# Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics

## Abstracts of the talks

**Alessio Belenchia ***IQOQI-Vienna, Austria***Quantum Superposition of Massive Objects and the Quantization of Gravity **

In this talk we analyse a gedankenexperiment, previously considered in the literature, which involves quantum superpositions of charged and/or massive bodies. In the electromagnetic case, we show that the quantization of electromagnetic radiation and vacuum fluctuations of the electromagnetic field both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment which was not correctly analyzed in the previous literature. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description, a relevant result in view of the growing interest in proposals for table-top experiments probing gravity-induce entanglement.

**Časlav Brukner ***IQOQI Vienna, Austria***Time and Causality in Quantum Physics**

In general relativity causal relations between any pair of events is uniquely determined by locally predefined variables – the distribution of matter-energy degrees of freedom in the events’ past light-cone. Under the assumption of locally predefined causal order, agents performing freely chosen local operations on an initially local quantum state cannot violate Bell inequalities. However, superposition of massive objects can effectively lead to “entanglement” in the temporal order between groups of local operations, enabling the violation of the inequalities. This shows that temporal orders between events can be “indefinite” in non-classical space-times.

**Daniela Cadamuro ***Technische Universität München, Germany***Lower bounds for the energy density in quantum integrable models**

The energy density is positive in classical field theory, a property that fails to be true in the quantum regime. However, if it were indefinitely negative, this would conflict with the stability of spacetime. Fortunately, lower bounds exist and have been proved for free quantum field theory and conformal theories. We study, in a class of massive quantum integrable models, lower bounds for local averages of the energy density, establishing results for QFTs with self-interaction.

**Tian Yu Cao ***Boston University, USA***Can we conceive a quantum field theory without classical spacetime underpinnings? -- Conceptual issues in gauging gravity: from Utiyama to the spin form approach**

When a quantum theory ventures into dealing with gravity, whose classical treatment was formulated by Einstein's general theory of relativity, it inevitably encounters numerous constraints, most severe among them is the non-availability of a spacetime underpinning that is the precondition for any quantum theory, or for any scientific theory, traditionally (meaning up-to-now) conceived. Implications of this constraint will be examined, and ways of addressing some of them, which require radical modifications of foundations of quantum field theory and clearer conception of the most fundamental quantum principle will be suggested in the talk.

**Dirk Deckert ***Ludwig Maximillian University of Munich, Germany***The phase of QED in external fields**

I will report on joint progress of my collaborators Franz Merkl and Markus Nöth and myself to construct the phase of the scattering operator of QED in external fields. This phase plays an important role in the computation of physical measurands such as the charge current. However, as it is well-known, it remains unidentified by the canonical lift of the corresponding one-particle scattering matrix and calls for a geometric construction which I will present.

**Chris Fewster ***University of York, United Kingdom***Generally covariant measurement schemes for quantum field theory in curved spacetimes**

Algebraic quantum field theory is founded on the idea of algebras of observables associated with local regions of spacetime, but not much attention has been given to how these observables can actually be measured. On the other hand, quantum measurement theory provides an operational understanding of measurement schemes for quantum observables, but is not framed in a spacetime context. This talk will describe a generally covariant formalism of measurement schemes adapted to quantum field thoery in curved spacetimes, illustrated by a specific model. (Joint work with Rainer Verch [Leipzig]).

**Ding Jia ***Perimeter Institute, Canada***The principle of causal neutrality**

The "principle of causal neutrality", motivated by quantum gravity, says that fundamental concepts of physics should be defined without assuming a definite spacetime causal structure.

Forced by this principle, I propose a generalization of standard AQFT using the free product of star-algebras. The state, rather than the algebra, encodes the spacetime causal structure, which can be quantum. Similarly, I propose a generalization of the notion of entanglement so that the parties sharing the correlation may have quantum indefinite causal structure.

As a payoff of the generalizations, I derive an ultraviolet regularization mechanism coming from causal structure fluctuations. This suggests a new condition to supersede the Hadamard condition to characterize the UV structure of physical states.

**Olaf Lechtenfeld ***University of Hanover, Germany***Yang-Mills and Maxwell configurations in de Sitter space: relevance for quantum theory?**

I will review analytic SU(2) Yang-Mills solutions with finite action on de Sitter space from a new perspective. As a byproduct, all abelian solutions are classified and related with rational electromagnetic knots. In an attempt to semiclassically quantize Yang-Mills or Maxwell theory on de Sitter space, these extremal configurations should play a role in the path integral. In the Yang-Mills case, the gravitational backreaction is easily taken in to account as well.

**Shahn Majid ***Queen Mary University of London, United Kingdom***Some finite quantum Riemannian geometries**

I outline a formulation of quantum Riemannian geometry using bimodule connections. I give some

examples in the finite case where it is possible for a fixed differential algebra to construct the moduli of all possible quantum Riemannian geometries on it, as a step towards quantum gravity.

In particular, this will be solved for the geometry of a square graph, including a reasonable Einstein-Hilbert action for the quantum metric as given by lengths assigned to the edges.

**Pierre Martin-Dussaud ***Aix-Marseille Université, France***The notion of locality in relational quantum mechanics**

The term 'locality' is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. We will show that the failure of 'locality' in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it. This approach questions the interplay between quantum mechanics and the causality structure of space-time.

**Gregory Naber ***Drexel University, USA***Understanding “Understanding”**

We are all engaged in the struggle to “understand” something.

The nature of the world that we seem to perceive around us.

- The properties of the primes.

- The unreasonable effectiveness of mathematics in physics.

