We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory (RMT) to reveal their underlying structure. We focus on the feature-feature covariance matrix, analyzing both its local and global eigenvalue statistics. Our main observations are: (i) The power-law scalings that the bulk of its eigenvalues exhibit are vastly different for uncorrelated random data compared to real-world data, (ii) this scaling behavior can be completely recovered by introducing long range correlations in a simple way to the synthetic data, (iii) both generated and real-world datasets lie in the same universality class from the RMT perspective, as chaotic rather than integrable systems, (iv) the expected RMT statistical behavior already manifests for empirical covariance matrices at dataset sizes significantly smaller than those conventionally used for real-world training, and can be related to the number of samples required to approximate the population power-law scaling behavior, (v) the Shannon entropy is correlated with local RMT structure and eigenvalues scaling, and substantially smaller in strongly correlated datasets compared to uncorrelated synthetic data, and requires fewer samples to reach the distribution entropy. These findings can have numerous implications to the characterization of the complexity of data sets, including differentiating synthetically generated from natural data, quantifying noise, developing better data pruning methods and classifying effective learning models utilizing these scaling laws.

The Underlying Scaling Laws and Universal Statistical Structure of Complex Datasets

Quantum mechanics is important for determining the geometry ofspacetime. We will review the role of quantum fluctuations that determinethe large scale structure of the universe. In some model universeswe can give an alternative description of the physics in termsof a theory of particles that lives on its boundary. This implies thatthe geometry is an emergent property. Furthermore, entanglementplays a crucial role in the emergence of geometry. Large amounts ofentanglement are conjectured to give rise to geometric connections,or wormholes, between distant and non-interacting systems.

Quantum mechanics is important for determining the geometry of spacetime. We will review the role of quantum fluctuations that determine the large scale structure of the universe. In some model universes we can give an alternative description of the physics in terms of a theory of particles that lives on its boundary. This implies that the geometry is an emergent property. Furthermore, entanglement plays a crucial role in the emergence of geometry. Large amounts of entanglement are conjectured to give rise to geometric connections, or wormholes, between distant and non-interacting systems.

Quantum Mechanics and Geometry of Spacetime

With Run II, the LHC experiment already reached an unprecedentedlevel of precision compared to previous hadron colliders. The amountof data collected in Run III and the High-Luminosity run will increasequickly and dramatically. I will discuss specific challenges to theoriststhat must be overcome to provide predictions that have the precisionnecessary to match the accuracy of data. A few novel ideas to exploitthis precision directly or indirectly will also be discussed.

With Run II, the LHC experiment already reached an unprecedented level of precision compared to previous hadron colliders. The amount of data collected in Run III and the High-Luminosity run will increase quickly and dramatically. I will discuss specific challenges to theorists that must be overcome to provide predictions that have the precision necessary to match the accuracy of data. A few novel ideas to exploit this precision directly or indirectly will also be discussed.

Precision at the LHC: why and how

Condensed matter is found in a variety of phases, the vast majority of which are characterized in terms of symmetry breaking. For example, magnets spontaneously break time-reversal and spin rotation symmetries. A notable exception was provided by the  discovery of the quantum Hall effects which exhibit new kinds of topological orders not associated with any symmetry breaking. One of the characterizing features of topological order is the existence of excitations withexotic properties. These so-called anyonic excitations might make topologically ordered systems ideal building blocks of fault-tolerant quantum computers. In this colloquium, I will start by giving a general introduction to the concept of topological order and then address some of the recent developments. In particular, I will introduce theoretical frameworks that allow us to classify topological phases and discuss dynamical signatures that are useful to experimentally detect them in experiments.

