Fundamental physics

Gravity's weight on unification

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Much research in theoretical physics is inspired at least in part by the idea of unifying all of the fundamental forces of nature. An analysis of how gravity affects other forces at subnuclear scales has major implications for that idea. See Article p.56

One of the main goals of modern theoretical physics is to find a common framework that explains all of the fundamental forces of nature: gravity; the strong force that binds quarks into protons and neutrons; and the forces of the electroweak theory (which encompasses electromagnetism on macroscopic scales, and the 'weak' and hypercharge forces on subnuclear scales). On page 56 of this issue, Toms1 reports results that could be significant for finding such a framework. The author describes a mathematical analysis of the behaviour of gravity at ultrashort distances and of how this most familiar of forces affects 'Abelian gauge' theories, which, notably, include the theory of electromagnetism and that of the hypercharge force.

Relevant to Toms's study1 is the fact that coupling constants — parameters that are used to characterize the strength of forces — are actually not constant but vary with the distance scale of the physical process in which they are measured. This phenomenon is both well established experimentally and predicted by current theories, and is known as 'running coupling constants'.

The author's results have implications for what might be the next revolution in fundamental physics, a hint of which is found by extrapolating the experimentally established 'running' of the coupling constants down to distance scales much shorter than can be accessed experimentally. Within the successful standard model of particle physics, we can make such an extrapolation for the running of the coupling constant of the hypercharge force (αY) — which is described by an Abelian gauge theory of the type studied by Toms1 — and for that of the strong (αS) and weak (αW) forces, which are described by non-Abelian gauge theories. The results are shown semi-quantitatively in Figure 1, together with a cruder estimate of the effective coupling constant of gravity (αG).

Figure 1: Meeting at ultrashort distance scales?

Extrapolation of experimental values, measured at relatively large distances (not shown), for the strength of the strong force (αS), weak force (αW) and hypercharge force (αY) indicates that these forces might merge with gravity for processes characterized by distance scales that are at least 13 orders of magnitude smaller than those currently being explored with the Large Hadron Collider (LHC). The strength of gravity is characterized by αG, and the strength of the electromagnetic force is not shown because at the distance scales displayed this force is replaced by the combination of the weak and hypercharge forces. Toms's analysis1 investigates a piece of the puzzle that theorists must resolve to correctly describe this unification: the behaviour of gravity in the range between 10−32 and 10−35 metres.

Gravity is the only force for which we currently do not have a reliable 'fundamental description', which would be applicable at subnuclear distances2,3. But several indirect arguments invite us to give a preliminary description of its effective strength in terms of the ratio of Newton's constant to the square of the characteristic distance scale of the gravitational processes of interest.

It is striking that the coupling constants of the three non-gravitational forces converge with distance. And, perhaps even more remarkably, the effective coupling constant of gravity, which at currently accessible distance scales is much smaller than the others, also approaches the region where the other coupling constants converge. Within our current theoretical framework, this behaviour can only be described as an extremely fine-tuned numerical accident, but it clearly hints that some unknown law of nature is driving the convergence.

All of the most-studied proposals of modern theoretical physics are inspired, at least in part, by this possibility of unification. In particular, one of the motivations for conjecturing the existence of 'superpartners' of known particles4, which will be looked for with the Large Hadron Collider at CERN, Europe's premier high-energy physics laboratory near Geneva in Switzerland, is the role of these extra particles in the derivation of the running of the non-gravitational coupling constants. Including the roles of superpartners in the calculations leads to a particularly accurate convergence of the three non-gravitational coupling constants at a scale of about 10−32 metres.

Achieving unification of the non-gravitational forces at 10−32 metres has some intrinsic appeal, especially where the running of αY is concerned, as this would otherwise keep growing, possibly reaching values too high for the computational techniques of modern theoretical physics to manage. However, according to some theorists, by assuming such a stage of partial unification, with gravity left out because at 10−32 m it should still be too weak to matter, we fail to profit fully from the evidence summarized in Figure 1 — a single stage of unification of all forces, plausibly at distance scales a couple of orders of magnitude smaller than 10−32 m.

Toms's study concerns the weakest link on the road to unification: the behaviour of gravity at ultrashort distances, particularly in the range between 10−32 m and 10−35 m. In this regime, the lack of a fundamental, microscopic theory of gravity not only limits us to describing its strength crudely in terms of Newton's constant, but also prevents us from establishing its influence on the strength of the non-gravitational forces. To circumvent these limitations, Toms adopts a mathematical approach that exploits the fact that inconsistencies in our current description of gravity manifest themselves only at distances smaller than 10−35 m. Therefore, valuable insight should be obtained from computations arranged in such a way that only distances larger than 10−35 m are involved.

The author's analysis1 suggests that the effect of gravity on αY is such that, as soon as the strength of gravity becomes comparable to the strength of the other forces (at some point between 10−33 m and 10−35 m), αY quickly becomes vanishingly small, a behaviour known as asymptotic freedom. A mechanism for gravity-induced asymptotic freedom of coupling constants has been advocated5 by Robinson and Wilczek. However, it relies on a more preliminary analysis, which has been received with some scepticism. By providing evidence in favour of the Robinson–Wilczek mechanism, Toms removes one of the perceived advantages of having a stage of partial unification, because the unwanted, uncontrollable growth of αY is avoided. What's more, Toms's study strengthens another preliminary observation reported by Robinson and Wilczek5 — that the effects of gravity on all three non-gravitational coupling constants combine to give a slower convergence of the non-gravitational forces, with the implication that the unification might occur at distances smaller than 10−32 m, at which it is easier to imagine gravity joining in.

Possibly even more important, Toms's findings provide encouragement for the idea that the role of gravity in the unification can be fruitfully investigated. And it might open the way to studies that compare different proposals for the sought-after fundamental description of gravity on the basis of their implications for unification6.

Perhaps we are one step closer to figuring out this amazing unification puzzle, and it is particularly exciting that this might rely on modelling the effect of gravity on distances much smaller than those of planets and galaxies.


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    Toms, D. J. Nature 468, 56–59 (2010).

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    Robinson, S. P. & Wilczek, F. Phys. Rev. Lett. 96, 231601 (2006).

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    Calmet, X., Hsu, S. D. H. & Reeb, D. Phys. Rev. D 81, 035007 (2010).

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Amelino-Camelia, G. Gravity's weight on unification. Nature 468, 40–41 (2010) doi:10.1038/468040a

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