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.