Condensed matter is found in a variety of phases, the vast majority of which are characterized in terms of symmetry breaking. For example, magnets spontaneously break time-reversal and spin rotation symmetries. A notable exception was provided by the discovery of the quantum Hall effects which exhibit new kinds of topological orders not associated with any symmetry breaking. One of the characterizing features of topological order is the existence of excitations with exotic properties. These so-called anyonic excitations might make topologically ordered systems ideal building blocks of fault-tolerant quantum computers. In this colloquium, I will start by giving a general introduction to the concept of topological order and then address some of the recent developments. In particular, I will introduce theoretical frameworks that allow us to classify topological phases and discuss dynamical signatures that are useful to experimentally detect them in experiments.

Topological phases of matter: From classification to detection in experiments

The Nobel Prize in Physics in 1930 was awarded to Raman for the discovery of the effect named after him. The next time physics prizes were announced was in November 1933, which makes this the longest peace-time gap in the history of the Nobel Prize in Physics. Considering that the 1932 year’s prize was awarded in 1933 to Heisenberg and the 1933 year’s prize to Schrödinger and Dirac for their contributions to the new quantum mechanics, this gap is the more puzzling. I will describe, based on archive material, the struggle facing the Nobel Committee during those years, and how it eventually arrived at a name combination comprising three of the greatest physicists of the twentieth century. I will also describe briefly the three Nobel Prizes concerning quantum mechanics that followed later, in 1945, 1954 and 2022.

The Nobel Prizes in Physics in 1932/33: Heisenberg, Schrödinger and Dirac

Wetting of liquid phases, such as water drops condensing at the surface of plant leaves, is ubiquitous in our daily life. Interestingly, the physics of wetting also plays a crucial role in our cells. Droplets composed of proteins can wet specific target sites in living cells and locally enrich biomolecules for specific chemical processes. Many droplet-forming proteins can also bind to membrane surfaces. Binding in cells is often chemically active since it is maintained away from equilibrium by supplying energy and matter. This non-equilibrium setting suggests a plethora of physical phenomena of soft condensed phases at biological interfaces.To investigate such phenomena, we derive the non-equilibrium thermodynamic theory of active wetting. By means of this theory, we show that active binding significantly alters the wetting behavior leading to non-equilibrium steady states with condensate shapes reminiscent of a fried egg or a mushroom. We further show that condensate shapes can switch upon changing the strength of active binding. The origin of such anomalous condensate shapes can be explained by an electrostatic analogy, where binding sinks and sources correspond to electrostatic dipoles along the triple line. This analogy suggests a general analogy between chemically active systems and electrodynamics.

Wetting of liquid phases, such as water drops condensing at the surface of plant leaves, is ubiquitous in our daily life. Interestingly, the physics of wetting also plays a crucial role in our cells. Droplets composed of proteins can wet specific target sites in living cells and locally enrich biomolecules for specific chemical processes. Many droplet-forming proteins can also bind to membrane surfaces. Binding in cells is often chemically active since it is maintained away from equilibrium by supplying energy and matter. This non-equilibrium setting suggests a plethora of physical phenomena of soft condensed phases at biological interfaces. To investigate such phenomena, we derive the non-equilibrium thermodynamic theory of active wetting. By means of this theory, we show that active binding significantly alters the wetting behavior leading to non-equilibrium steady states with condensate shapes reminiscent of a fried egg or a mushroom. We further show that condensate shapes can switch upon changing the strength of active binding. The origin of such anomalous condensate shapes can be explained by an electrostatic analogy, where binding sinks and sources correspond to electrostatic dipoles along the triple line. This analogy suggests a general analogy between chemically active systems and electrodynamics.

Chemically Active Wetting

Arnold Sommerfeld

The "Inverse Ising Problem" refers to finding the parameters (the Jij's and the hi's) in an Ising model given the first and second moments (the magnetizations mi and the correlation functions cij).This is of considerable interest in machine learning and data analysis whenever the data set and the number of variables is large, but the values taken by the variables can be taken to be "high" and "low". The maximum entropy distributions with given first and second moments then has the Ising form where the hi's and Jij's are Lagrange parameters.Several perturbative methods to solve the inverse Ising problem approximately have been proposed in the last few years. I will give a survey of the situation, with a focus on what we have know about the applicability of these methods to data such as gene expression and recordings from many neurons, where an underlying exact description is surely not of the Ising form.This is work with John Hertz and Yasser Roudi (Frontiers Comp Neuroscience, 2009) and work in progress.

