the process of one network
evolving into another. In the 2030s, Sarumpaet began to synthesise these
results into a new model, based on graphs of arbitrary valence with
 unlabelled edges. The geometry of three-dimensional space arises from
tetravalent graphs, with the four edges emerging from each node giving area
to the faces of a “quantum tetrahedron”. Allowing graphs of higher valence
runs the risk of producing an explosion of unwanted dimensions, but Sarumpaet
found a simple dynamical law which always leads to the average valence
stabilising at four. However, trivalent and pentavalent nodes — which have
come to be known as “dopant” nodes, in analogy with the impurities added to
semiconductors — can persist under the Sarumpaet rules if they're arranged in
special patterns: closed, possibly knotted chains of alternating valence.
These loops of dopant nodes, classified by their symmetries and mutual
interactions, match up perfectly with the particles of the Standard
Model. Since the area associated with the edges of a quantum graph is of the
order of a few square Planck lengths, some 1050 times smaller than the
surface area of a hydrogen atom, it was once feared that QGT would remain
untestable for centuries. However, in 2043 computer simulations identified a
new class of “polymer states”: long, open chains of dopant nodes that were
predicted to have energies and half-lives within the grasp of current
technology to create and detect. A search for polymer states that commenced
at the Orbital Accelerator Facility in 2049 has now yielded its first
success. If the result can be repeated, Sarumpaet's graphs will shift rapidly
from being merely the most elegant known description of the universe, to the
most likely one.      Appearance of the Border | “Only Connect” | Decoherence
| Spin Networks    Schild's Ladder contents    Back to home page | Site Map |
Framed Site Map     Schild's Ladder / Only Connect / revised Thursday, 10
August 2000 Copyright © Greg Egan, 2000. All rights reserved. First published
in Nature, 10 February 2000.




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