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|09:00||Claus Kiefer (Cologne): Quantum Geometrodynamics - Whence, Whither|
|09:50||Johanna Erdmenge (Heisenberg Institute): New Dualities Between Gauge Theories and Gravity|
|11:00||Sabine Hossenfelder (NORDITA): Experimental Searche for Quantum Gravity|
|12:00||Robert Helling (LMU Munich): The "Shut up and Calculate" Approach to Quantum Gravity|
|14:00||Igor Khavkine (Utrecht): Gravity, An Exercise in Quantisation|
|15:10||Dennis Lehmkuhl (Wuppertal): Einstein's Approach to Quantum Gravity|
|16:00||Alexander Blum (MPIWG): The Moving Frontier, How Quantum Gravity Became The Great Unsolved Problem of Modern Physics|
|19:00||Workshop Dinner at Kaisergarten|
|09:00||Chris Wuthrich (UCSD): Time and Space in Causal Set Theory|
|09:50||J. Brian Pitts (Cambridge): Real Change Happens in Hamiltonian Relativity, Just Ask the Lagrangian (about Time-like Killing Vectors, First-Class Constraints and Observables)|
|11:00||Karim Thebault (LMU Munich): Time Remains|
|11:50||Daniele Oriti (Einstein Institute): Dissappearance and Emergence of Space and Time in Quantum Gravity|
|14:00||Nazim Bouatta (Cambridge): On Emergence and Reduction in String Theory|
|15:10||Richard Dawid (Vienna): String Theory, Final Theory Claim and Scientific Realism|
|16:10||Dean Rickles (Sydney): Dualities and the Physical Content of Theories|
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler-DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the convariant theory, the semiclassical approximation as well as applicatoins to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.
Based on string theory, AdS / CFT correspondence (AdS: Anti-de Sitter space, CFT: Conformal field theory) provide a new map between quantum gauge theories and classical gravity theories. This new map arises from a specific low-energy limit of string theory. It is a duality, mapping strongly coupled quantum gauge theories to weakly coupled gravity theories. Moreover, this duality maps classical gravity theories on five-dimensional Anti-de Sitter space to quantum gauge theories on the four-dimensional boundary of this space, a property referred to as holography. In addition to its significance for quantum gravity, the AdS / CFT correspondence has been generalized to further examples of gauge / gravity duality. These have practical applications to the study of systems relevant in elementary particle and condensed matter physics. We will give an introduction to gauge / gravity duality.
The development of a theory for quantum gravity cannot proceed without phenomenology. In this talk I will lay out the methodology of the phenomenology of quantum gravity, and the difficulities this research area faces due to the peculiarity of the subject. I will then discuss some examples of models for quantum gravity phenomenology and possible experiments to test them.
Quantum mechanics would have never been developed requiring to first understand all foundational issues. Rahter, it was approached in a pragmatic way summarized as shut up and calculate. For quantum gravity we already understand a number of its properties even if it is still unclear what form the final theory will have and how it solves its conceptual conundrums. The often repeated claim that quantum gravity lacks empirical data is - taken without qualification - not true. Rather, the requirement to reduce to known theories relativity in the appropiate limits togehter with our expericence of everyday physics rule out most creative proposals for a theory of quantum gravity. We want to pursue the effective-filed-theory line-of-thought neglecting conceptual expectations. The effective field theory approach still leaves room for a wide variety of ideas like string theory, loop quantum gravity or emergent gravity as we will show in a number of examples.
The quantization of General Relativity (GR) is an old and chellenging prob- lem that is in many ways still awaiting a satisfactory solution. GR is a partic- ularly complicated field theory in several respects: non-linearity, gauge invari- ance, dynamibal causal structure, renormalization, singularities, infared effects. Fortunately, much progress has been made on each of these fronts. Our under- standing of these problems has evolved greatly over the past century, together with our understandig of quantum field theory (QFT) in general. Today, the state of the art in QFT knows how to address each of these challenges, as they occur in isolation in ohter field theories. There is still an active research program aiming to combine the relevant methods and apply them to GR. But, at the very least, the problem of the quantization of GR can be formulated as a well defined mathematical question. On the other hand, quantum GR also faces a different set of obstacles: timelessness, non-renormalizability, naturality, unification, which reflect, not its technical difficulty, but rather the aesthetic and philosophical preferences of practing theoretical physicists. I will briefly discuss how the technical state of the art and a scientifically conservative philosophical position make these obstacles irrelevant. Time per- mitting, I will also briefly touch on some aspects of the state of technical state of the art that have turned the quantization of GR into a (still challenging) exercise: covariant Poisson structure, BV-BRST treatment of gauge theories, deformation quantization, Epstein-Glaser renormalization.
