CERN Courier January/February 2017 Quantum gravity and unification Gravity’s quantum side Theoretical physics has arrived at crossroads, with no clues so far as to what lies beyond general relativity or the Standard Model. If we are ever to break through this impasse, we need to borrow from Einstein’s epochal feats. There is little doubt that, in spite of their overwhelm- ing success in describing phenomena over a vast range of distances, general relativity (GR) and the Standard Model (SM) of particle physics are incomplete theo- ries. Concerning the SM, the problem is often cast in terms of the remaining open issues in particle physics, such as its failure to account for the origin of the mat- Vecto_CERN Courier_193x125.indd 1 12/12/2016 09:23:06 ter–antimatter asymmetry or the nature of dark matter. But the real problem with the SM is theoretical: it is not clear whether it makes sense at all as a theory beyond perturba- tion theory, and these doubts extend to the whole framework Progress of of quantum fi eld theory (QFT) (with perturbation theory as the main tool to extract quantitative predictions). The occurrence of Theoretical and “ultraviolet” (UV) divergences in Feynman diagrams, and the need for an elaborate mathematical procedure called renormalisa- Experimental Physics tion to remove these infinities and make testable predictions order- by-order in perturbation theory, strongly point to the necessity of A slice Progress of Theoretical and Experimental Physics is a some other and more complete theory of elementary particles. through the On the GR side, we are faced with a similar dilemma. Like the root space of the fully open access, online-only journal. SM, GR works extremely well in its domain of applicability and symmetry group E10, a possible has so far passed all experimental tests with flying colours, most symmetry for quantum gravity. Each point is associated with Read our latest Special Section: recently and impressively with the direct detection of gravitational one or more independent symmetry operations – similar to the waves (see p21). Nevertheless, the need for a theory beyond Ein- fl avour SU(3) root diagram for the meson octet, but vastly more Nambu, A Foreteller of Modern Physics III stein is plainly evident from the existence of space–time singulari- complicated. There are infi nitely many such layers, and the This Special Section is based on a symposium ties such as those occurring inside black holes or at the moment of number of symmetry operations grows exponentially as one the Big Bang. Such singularities are an unavoidable consequence penetrates deeper and deeper into the E10 Lie algebra. held at the University of Chicago in memory of of Einstein’s equations, and the failure of GR to provide an answer (Image credit: T Nutma.) Professor Yoichiro Nambu. calls into question the very conceptual foundations of the theory. Unlike quantum theory, which is rooted in probability and Applying conventional particle-physics wisdom to Einstein’s uncertainty, GR is based on notions of smoothness and geom- theory by quantising small fluctuations of the metric field (cor- academic.oup.com/ptep etry and is therefore subject to classical determinism. Near a responding to gravitational waves) cannot help either, since it pro- space–time singularity, however, the description of space–time duces non-renormalisable infinities that undermine the predictive as a continuum is expected to break down. Likewise, the assump- power of perturbatively quantised GR. tion that elementary particles are point-like, a cornerstone of In the face of these problems, there is a wide consensus that the QFT and the reason for the occurrence of ultraviolet infinities outstanding problems of both the SM and GR can only be over- ▲ in the SM, is expected to fail in such extreme circumstances. come by a more complete and deeper theory: a theory of quantum PTEP Physics World half page no3.indd 1 21/12/2016 12:15 27 CERNCOURIER www. V OLUME 5 7 N UMBER 1 J AARYN U /F EBRUARY 2 0 1 7 CERN Courier January/February 2017 CERN Courier January/February 2017 Quantum gravity and unification Quantum gravity and unification to try to emulate Einstein’s epochal feat of creating a new theory The success of symmetry has fuelled hopes that we temperature 32 27 15 13 out of purely theoretical considerations. of universe 10 K10 K10 K10 K3 K might ultimately understand the evolution of the universe from its beginning as a symmetry-breaking Emulating Einstein cascade, where at each step more and more of the Yet, after more than 40 years of unprecedented collective intel- strong force initial symmetry is lost as the universe expands and lectual effort, different points of view have given rise to a growing electromagnetic force cools down. In this view, the unsymmetrical world that j3 j3 diversification of approaches to QG – with no convergence in sight. weak force we see around us is only the broken