Vidotto argues that both QM and GR are relational in an important sense. In both theories, understood properly, everything observable and measurable amounts to the relationship between one system and another.
In GR and QG, this leads to a kind of locality: all interactions are between contiguous systems.
Audience: how does this square with EPR non-locality? Vidotto: Relational QM resolves the EPR ‘paradox’ by allowing a way of understanding what’s going on without anything non-local happening.
Quantum mechanics + gravity (GR) entails minimum length in nature; as Bronstein argued in 1933, the fact that finer and finer localization requires higher and higher energy, and energy gravitates in GR, puts a limit on how finely localized something can be without the energy of localization being such as to hide the localized system inside its own Schwarzschild limit.
Vidotto distinguishes two senses of discreteness in LQG: a real physical discreteness that follows just from the existence of a minimum length scale, and the discreteness that comes with starting from spin networks, graphs etc.
Historical evolution of notions of space, matter and relations
Getting started
Judging from the discussion paper (here) and the slides, Vidotto’s talk will argue that in LQG, the ancient dispute between substantivalists and relationalists gets resolved by being dissolved: space(time) is a real quantum field, but quantum theory is inherently relational, and moreover the classical gravitational field (= spacetime) emerges from a discrete, i.e. atomistic, basis. Her talk will represent a Rovellian philosophy and approach to quantum gravity.
Butterfield: question on spin foam cosmology, about relaxing the various approximations and about obtaining more genaral anisotropic geometries. Vidotto: one can indeed generalize the class of states used, and use them to study anisotropic situations. A more difficult question is the dynamical one, i.e. relaxing the approximation to the dynamics that are used. But results are encouraging.
Conclusions: highlight two main open issues. One: dynamical – what physical processes lead to decoherence in this context. Two: conceptual – do spin foams resolve the problem of time?
Application of general idea to the setting of “spin foam cosmology”, where results are available about obtaining semi-classicality in the spin foam setting. Lots of unsettled questions but interesting results to consider. Brief summary of framework and of approximations used.
Can write down formaly the decoherence functional in terms of the sum over 2-complexes, which is however very difficult to control. Still, one can at least identify which properties such functional should satisfy.
Beyond Spacetime 