Workshop: Exploring gravity with quantum mechanics and vice versa

Tim Koslowski: The geometric description of pure shape dynamics

Scientific statements about the universe as a whole are necessarily relational, since all scientific refence structures are objects within the universe itself. Pure shape dynamics implements this requirement by describing the dynamics of the universe in terms of an "equation of state" for an (unparametrized) curve of relational configurations. These equations can be obtained by an explicit algorithm that I will present in a toy model. Thereafter I will explain the geometric structure that makes it possible to describe an interesting class of models in terms of equations of state on relational configuration space.

Robert Wald: State Vector Reduction in Quantum Field Theory

The key issues in quantum measurement theory are briefly discussed/reviewed. The nature of "state vector reduction" is examined in the context where the quantum system is a field rather than (a collection of) non-relativistic particle(s). For particles, one might believe that state vector reduction brings one to (approximate) position eigenstates of the particles. It is argued that no such natural basis of states exists for a quantum field. This talk is intended to get various discussions started rather than to present any definitive results.

Wayne Myrvold: Relativistic Considerations Concerning Interpretations of Quantum Mechanics

In this talk I will outline results regarding compatibility of the main avenues of approach to interpretations of quantum mechanics with relativistic causality, focussing on hidden-variables theories and on dynamical collapse theories.  In brief: hidden-variables theories, such as de Broglie-Bohm require a distinguished relation of distant simulataneity, while collapse theories don't. I will also discuss how to talk about quantum state evolution in a relativistic context, and about ontology for relativistic collapse theories. Time permitting, I will say something about Everettian theories.

Tim Maudlin: Topology and the Structure of Space-Time

Mathematical representations of physical entities are shaped by the mathematical tools used to create them. Space, time, and space-time have traditionally been represented by topological spaces: sets of points that are knit together, at the most fundamental level, by a structure of open sets that satisfies the axioms of standard topology.  Notions such as the connectedness of a space, the boundary of a set, and the continuity of a function are defined by reference to these open sets. Additional geometrical structure (such as metrical or affine structure) can be added to a topological space, but the mathematical representation typically begins with a topological manifold. 

I will argue that standard topology is wrong mathematical tool to use for representing the structure of space and time (or space-time). I will present an alternative mathematical tool, the Theory of Linear Structures, whose primitive notion is the line rather than the open set. The Theory of Linear Structures has a wider field of useful application than topology in that it can be used to capture the geometry of discrete spaces as well as continua. It provides alternative, non-equivalent definitions of, e.g., connectedness, boundaries, and the continuity of a function. And it offers a more detailed account of the sub-metrical geometry of a space: every Linear Structure induces a topology on a space, but many different Linear Structures give rise to the same topology.

Using the Theory of Linear Structures rather than standard topology to describe space-time has a powerful ontological payoff: one can show that the basic organizing principle of a Relativistic space-time (but not a classical space-time) is time. Contrary to common belief, Relativity does not “spatialize time”, it rather “temporalizes space”.

Bartek Czech: A stereoscopic look into the bulk

I introduce a new "stereoscopic" entry in the holographic dictionary, which allows the CFT to register depth in AdS. On the CFT side, stereoscopic operators are OPE blocks--contributions to the OPE from a single conformal family. In holographic theories, OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in AdS. To illustrate the usefulness of stereoscopic variables, I will sketch new, conceptually clean derivations of the following known results: (1) the form of the vacuum modular Hamiltonian, (2) the first law of entanglement in holography, (3) linearized Einstein's equations, (4) the HKLL form of local bulk operators, (5) geodesic Witten diagrams.

Daniel Sudarsky: Usefulness of Dynamical reduction theories in situations involving Quantum Theory and  Gravitation

I will present some motivation to explore this path. I will argue that such theories seem to offer appealing resolutions of some difficult issues in appearing the above context, such as the origin of the seeds of structure in  the inflationary  era,  and the  so called “ Black Hole information paradox”. As a by product I will offer an  explanation of the fact that we have not detected the famous B-modes in the CMB. I will then focus in the difficulties that must be addressed before considering the approach as truly viable.

Viqar Husain: Polymer quantization and its consequences

I will describe some results from the application of polymer quantization  to cosmology and field theory. The results range from  generation of inflation and a graceful exit in semiclassical  gravity to Lorentz violation in the Unruh detector.