# Shape Dynamics Workshop

Conference Date:
Monday, May 15, 2017 (All day) to Wednesday, May 17, 2017 (All day)
Scientific Areas:
Quantum Gravity

Shape dynamics is a new, completely relational description of gravity. This description is derived from first principles which implement the observation that all objective observables in physics are ratios between physical objects and locally available reference quantities. The theory provides a different understanding of the nature of gravity: no longer described as a geometrical block of spacetime but as the temporal evolution of spatial conformal geometry. Such an understanding clears major obstructions to the construction of quantum gravity theories, e.g. the nature of observables and their evolution. The methods of the theory bear strong connections to the mathematics of the initial value problem of GR, and to studies of dissipative dynamical systems. Since shape evolution is blind to certain types of singular behavior of the gravitational field, the study of cosmological and local evolution acquires new possibilities. Moreover, Its distinct theory space opens new opportunities for the application of effective field theory treatments and renormalization group methods.  This conference brings researchers in these areas together to foster new interdisciplinary discourse and collaboration in this fascinating interplay between conformal symmetry, cosmology, and gravitational physics.

• Julian Barbour, University of Oxford
• Yuri Bonder, UNAM
• Beatrice Bonga, State College, Pennsylvania
• Bianca Dittrich, Perimeter Institute
• Astrid Eichhorn, University of Heidelberg
• Sean Gryb, University of Bristol
• James Isenberg, University of Oregon
• Tim Koslowski, UNAM
• Flavio Mercati, Sapinza University of Rome
• Roberto Percacci, SISSA
• David Sloan, University of Oxford
• Julian Barbour, University of Oxford
• Yuri Bonder, UNAM
• Beatrice Bonga, State College, Pennsylvania
• Bianca Dittrich, Perimeter Institute
• Astrid Eichhorn, University of Heidelberg
• Henrique Gomes, Perimeter Institute
• Sean Gryb, University of Bristol
• Daniel Guariento, Perimeter Institute
• James Isenberg, University of Oregon
• Etera Livine, École Normale Supérieure de Lyon
• Tim Koslowski, UNAM
• Flavio Mercati, Sapinza University of Rome
• Seyed Faroogh Moosavian, Perimeter Institute
• Pedro Naranjo, UNAM
• Roberto Percacci, SISSA
• David Sloan, University of Oxford
• Lee Smolin, Perimeter Institute
• Barak Shoshany, Perimeter Institute

Monday, May 15, 2017

 Time Event Location 9:00 – 9:30am Registration Reception 9:30 – 9:35am Welcome and Opening Remarks Sky Room 9:35 – 10:30am Julian Barbour, University of OxfordShape Dynamics: Perspectives and Problems Sky Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:00pm Tim Koslowski, UNAMThe quantum equation of state of the universe produces a small cosmological constant Sky Room 12:00 – 12:30pm Discussion 1 Sky Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 2:45pm Beatrice Bonga, State College, PennsylvaniaTBA Sky Room 2:45 – 3:30pm Yuri Bonder, UNAMRelationalism and the speed of light: Are we in a relationship? Sky Room 3:30 -4:00pm Coffee Break Bistro – 1st Floor 4:00 – 4:45pm Flavio Mercati, Sapienza University of RomeTBA Sky Room 4:45 – 5:30pm Discussion 2 Sky Room 5:30pm onwards Wine and Cheese Reception Bistro – 2nd Floor

Tuesday, May 16, 2017

 Time Event Location 9:30 – 10:30am James Isenberg, University of OregonWhat we know and don’t know about solutions to the Einstein Constraint Equations Sky Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:00pm Stephen Adler, Institute for Advanced StudyImplications of a Frame-Dependent Dark Energy Action Sky Room 12:00 – 12:30pm Discussion 3 Sky Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 2:45pm Roberto Percacci, SISSATBA Reflecting Lounge 2:45 – 3:30pm Astrid Eichhorn, University of HeidelbergRenormalization Group flows of spacetime Sky Room 3:30 – 4:00pm Coffee Break Bistro – 1st Floor 4:00 – 4:45pm Lee Smolin, Perimeter InstituteTBA Sky Room 4:45 - 5:30pm Discussion 4 Sky Room

Wednesday, May 17, 2017

 Time Event Location 9:30 – 10:30am David Sloan, University of OxfordTBA Sky Room 10:30 – 11:00am Coffee Break Bistro – 1st Floor 11:00 – 12:00pm Claes Uggla, Karlstad UniversityDynamical systems approaches and methods in cosmology Sky Room 12:00 – 12:30pm Discussion 5 Sky Room 12:30 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 2:45pm Sean Gryb, University of BristolQuantum singularity resolution in homogeneous cosmology and the implications for shape dynamics Sky Room 2:45 – 3:30pm Henrique Gomes, Perimeter InstituteTBA Sky Room 3:30 – 4:00pm Coffee Break Bistro – 1st Floor 4:00 – 5:00pm Discussion 6 Sky Room

Implications of a Frame-Dependent Dark Energy Action

I review motivations for a frame-dependent dark energy action  proportional to  $\int d^4x (-g)^{1/2}/g_{00}^2$,  and discuss implications for the black hole horizon and  for perturbations  on the Robertson-Walker line element.

