Dear all,

As announced, we are hosting a tutorial on shape dynamics (a relational approach to quantum gravity) on Thursday at 4pm.

Best,

Lídia

--

Henrique Gomes, University of Oxford

A brief tutorial in geometrodynamics in general and shape dynamics in particular

Thursday, 13th of June, HIL E5

A recurring theme in the obstacles we face on our way to quantum gravity --- placed at the intersection between the conceptual and technical categories ---  is Time, with a capital T. In quantum mechanics, an absolute evolution in time is an essential ingredient. Time flows from past to future, and with it, one instantaneous quantum state is brought to another. In general relativity, Time is a dynamical concept, with no absolute notion of past and future. One instant is given by the value of an arbitrary label, with no physical meaning. Conflict ensues when quantization is applied to space-time itself.

 In the words of two icons of the field, R. Wald and W. Unruh:

 "In quantum mechanics, all measurements are made at "instants of time"; only quantities referring to the instantaneous state of a system have physical meaning. In particular, "histories" are unmeasurable in quantum theory. On the other hand, in general relativity "time" is merely an arbitrary label [...]. The physically meaningful quantities must be independent of such labels [...]. In other words, only the spacetime geometry is measurable; i.e., only histories have physical meaning. Thus, it should not be surprising that when one naively combines quantum theory and general relativity, the only meaningful quantities which survive are those which are both instantaneously measurable [...] and yet depend only on the spacetime geometry [...]".

This is certainly confusing at a conceptual level. After all, we believe quantum evolution in time amounts to a transformation between physically distinct states, whereas in gravity different instants would be associated with the same physical state.

 In these tutorials, I will introduce the geometrodynamical approach to general relativity, with a special emphasis on the role played by time.  I will then describe the theory of shape dynamics. Shape dynamics amounts to taking many hints ---coming from the initial value formulation of general relativity and from the consideration of symmetries compatible with a quantum mechanical evolution between instantaneous physical configuration states--- seriously. It does this by considering dynamical systems whose natural configuration space is not the space of spacetime geometries, but that of conformally invariant spatial geometries: conformal superspace. Such a configuration space embodies natural tenets of relationalism (with respect to size and location).  By using shape dynamics, we trade Lorentz invariance (or refoliation invariance), by spatial scale invariance and a spatially non-local Hamiltonian. Such characteristics may render shape dynamics more congenial to the Bohmian interpretation of quantum mechanics than other geometrodynamical theories.