It is common knowledge that despite being a pioneer of the early quantum theory, Einstein opposed the probabilistic interpretation of the new quantum mechanics of 1925 / 1926, and he would have opposed any approach of a quantization of gravity relying on this interpretation. What is less well-known is that Einstein had an alternative approach that bears some similarities to more recent ideas to general relativize quantum mechancis rather than quantizing general relativity. Einstein identified discreteness in nature with quantum theory: the existence of photons, the quantisation of electric charge, etc. Roughly speaking, his idea was that these quantum features of reality could be derived from a generally covariant field theory of gravitation and electromagnetism by finding overdetermined partial differential equations which allow for solutions capable of represtenting quantum particles. If this were to be achieved, the groundfloor ontology of the world would have turned out to be one of classical fields described by generally covariant partial differential field equations, while the quantum would only enter on the level of the solutions to these equations. The talk reviews the above research programme of Einsteins, and reflects on whether it can lend some inspiration to modern quantum gravity research.
Alexander Blum: The Moving Frontier, How Quantum Gravity Became The Great Unsolved Problem of Modern Physics
The immense difficulties encountered in finding a quantum theory of gravity are generally understood as revealing a deep conceptual divide between the two major physical theories of the 20th century: quantum mechanics (or quantum field theory) and the general theory of relativity. It was, however, far from clear from the outset (the outset here being physics after the quantum and relatvity revolutions) that this would be the essential fault line of modern physics. It seemed rather, all through the 1930s and 1940s that there was a conceptual incompatibility between quantum theory and field theories in general (which included general relativity as a rather esoteric and empirically irrelevant example), revealed through the divergence difficulties of the attempted quantum field theories. In my talk, I will attempt to trace how the perceived conceptual divide shifted in the course of the Twentieth Century. It is hoped that this analysis can simultaneously address general historical questions of scientific development, especially at the boundaries of distinct well-established theories, and at the same time help understand what the unique features of quantumg gravity are that have established it, in the course of the last century, as the prime unsolved problem of theoretical physics.
Causal set theory offers an elegant and philosophically rich, though admittedly inchoate, approach to quantum gravity. After presenting its basic theoretical framwork, I will show how space and time vanish from the fundamental picture it offers. The absence of space and time from the theory raises the serious question of whether such a theory can be empirically coherent at all, i.e, whether its truth would not undermine any justification we may heave for believing it. If it can be shown that spacetime re-emerges from the fundamental structure itn the appropriate limit, I will argue, then the threat of empirical incoherence is averted and it can be appreciated how space and time emerge from what there is, fundamentally, according to causal set theory. I shall close by sketching the prospects of the antecedent of this conditional claim.
In Hamiltonian GR, change has seemed absent. Attention to the gauge generator G facilitates a neglected calculation: a first-class constraint generates a bad physical change in electromagnetism and GR, spoiling the constraints, Gauss's law or the momentum and Hamiltonian constraints in the (physically relevant) velocities. Only as a team G do first-calss constraints generate a gauge transformation. To find change, insist on Hamiltonian-Lagrangian equivalence. Change is ineliminable time dependence; in vaccum GR it is the absence of a time-like Killing vector field. Neglecting spatial dependence, invariantly something depends on time via Hamilton's equations iff there is no time-like Killing vector. According to Bergmann, reality is not confined to observables, defined as both gauge invariant (hence real) and economical (Cauchy data on space). Thus change can exist outside observables. Bergmanns lemma that observables have vanishing Poisson brackets for gauge transformations was imported by analogy to electromagnetism, neglecting the external vs. internal distinction and Hamiltonaian-Lagrangian equivalence. The resulting implausible Killing-type condition lacks the local examples required by Bergmann. Taking observables to be geometric objects (tensors, etc.) as usual in the 4-dimensional Lagrangian formalism makes the Poisson bracket of G with an observable the Lie derivative of a geometric object (on-shell): covariance, not invariance.