The "Inverse Ising Problem" refers to finding the parameters (the Jij's and the hi's) in an Ising model given the first and second moments (the magnetizations mi and the correlation functions cij). This is of considerable interest in machine learning and data analysis whenever the data set and the number of variables is large, but the values taken by the variables can be taken to be "high" and "low". The maximum entropy distributions with given first and second moments then has the Ising form where the hi's and Jij's are Lagrange parameters. Several perturbative methods to solve the inverse Ising problem approximately have been proposed in the last few years. I will give a survey of the situation, with a focus on what we have know about the applicability of these methods to data such as gene expression and recordings from many neurons, where an underlying exact description is surely not of the Ising form. This is work with John Hertz and Yasser Roudi (Frontiers Comp Neuroscience, 2009) and work in progress.

Arnold Sommerfeld Theory Colloquium

What can we compute with quantum devices?

Revisiting the S-matrix bootstrap

In this talk I will discuss connections between the physics of complexsystems such as spin glasses and attempts to solve optimizationproblems by ”Adiabatic Quantum Computing” (AQC), a version of ”Quantum Annealing” (QA). An optimization problem is one in which one has to minimize (or maximize) an energy function in whichthere is competition between different terms so no single configurationof the variables minimizes each term in the energy. In statisticalphysics this competition is called ”frustration”. It leads to a complexenergy ”landscape” with many valleys separated by barriers, sosimple algorithms easily get trapped in local minima which have ahigher energy than the global minimum. Many problems in science,and engineering are formulated as optimization problems. In quantumannealing one tries to avoid being trapped in a local minimum byadding quantum fluctuations so the system can tunnel to regions oflower energy. The strength of the quantum fluctuations is graduallyreduced to zero during the annealing schedule. This method appliesto problems with binary variables, known as qubits in the quantumcase. There is considerable interest in AQC at present, in large partbecause a company, D-Wave, has produced an actual device, the latestversion of which has about one thousand qubits. In addition,there has been considerable theoretical work mainly using computersimulations to see if there is a ”quantum speedup” compared withanalogous classical algorithms in which thermal, rather than quantum,fluctuations are used to escape from local minima. In the talkI will discuss difficulties in obtaining a quantum speedup due to (i)(quantum) phase transitions that the system can undergo during theannealing schedule, and (ii) the sensitivity of the state of the systemto the precise values of the interactions, i.e. chaos. A related chaoticeffect is that the state of the system can change dramatically withsmall changes in the temperature (temperature-chaos), for thermalannealing, and the strength of the quantum fluctuations, for quantumannealing.

In this talk I will discuss connections between the physics of complex systems such as spin glasses and attempts to solve optimization problems by ”Adiabatic Quantum Computing” (AQC), a version of ”Quantum Annealing” (QA). An optimization problem is one in which one has to minimize (or maximize) an energy function in which there is competition between different terms so no single configuration of the variables minimizes each term in the energy. In statistical physics this competition is called ”frustration”. It leads to a complex energy ”landscape” with many valleys separated by barriers, so simple algorithms easily get trapped in local minima which have a higher energy than the global minimum. Many problems in science, and engineering are formulated as optimization problems. In quantum annealing one tries to avoid being trapped in a local minimum by adding quantum fluctuations so the system can tunnel to regions of lower energy. The strength of the quantum fluctuations is gradually reduced to zero during the annealing schedule. This method applies to problems with binary variables, known as qubits in the quantum case. There is considerable interest in AQC at present, in large part because a company, D-Wave, has produced an actual device, the latest version of which has about one thousand qubits. In addition, there has been considerable theoretical work mainly using computer simulations to see if there is a ”quantum speedup” compared with analogous classical algorithms in which thermal, rather than quantum, fluctuations are used to escape from local minima. In the talk I will discuss difficulties in obtaining a quantum speedup due to (i) (quantum) phase transitions that the system can undergo during the annealing schedule, and (ii) the sensitivity of the state of the system to the precise values of the interactions, i.e. chaos. A related chaotic effect is that the state of the system can change dramatically with small changes in the temperature (temperature-chaos), for thermal annealing, and the strength of the quantum fluctuations, for quantum annealing.

