by Greg Egan
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.