Major assumption: one only gets problem of change if approach to q grav reliant upon gauge-invar quantities. 

“Dirac observables ” : function or set of functions in phase-space with weakly vanishing Poisson brackets with all first-class constraints imposed

 All the fundamental “stuff” in LQG approach is [meant to be] captured by Dirac observables

‘Parmenides’s revenge’ [Earman/Belot): change is an illusion arising from fundamentally unchanging world.  Turns out that things fundamentally are not changing [when understanding GR as constrained] .  CW suggests we should call it the problem of change rather than problem of time– the latter might be philosophically misleading 

Get from these processes a sub-manifold ‘constraint surface’.

GR is permissive theory in that it allows all sorts of crazy S-Ts and wild topologies.

-can start from Lagrangian basis; eqns are 2nd order and will be uniquely determined by generalized variables of Lagrange approach.
-Hamiltonian approach: transpose Euler-Lagrange eqns to Hamiltonian eqns of motion by introducing canonical momenta. Dependencies articulated by constrain eqns

Pro [Earman 2003]: most important for present purposes: makes GR amenable to quantization procedure.

Main disadvantage [Maudlin 2002]: “metaphysical monstrosities”, esp regarding recasting GR in Hamiltonian formalism. 

(D Schroeren’s cell phone rings]

LQG meant to be conservative approach, and can be considered a family of theories.  Large parts of what follows covered in papers one can find on CW’s personal website

Loop Q Grav:

Presentation is meant to be a review or instructive, and not novel research.Two major problems to be discussed: [1] problem of time and [2] dissolution/re-emergence of S-T

E Crull here.  First time blogger, long time listener.

We can apply all this to spin foams / spin nets!

The key question is this. Is there a phase which leads to smooth space times?

Some promising results! Dittrich & collaborators have found fix points from which one could extract different systems of embedding maps. Those would correspond to different (non-) realisations of ’emergence of space-time).

Task for the future: Expand the theory around this vacuum!

Coming back to the initial question: What is (quantum) space-time? Dittrich suggests the time scales for constructing an answer are ~2500ys. Challenge accepted!