Can a quantum computer solve optimization problems more Efficiently than a classical computer?

The Arnold Sommerfeld Center for Theoretical Physics organizes regular colloquia about topics of current interest in the field of theoretical physics.

Quantum field theory (QFT) is the universal language of theoretical physics, underlying the Standard Model of elementary particles, the physics of the early Universe and a host of condensed matter phenomena such as phase transitions and superconductivity. A great achievement of 20th-century physics was the understanding of weaklycoupled quantum field theories where interactions can be treated as small perturbations of otherwise freely moving particles. Critical challenges for the 21st century include solving the problem of strong coupling and mapping the whole space of consistent QFTs. In this lecture, I will overview the bootstrap approach, the idea thattheory space can be determined from the general principles of symmetry and quantum mechanics. This strategy provides a new unifying language for QFT and has allowed researchers to make predictionsfor physical observables even in strongly coupled theories. I will illustrate the general framework in a few examples, ranging from the concrete (boiling water) to the abstract (supersymmetric theories in various spacetime dimensions).

Quantum field theory (QFT) is the universal language of theoretical physics, underlying the Standard Model of elementary particles, the physics of the early Universe and a host of condensed matter phenomena such as phase transitions and superconductivity. A great achievement of 20th-century physics was the understanding of weakly coupled quantum field theories where interactions can be treated as small perturbations of otherwise freely moving particles. Critical challenges for the 21st century include solving the problem of strong coupling and mapping the whole space of consistent QFTs. In this lecture, I will overview the bootstrap approach, the idea that theory space can be determined from the general principles of symmetry and quantum mechanics. This strategy provides a new unifying language for QFT and has allowed researchers to make predictions for physical observables even in strongly coupled theories. I will illustrate the general framework in a few examples, ranging from the concrete (boiling water) to the abstract (supersymmetric theories in various spacetime dimensions).

Pulling Yourself by your Bootstraps in Quantum Field Theory

The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-bodyproblem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is inmany cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Completefactorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. Iwill give examples how one can apply this powerful theoretical concept in experiment.A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system oftwo 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble[2]. This is verified through phase correlations up to 10th order.Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon /massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize[3]. This allowed us to characterize the essential features of the model solely from our experimental measurements:detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states thequasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve anon-trivial quantum field theory.Our examples establish a general method to analyse quantum systems through experiments. It thus represents acrucial ingredient towards the implementation and verification of quantum simulators.Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg).Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 andthe EU: ERC-AdG QuantumRelax[1] M. Gring et al., Science, 337, 1318 (2012);[2] T. Langen et al., Science 348 207-211 (2015).[3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I will give examples how one can apply this powerful theoretical concept in experiment. A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble [2]. This is verified through phase correlations up to 10th order. Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon / massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize [3]. This allowed us to characterize the essential features of the model solely from our experimental measurements: detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a non-trivial quantum field theory. Our examples establish a general method to analyse quantum systems through experiments. It thus represents a crucial ingredient towards the implementation and verification of quantum simulators. Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg). Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and the EU: ERC-AdG QuantumRelax [1] M. Gring et al., Science, 337, 1318 (2012); [2] T. Langen et al., Science 348 207-211 (2015). [3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

High order correlation and what we can learn about the solution for many body problems from experiment

String theory seems to offer an enormous number of possibilities for low energy physics. The huge set of solutions is often known as the String Theory Landscape. In recent years, however, it has become clear that not all quantum field theories can be consistently coupled to gravity. Theories that cannot be ultraviolet completed in quantum gravity are said to be in the Swampland. In this talk, I'll discuss some conjectured properties of quantum gravity, evidences for them, and their applications to cosmology and particle physics.