- The unreasonable effectiveness of physics in mathematics.

- The meaning of “consciousness”.

- The meaning of “right” and “wrong”.

- Finnegans Wake.

- The music of Schönberg.

- The meaning of “understanding”.

Does “understanding” mean the ability to “explain”? Does it mean the ability to “predict”? Is

there more than one way to “understand”? Is “understanding” always “rational”? Is “understand-

ing” psychological, physiological, cultural, a matter of training, or of language, or something else altogether? Is the meaning of “understanding” any more transparent in physics and mathematics?

**Hermann Nicolai ***Max Planck Institute for Gravitational Physics, Germany***E10, K(E10) and the Standard Model**

Results from LHC so far have shown no hints of `new physics' beyond the well established Standard Model of Particle Physics -- in obvious conflict with numerous proposed extensions postulating a large number of new particles. Exploiting a remarkable coincidence with N=8 supergravity first observed by M. Gell-Mann, I will describe a very different approach whereby novel infinite-dimensional duality symmetries (closely related to the `maximally extended' hyperbolic Kac-Moody algebra E10) could account for the observed spectrum of quarks and leptons including right-chiral neutrinos, together with its replication in three and only three generations.

First hints of these symmetries had previously emerged from maximal

supergravity and from studies of the `near singularity limit' of Einstein's equations, that is, solutions describing the gravitational evolution of the Universe in the immediate vicinity of the Big Bang.

As a by-product, the present approach predicts fractionally charged and possibly strongly interacting very massive and stable gravitinos as new Dark Matter candidates.

**Antonio Pereira ***Universität Heidelberg, Germany***The asymptotic safety scenario for quantum gravity **

General relativity is known to be perturbatively non-renormalizable as a standard quantum field theory. Nevertheless, it is logically possible that an interacting ultraviolet fixed-point exists in the renormalization group flow and quantum gravity can be described as a predictive and UV-complete quantum field theory. Such a possibility was baptized as the asymptotic safety scenario for quantum gravity. In this talk I will discuss this approach, some of its important achievements and supporting evidences and

point out present challenges.

**Sofia Qvarfort ***University College London, United Kingdom***Gravitational entanglement for Gaussian states**

Is gravity a quantum force? This question was recently addressed by two proposals (see [1] and [2]) which explored the possibility of detecting entanglement as generated by gravity. Successful detection of entanglement due to a gravitational interaction would imply that gravity is fundamentally a quantum force, since only quantum systems can mediate entanglement. In my talk, I will show how the experimental scheme in [1] can be modelled for Gaussian states in the continuous variable regime for two different settings using optomechanical spheres: trapped systems and freely-falling systems. We evaluate the entanglement generated by the Newtonian potential for both cases and propose the use of two specific continuous variable entanglement witnesses to make detection easier. The approach also allows us to include other forces, such as the attractive Casimir effect. Our main results concern bounds on the various experimental parameters necessary for the successful detection of entanglement.

References:

[1] Bose, Sougato, et al. "Spin entanglement witness for quantum gravity." Physical Review Letters 119.24 (2017): 240401.

[2] Marletto, Chiara, and Vlatko Vedral. "Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity." Physical Review Letters 119.24 (2017): 240402.

**Mojtaba Taslimitehrani ***Max Planck Institute for Mathematics in the Sciences, Germany***Background independence in gauge theories**

Classical field theory is background independent in the sense that it is insensitive to the split of the field into a background configuration and a dynamical perturbation. At the quantum level, we define background independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A QFT is then called background independent if such

a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and show that all potential obstructions can be removed by finite renormalization. We also comment on the background-independence of perturbative quantum gravity. Joint work with Jochen Zahn. Based on arXiv:1804.07640.

**Rainer Verch ***Leipzig University, Germany***Quantum physics, fields and closed timelike curves:The D-CTC condition in quantum field theory**

The D-CTC condition has originally been proposed by David Deutsch as a condition on states of a quantum communication network that contains ``backward time-steps'' in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the D-CTC condition have been discussed extensively in recent literature. In this work, the D-CTC condition is investigated in the framework of quantum field theory in the local, operator-algebraic approach due to Haag and Kastler. It is shown that the D-CTC condition cannot be fulfilled in states which are{\tcb analytic in the energy}, or satisfy the Reeh-Schlieder property, for a certain class of processes and initial conditions.

On the other hand, if a quantum field theory admits sufficiently many uncorrelated states across acausally related spacetime regions (as implied by the split property), then the D-CTC condition can always be fulfilled approximately to arbitrary precision. As this result pertains to quantum field theory on globally hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting the D-CTC condition as characteristic for quantum processes in the presence of CTCs could be misleading, and should be regarded with caution. Furthermore, a construction of the quantized

massless Klein-Gordon field on the Politzer spacetime, often viewed as spacetime analogue for quantum communication networks with backward time-steps, is proposed in this work. [The talk is based on a joint paper with Jürgen Tolksdorf, published in Commun. Math. Phys. (2017)]

## Date and Location

**October 01 - 05, 2018**

Max Planck Institute for Mathematics in the Sciences

Inselstraße 22

04103 Leipzig

Germany

see travel instructions

## Scientific Organizers

**Felix Finster**, University of Regensburg, Regensburg (Germany)**Domenico Giulini**, University of Hanover (Germany)**Johannes Kleiner**, University of Hanover (Germany)**Jürgen Tolksdorf**, MPI for Mathematics in the Sciences, Leipzig (Germany)

## Administrative Contact

**Antje Vandenberg**

MPI for Mathematics in the Sciences

Leipzig (Germany)

Contact by Email