Even classically, it is not entirely clear how one should understand the implications of general covariance for the role of time in physical theory. On one popular view, the essential lesson is that change is relational in a strong sense, such that all that it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. This implies that there is no unique parameterziation of time slices, and also that there is no unique temporal ordering of states. At a quantum level this approach to general relativity is generally understood lead to a universe eternally frozen in an energy eigenstate. Here we will start from a different interpretation of the classical theory, and in doing so show one may avoid this acute "problem of time" in quantum gravity. Under our view, duration is still regarded as relative, but temporal succession is taken to be absolute. This is consistent with general covariance because it can be maintained only ba the addition of an arbitrary time parameter corresponding to the minimal temporal structure necessary for a succession of observations to be represented. This approach to the classical theory of gravity is argued to then lead to a relational quantization methodology, such that it is possible to conceive of dynamical observables within a theory of quantum gravity.
We recall the hints for the disappearance of continuum space and time at microsopic scales, coming from classical and semi-classical gravitational physics. These include arguments for discreteness or for a fundamental non-locality, in a quantum theory of gravity. We compare how these ideas are realized in specific quantum gravity approaches, and focus in particular on the group field theory formalism, itself strictly related to other approaches, in particular loop quantum gravity. Next, we consider the emergence of continuum space and time from the collective behaviour of discrete, pre-geometric and non-spatio-temporal atoms of quantum space. After discussing the notion of emergence, with Bose condensates as one paradigmatic examples, and some specific cenceptual difficulties with the notion of emergent spacetime, we argue for spacetime as a kind fo cendsate, result of a phase transition, physically identified with the big bang. We then illustrate recent results, in the context of the group field theory framework, establishing a tentative procedure for the emergence of cosmological (homogeneous) spacetime and their effective quantum dynamics from fundamental, pre-geometric models. Last, we re-examine the conceptual issues raised by the emergent spacetime scenario in light of this concrete example.
Emergence and reduction are compatible, despite the widespread "ideology" that they contradict each other. The overarching theme is that the reconciliation of emergence reduction turns on subtle uses of infinite limits. Previous philosophical literature about how one theory or a sector, or regime, of a theory might be emergent from, and-or reduced to, another one has tended to emphasise cases, such as occur in statistical mechanics. But here, we will develop this viewpoint for quantum field theories, including those on the way to the 't Hooft limit. This aspect relates closely to the string-gravity connection.
T-duality, which is an important feature of string theory, implies that the string scale constitutes a minimal length scale: within the conceptual framework of the theory, no higher energy scale can provide new information. This in turn may be taken to suggest that, if ST is valid at its own characteristic scale, no new theories which become empirically distinguishable from string theory at higher energy scales should be expected to be found. The problem with this final theory claim hinges on the fact that it seems to beg the question by presupposing the conceptual framwork the finality of which it aims to establish. In the talk I aim at understanding significance an limitations of string theorys final theory claim based on the distinction between local and global limitations to scientific underdetermination. It will be argued that the final theory claim does carry some weight but cannot be understood independently from more general considerations about the scientific role of limitations to underdetermination. Some implications of final theory claims for the scientific realism debate are discussed in the second part of the talk.
A duality expresses a reltionship between a pair of putatively distinct physical theories. Theories are said to be dualwhen they generate "the same physics", where same physics is parsed in terms of, e.g., having the same amplitudes, expectation values, observable spectra, and so on. Hence, theories related by dualities can look very different while making exactly the same predictions about observatle phenomena. Indeed, such theories can look sufficiently different that would-be interpreters would surely consider them to be representations of very different possible worlds. In this talk I will be concerned with the question of whether dualites reflect some deep aspect of reality, or whether they are simply a formal device that aids computations in difficult contexts (functioning in much the same way as a change of variables). This links quite naturally to problems of underdetermination, and also to the issue of what we mean by theory in such contexts. I defend a rather deflationary account fo the philosophical implications of dualities. Since the underdetermination is taken to apply to structurally distinct theories (that is, it is structure that is underdetermined), I will also consider whether dualities pose a problem for structural realists.