Quantum Gravity and the Swampland

The functional renormalization group (RG) is an ideal tool for dealing with the diversity of energy scales and competition of instabilities in interacting fermion systems. Starting point is an exact flow equation which yields the gradual evolution from a microscopic model action to the effective low-energy action as a function of a continuously decreasing energy scale. Expanding in powers of the fields yields an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes [1].Applications reviewed in the colloqium include: (i) d-wave superconductivity and other instabilities in the two-dimensional Hubbard model, and (ii) transport through a barrier and resonant tunneling in a one-dimensional Luttinger liquid metal. Recently, the functional RG has been upgraded from a weak-coupling method to a computational tool for strongly interacting fermion systems [2,3].[1] W. Metzner et al., Rev. Mod. Phys. 84, 299 (2012).[2] C. Taranto et al., Phys. Rev. Lett. 112, 196402 (2014).[3] D. Vilardi et al., Phys. Rev. B 99, 104501 (2019).

The functional renormalization group (RG) is an ideal tool for dealing with the diversity of energy scales and competition of instabilities in interacting fermion systems. Starting point is an exact flow equation which yields the gradual evolution from a microscopic model action to the effective low-energy action as a function of a continuously decreasing energy scale. Expanding in powers of the fields yields an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes [1]. Applications reviewed in the colloqium include: (i) d-wave superconductivity and other instabilities in the two-dimensional Hubbard model, and (ii) transport through a barrier and resonant tunneling in a one-dimensional Luttinger liquid metal. Recently, the functional RG has been upgraded from a weak-coupling method to a computational tool for strongly interacting fermion systems [2,3]. [1] W. Metzner et al., Rev. Mod. Phys. 84, 299 (2012). [2] C. Taranto et al., Phys. Rev. Lett. 112, 196402 (2014). [3] D. Vilardi et al., Phys. Rev. B 99, 104501 (2019).

Functional renormalization group approach to correlated fermion systems

Although the neutrino oscillations are well established phenomenon, new and unusual oscillation effects in matter are still emerging. I will describe three such effects which have applications to the solar, supernova and low energy atmospheric neutrinos: (i) Parametric resonance for neutrinos propagating in a flux of background neutrinos. (ii) Oscillation waves emitted from borders between layers in a multilayer medium, like in the Earth. (iii) The attenuation effect related to the energy uncertainty in oscillation setup.

Strange effects in the neutrino oscillations

The apparent crisis of black holes inconsistency with foundational physical principles provides a sharp focus for the conflict between quantum mechanics and classical spacetime. Various resolutions havebeen proposed; a very plausible one is that small interactions can transfer sufficient information between the black hole and outgoing radiation, with a quantum enhancement from the enormous number of black hole states. Such interactions must however violate conventional notions of locality, perhaps as a symptom of the more basic subtlety of information localization in quantum gravity, and hinting at aspects of the fundamental structure of quantum gravity. An intriguing question is whether further clues can be found from new observational windows on black holes.

The apparent crisis of black holes inconsistency with foundational physical principles provides a sharp focus for the conflict between quantum mechanics and classical spacetime. Various resolutions have been proposed; a very plausible one is that small interactions can transfer sufficient information between the black hole and outgoing radiation, with a quantum enhancement from the enormous number of black hole states. Such interactions must however violate conventional notions of locality, perhaps as a symptom of the more basic subtlety of information localization in quantum gravity, and hinting at aspects of the fundamental structure of quantum gravity. An intriguing question is whether further clues can be found from new observational windows on black holes.

