Finding a quantum theory of gravity has eluded the world’s best physicists for almost a century. As well as the fearsome mathematical challenge of marrying quantum theory with Einstein’s general theory of relativity, the extreme conditions at which quantum gravity applies — corresponding, for example, to the first 10-43 seconds of the universe — make it virtually impossible to test in an experiment. At least that’s what researchers used to think.

In 1998, physicists realized that the natural scale of quantum gravity (the Planck scale, which corresponds to an energy of 1019  GeV) could be 15 orders of magnitude lower if the universe has additional spatial dimensions into which the true strength of gravity can “leak”. This raises the prospect of studying quantum gravity at CERN’s Large Hadron Collider (LHC), which will soon be smashing protons into one another to produce an energy of 14 TeV (about 104 GeV).

Taking the existence of large extra dimensions as a starting point, Daniel Litim of the University of Sussex and Tilman Plehn of the University of Edinburgh have now calculated that quantum gravity would modify the rate of a which leptons, such as electrons and muons, are produced in the LHC’s collisions — and that the effect could be present at energies as low as 6 TeV (Phys. Rev. Lett. 100 131301). While there are hundreds of papers predicting the effects of large-extra dimensions at the LHC, most notably the production of mini black-holes, most have large uncertainties and do not make such quantitative predictions.

Fluctuating fields

The most advanced progress in quantum gravity comes from string theory, which describes particles as vibrations of 1D strings that oscillate in a higher dimensional space (and is the inspiration behind large-extra dimension models). An alternative attempt is loop quantum gravity, which tears up our basic notions of space-time at the smallest scales. Litim and Plehn took a more conventional approach by allowing the “metric” in general relativity, which connects the curvature of space-time to the local matter present, to fluctuate as if it were a quantum field.

In 1979 Steven Weinberg performed this exercise for 2D gravity, revealing that the strength of the gravitational interaction between two particles depends on the energy at which those interactions are probed. Similar behaviour is observed for the electromagnetic and the strong interactions, which are described by quantum field theories. Like the strong interaction, the gravitational coupling turns out to be weaker at large energies.

Using computational tools developed in the last two years, Litim and Plehn found the same behaviour in four and higher dimensions. As such, they avoided the “divergent” calculations that normally yield uncertain predictions in quantum gravity theories based on metric fluctuations. “To my understanding, this the first time the effect of these fluctuations for LHC observables has been calculated without any unphysical cut-off,” Litim told

Computing observables

Taking the energy-dependence of the gravitational coupling into account, Litim and Plehn worked out the rate at which pairs of leptons are produced from virtual gravitons (the “messenger” particles of gravity that come from fluctuations of the metric) created in the LHC’s collisions. Because this rate is predicted with great precision by the standard model of particle physics, any increase could be a signal for quantum gravity. Despite gravity becoming weaker at high energies, the LHC turns out to be sensitive to this quantum gravitational phenomenon up to a fundamental Planck scale of 6 TeV. Furthermore, says Litim, the well-behaved nature of gravity at high energies yields a consistent theory of quantum gravity.

The researchers are currently working out how to differentiate an effect due to quantum gravity from others due to different theories, such as string theory or supersymmetry. For some, however, the likelihood of observing such an effect is slim. “The existence of gravitational fixed points [which arise from the variation of the gravitational coupling with energy] would alter the standard signal for extra dimensions,” says JoAnne Hewett of Stanford University, who perfomed a similar calculation around the same time as Litim and Plehn (JHEP 12(2007)009). “These are cute calculations, but it is a long shot to connect them with reality.”