Julian Barbour, University of Oxford

Shape Dynamics: Perspectives and Problems

Shape Dynamics(SD) can be derived from principles that differ in significant respects from Einstein's derivation of GR. It requires a spatially closed universe and allows a smaller set of solutions than GR does for this case. There are indications that its solution space can be fully characterized and endowed with a measure. These architectonic features suggest that SD can explain the arrows of time as direct consequences of the law of the universe. They do not require special initial conditions. I will discuss these and other major issues on which SD may cast light. I will also discuss the problems that face SD.

Yuri Bonder, UNAM

Relationalism and the speed of light: Are we in a relationship?

Most practical studies in Shape Dynamics involve an N-body Newtonian interaction which is described by a homogeneous potential. This property allows one to proof several interesting features like the emergence of an arrow of time. However, more generic interactions are not described by these kind of potentials and introduce additional dimensionful coupling constants. Thus, it is an open question whether more generic interactions can be written in a fully relational manner. By studying the concrete example of the gravitational Weber interaction which is, in a sense, a more realistic theory of gravity, we show that it is possible translate non-Newtonian interactions, which have inhomogeneous potentials and additional coupling constants, into a relational language. This opens the door to study other interactions and may shed light into the relationalization of gravity as described by general relativity.

Astrid Eichhorn, University of Heidelberg

Renormalization Group flows of spacetime

I will discuss the use of (functional) Renormalization Group in models of quantum gravity. I will highlight the challenges that occur in continuum approaches to quantum gravity, such as asymptotically safe gravity, as well as challenges in discrete approaches, such as tensor models.

Sean Gryb, University of Bristol

Quantum singularity resolution in homogeneous cosmology and the implications for shape dynamics

I will present results on the quantization of an FRLW model that utilises a Schrodinger-type evolution equation. In contrast to standard Wheeler--DeWitt-type quantisations, the quantum model resolves the classical singularity, exhibits a quantum bounce, and displays novel early-universe phenomenology. A global scale emerges because of a scale anomaly, and suggests an interesting scenario for quantum shape dynamics. I will give the details of the quantization procedure and show how these techniques can be used more generally for anisotropic models. I will end by speculating about how these techniques might be applicable to a genuine quantum shape model of the universe.

James Isenberg, University of Oregon

What we know and don’t know about solutions to the Einstein Constraint Equations

Tim Koslowski, UNAM

The quantum equation of state of the universe produces a small cosmological constant

Relationalism is the strict disentanglement of physical law from the definition of physical object. This can be formalized in the shape dynamcis postulate that the objective evolution of the universe is described by an "equation of state of a curve in relational configuration space." The application of this postulate to General Relativity implies that gravity is described by an equation of state of a curve on conformal superspace. It turns out that the naive quantization of these equations of state introduces an undesired preferred time parametrization. However, it turns out that one can still describe the quantum evolution of the system as an equation of state of the Bohmian trajectory which remains manifestly parametrization independent. These quantum systems generically develop quasi-isolated bound states (atoms) that can be used as reference systems. It turns out that the system as a whole expands if described in units defined by these atoms. This produces phenomenological effects that are usually ascribed to the presence of a cosmological constant. This "effective cosmological constant" is however unaffected by vacuum energy. I pesent the formal argument for this statement and show this explicitly by remormalizing a scalar field coupled to shape dynamics.

Dynamical systems approaches and methods in cosmology

I will with simple examples from spatially homogeneous and isotropic cosmology illustrate the importance of respecting the global features of a state space for a given model when reformulating field equations to useful dynamical systems. In particular I will use examples from f(R) gravity and GR with a minimally coupled scalar field. In this context I will also illustrate how various dynamical systems methods, such as, e.g., monotonic functions, center manifold techniques, averaging methods, can yield a global understanding of the solution spaces as well as approximations, complementing, e.g., the slow-roll approximation.

Scientific Organizers:

• Henrique Gomes, Perimeter Institute
• Daniel Guariento, Perimeter Institute
• David Sloan, Universiy of Oxford
• Lee Smolin, Perimeter Institute