Black holes as harbingers of new gravitational physics

From the softest of interactions of a magnetic field with an electron, to the most violent collisions at the Large Hadron Collider, precision quantum field theory produces numbers and functions with interesting number-theoretic properties. In many examples a co-action principle holds, an invariance under a ”cosmic” Galois group. I will provide several arenas in which this principle can be seen at work, including perhaps the richest set of theoretical data, scattering amplitudes in planar N = 4 super-Yang-Mills theory.

Particle Scattering and Number Theory

A unified theory for space-time and matter might be based on finiteprojective geometries instead of differentiable manifolds and gaugegroups. Each point is equipped with a quadratic form over a finite Galois field which define neighbors in the finite set of points.Due to the projective equivalence of all quadratic forms this worldis necessarily a 4-dimensional Lorentz-invariant space-time with agauge symmetry G(3)xG(2)xG(1) for internal points which represent elementary particle degrees of freedom. Matter appears as ageometric distortion by an inhomogeneous field of quadrics and allphysical properties (spins, charges) of the standard model seem tofollow from its geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fieldsand a bosonic for gauge fields. This unity of space-time and matterwas already sought 1918 by Hermann Weyl in a gauge theory as anextension of Einstein’s general theory of relativity, but not found -probably because of the assumption of a continuous geometry.

A unified theory for space-time and matter might be based on finite projective geometries instead of differentiable manifolds and gauge groups. Each point is equipped with a quadratic form over a finite Galois field which define neighbors in the finite set of points. Due to the projective equivalence of all quadratic forms this world is necessarily a 4-dimensional Lorentz-invariant space-time with a gauge symmetry G(3)xG(2)xG(1) for internal points which represent elementary particle degrees of freedom. Matter appears as a geometric distortion by an inhomogeneous field of quadrics and all physical properties (spins, charges) of the standard model seem to follow from its geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fields and a bosonic for gauge fields. This unity of space-time and matter was already sought 1918 by Hermann Weyl in a gauge theory as an extension of Einstein’s general theory of relativity, but not found - probably because of the assumption of a continuous geometry.

Space-Time-Matter: Finite Projective Geometry as a Quantum World with Elementary Particles

I describe an algebraic scheme for quantizing the Ruijsenaars-Schneidermodels in the R-matrix formalism. It is based on a special parametrizationof the cotangent bundle over GL(n,C). In new variablesthe standard symplectic structure is described by a classical (Frobenius)r-matrix and by a new dynamical r¯-matrix. Quantizing theser-matrices, I will exhibit the quantum L-operator algebra and constructits particular representation corresponding to the RuijsenaarsSchneidersystem. I will also indicate a couple of open problems.

I describe an algebraic scheme for quantizing the Ruijsenaars-Schneider models in the R-matrix formalism. It is based on a special parametrization of the cotangent bundle over GL(n,C). In new variables the standard symplectic structure is described by a classical (Frobenius) r-matrix and by a new dynamical r¯-matrix. Quantizing these r-matrices, I will exhibit the quantum L-operator algebra and construct its particular representation corresponding to the RuijsenaarsSchneider system. I will also indicate a couple of open problems.

R-matrix Quantization of the Ruijsenaars-Schneider Models

The study of black holes has revealed a deep connection betweenquantum information and spacetime geometry. Its origin must liein the quantum theory of gravity, which offers a valuable hint inour search for a unified theory. Precise formulations of this relationrecently led to new insights in Quantum Field Theory, some of whichhave been rigorously proven. An important example is our discoveryof the first universal lower bound on the local energy density. Theenergy near a point can be negative but it is bounded below by aquantity related to the information flowing past the point.

The study of black holes has revealed a deep connection between quantum information and spacetime geometry. Its origin must lie in the quantum theory of gravity, which offers a valuable hint in our search for a unified theory. Precise formulations of this relation recently led to new insights in Quantum Field Theory, some of which have been rigorously proven. An important example is our discovery of the first universal lower bound on the local energy density. The energy near a point can be negative but it is bounded below by a quantity related to the information flowing past the point.

Black Holes, Quantum Information, and Unification

Sommerfeld Theory Colloquium (ASC)

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