The Measure

In the last two seasons, we focused on what can be directly observed in quantum gravity and on the imprints quantum gravitational effects could leave behind in observations. In the third season we will dive deeper into the foundations of quantum gravity and ask: what determines the measure in a quantum theory of gravity?

This question may manifest in various guises in different perspectives. Does the “measure” refer to that of a path integral, of a class of geometries summed over in computer simulations, of a quantized phase space, or something else entirely?

On the one hand, should a theory of quantum gravity take geometry as the starting point? If so, is the geometry discrete or continuous? Should the appropriate measure be defined on Euclidean, Lorentzian or complexified geometries? Is there an appropriate notion of topology on these geometries, and if so, should different topologies be included in the measure?

On the other hand, if geometry is not fundamental, what are the underlying building blocks of a quantum theory of gravity?