# Does gravity work at the quantum level

## Quantum Gravity and Unification

### Research Report 2016 - Max Planck Institute for Gravitational Physics

### Where is quantum gravity today?

General relativity theory (GTR) and quantum theory cannot be reconciled within the framework of the known physical laws. Contradictions only arise at unimaginably small intervals of 10^{-33} cm to the surface, but if we want to understand what “happens” inside a black hole or in the first fractions of a second after the Big Bang, they have to be resolved.

### The limits of the theories

ART and the Standard Model of Particle Physics (SM) describe physical phenomena correctly over a vast range of distances, yet are incomplete. It is true that one day the open questions in particle physics will be answered with the help of experiments such as those carried out at CERN's Large Hadron Collider (LHC). Questions like the origin of matter-antimatter asymmetry in the universe, or the matter of which dark matter is made. However, it is unclear whether the SM is at all suitable for a model that goes beyond perturbation theory. Occurring infinities (the so-called UV divergences), which have to be removed in a mathematically complex manner, indicate that another and more complete theory is necessary.

The ART shows a similar dilemma: Like the SM, it also works extremely well in its area of application and has so far passed all experimental tests with flying colors. The proof of gravitational waves [1] is the latest example of the efficiency and predictive power of Einstein's theory. Nevertheless, the necessity of a theory 'beyond Einstein' becomes clear through the existence of space-time singularities, such as those occurring inside black holes or at the Big Bang: every observer who crosses the horizon of a black hole will in finite time through the singularity in his Center crushed. ART cannot explain this phenomenon, which suggests that the conceptual foundations of the theory must be questioned in such extreme circumstances.

In view of these problems there is a broad consensus that the outstanding problems of both particle physics and GTR can only be overcome by a more complete and in-depth theory, namely a theory of quantum gravity (QG), which can reconcile GTR and quantum theory, thus unifying gravity with the other fundamental interactions in nature.

### Are there any hints in the experimental data?

While quantum mechanics and GTR were developed to explain observed phenomena (e.g. the spectral lines in atomic physics), nature gives us very few clues as to where to look for a theory of quantum gravity. A major obstacle here is that the magnitude of the expected effects is incredibly small. The decisive factor is the Planck length of around 10^{−33} cm; accordingly, the relevant scale for energy is around 10^{19} GeV, an incredible 15 orders of magnitude above the energy range accessible to the LHC. There is therefore no hope of ever directly measuring actual QG effects in the laboratory. However, one can speculate that QG might *indirectly* shows, for example in the cosmic background radiation or by providing a valid explanation for inflation, the dark energy and the origin of the universe. However, one must be aware that such proposals cannot unequivocally distinguish between very different approaches. For example, when such contradicting designs as string theory and loop quantum gravity vie to explain the properties of the early universe.

### How do you approach a unified theory of quantum gravity?

Approaches to QG can be roughly divided into two categories. One is based on the assumption that Einstein's theory still holds true when confronted with quantum mechanics. This assumption would imply that QG is essentially nothing more than the non-perturbation-theoretical quantization of Einstein's theory and that the GTR, with appropriate treatment and ultimately supplemented by the SM of particle physics (or an extension of it), also increases the physical degrees of freedom in the describes the smallest distances correctly. Current approaches in the context of loop and spin foam quantum gravity (LQG:*Loop Quantum Gravity*) replace space-time metrics with holonomies and flows as the canonical variables, trying to overcome the mathematical difficulties.

The opposite attitude is that the GTR is only an effective low-energy theory, which results from a more fundamental, hitherto unknown Planck scale theory, the degrees of freedom of which are very different from those of the GTR or quantum field theory (QFT). With this approach, it is assumed that the GTR and with it the continuous spacetime “arise” from this still to be found theory in the Limes of large distances in a similar way as the macroscopic physics results from the quantum world of atoms and molecules. The need to replace Einstein's theory with another and more fundamental theory is the basic hypothesis on which supergravity and superstring theory and their relatives are based. This approach has given birth to a number of extremely diverse activities over the years that are nowadays associated with the term string theory. An important idea that arose from these developments is the so-called AdS / CFT correspondence, the best-known implementation of the so-called "holographic principle" [2]. Accordingly, the physics that “takes place” in a volume can be completely encoded in the surface that encloses the volume - like a hologram. Consequently, the QG should be equivalent (“dual”) in volume to a pure QFT at its edge.

As for the approaches from the other category, however, important questions remain unanswered. A main inadequacy concerns the background dependency of the quantization procedure, for which both supergravity and string theory have to rely on perturbation developments around a given space-time geometry. What is even more fatal is that in its currently known form, string theory cannot even be formulated without referring to a specific spacetime background.

### Why unify at all?

Perhaps the strongest argument for unification is that the underlying symmetry enlargement is probably the most successful principle in the establishment of physical theories: the search for symmetry has the development of modern physics from Maxwell's theory to ART to the Yang-Mills Theories and the SM led. The hope is therefore that one could ultimately understand the evolution of the universe from its beginning as a cascade of symmetry breaking, where with each step more and more of the initial symmetry is lost as the universe expands and cools. From this point of view, the asymmetrical world that we see around us is only the broken phase of a highly symmetrical theory at the beginning of the universe, when forces, matter and space-time were united in a single structure. **illustration 1** should give an artistic impression of this process. However, this image has so far only been validated up to the energy scales accessible to the LHC at CERN, or equivalent distances down to 10^{−18} cm. So far, the unanswered question is whether the strong and electroweak forces also merge into a large, unified theory before reaching the Planck scale, and if so, at what energy this takes place. One cannot avoid including gravitation when the strength of the gravitational coupling is comparable to the strength of the other forces.

Among the competing theories, the most promising is supersymmetry, a new type of symmetry that connects bosons and fermions, thereby uniting forces with matter (quarks and leptons) and adding fermionic dimensions to space-time. Supersymmetry is very natural from the point of view of canceling divergences, because bosons and fermions basically contribute to the loop diagrams with opposite signs. While recent evidence from the LHC strongly suggests that nature does not make use of this option, there is no reason to abandon the idea of supersymmetry itself. Because maybe supersymmetry isn't the end of the story.

Indications of an enormous increase in symmetry have also appeared at a completely different point, namely when investigating the cosmological solutions of Einstein’s equations in the vicinity of a space-like singularity. This mathematical analysis has revealed fascinating indications of an infinite-dimensional duality symmetry, which is called 'E10' [3, 4] and which "opens" when one approaches the cosmological (Big Bang) singularity. Could it be that Einstein’s equations in the borderline case near the singularity tell us something about the underlying symmetries of the QG? One can rightly argue that this vast (and monstrously complex) symmetry "knows" all about the maximum supersymmetry and finite dimensional dualities that have been identified so far. It is just as important that this symmetry continues to make sense in areas where conventional ideas of space and time fail. This is one of the key qualities that we expect in the QG. For this reason, the duality symmetry could even replace the (space-time) supersymmetry as the unifying principle.

In summary it can be stated: All important questions remain unanswered so far, despite great efforts and numerous promising ideas. Regardless of the results of further experiments, symmetries will play a crucial role in trying to identify “what holds the world together at its core”. This is all the more true if the SM survives without major “scratches” up to higher energies, with only “small” additions by additional elementary particles such as eg. B. axions or heavy Higgs bosons. It remains a central challenge in physics to explain the structure of the low-energy world from the standpoint of a Planck scale theory.

#### Bibliography

**116**, 061102 (2016)

**17**, 74-81 (2007)

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_{10}and a Small Tension Expansion of M Theory

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**3**, 134-140 (2010)

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