phase of a highly It seems that theoretical physics has arrived at crossroads, with symmetrical theory at the origin of the universe, when nature remaining tight-lipped about what comes after Einstein gravity forces, matter and space–time were unified into a j2 and the SM. There is currently no evidence whatsoever for any of single entity. However, this picture has so far been the numerous QG schemes that have been proposed – no signs of time after –43 –35 –12 –6 17 validated only up to energy scales accessible to the j1 10 s10 s10 s10 s5 × 10 s −18 low-energy supersymmetry, large extra dimensions or “stringy” Big Bang ( = now) LHC, or equivalently distances down to 10 cm. j1 j2 excitations have been seen at the LHC so far. The situation is no better for approaches that do not even attempt to make predictions or “canonical” approaches, the main unsolved problems concern graphic entanglement, as advocated by AdS/CFT aficionados? that could be tested at the LHC. the emergence of classical space–time and the Einstein fi eld There is cer tainly no lack of enticing ideas, but without a firm guid- If quantum space is made of web-like structures (spin networks), Existing approaches to QG fall roughly into two catego- equations in the semiclassical limit, and their inability to recover ing principle and the prospect of making a falsifiable prediction, as postulated by LQG-like approaches, a spin foam describes ries, refl ecting a basic schism that has developed in the com- standard QFT results such as anomalies. On the other side, a main such speculations may well end up in the nirvana of undecidable the quantum evolution of such spin networks in time. In the munity. One is based on the assumption that Einstein’s theory shortcoming is the “background dependence” of the quantisation propositions and untestable expectations. abstract description, the ambient space–time in which the spin can stand on its own feet, even when confronted with quantum procedure, for which both supergravity and string theory have to Why then consider unification? Perhaps the strongest argument in foam is “embedded” is simply not there, since all of the geometry mechanics. This would imply that QG is nothing more than the rely on perturbative expansions about some given space–time favour of unification is that the underlying principle of symmetry has resides on the spin foam. non-perturbative quantisation of Einstein’s theory and that GR, background geometry. In fact, in its presently known form, string so far guided the development of modern physics from Maxwell’s suitably treated and eventually complemented by the SM, cor- theory cannot even be formulated without reference to a specific theory to GR all the way to Yang–Mills theories and the SM (see gravity (QG) that possibly unifi es gravity with the other fundamental rectly describes the physical degrees of freedom also at the very space–time background. diagram above). It is therefore reasonable to suppose that unification interactions in nature. But how are we to approach this challenge? smallest distances. The earliest incarnation of this approach goes These fundamentally different viewpoints also offer different and symmetry may also point the way to a consistent theory of QG. back to the pioneering work of John Wheeler and Bryce DeWitt in perspectives on how to address the non-renormalisability of Ein- This point of view is reinforced by the fact that the SM, although Planck-scale physics the early 1960s, who derived a GR analogue of the Schrödinger stein’s theory, and consequently on the need (or not) for unification. only a partially unified theory, does already afford glimpses of trans- Unlike with quantum mechanics, whose development was driven equation in which the “wave function of the universe” encodes Supergravity and superstring theory try to eliminate the infinities of Planckian physics, independently of whether new physics shows up by the need to explain observed phenomena such as the existence the entire information about the universe as a quantum system. the perturbatively quantised theory, in particular by including fer- at the LHC or not. This is because the requirements of renormalis- of spectral lines in atomic physics, nature gives us very few hints of Alas, the non-renormalisable infi nities resurface in a different mionic matter in Einstein’s theory, thus providing a raison d’être for ability and vanishing gauge anomalies put very strong constraints on where to look for QG effects. One main obstacle is the sheer small- guise: the Wheeler–DeWitt equation is so ill-defined mathemati- the existence of matter in the world. They therefore automatically the particle content of the SM, which are indeed in perfect agreement ness of the Planck length, of the order 10−33 cm, which is the scale cally that no one until now has been able to make sense of it arrive at some kind of unification of gravity, space–time and matter.