Worry here is that states in superpositions generally don’t have connectivity [and perhaps have different cardinality].  Not obvious what the dimensionality of these fundamental structures must be, then.

Another issue involves locality structure arising from emergent ST described via LQG approach.  I.e., how local or topological structures like relativistic STs emerge from spin networks.  This will be key for q cosmological investigations…

Moving on to the problem of ST in LQG: Hamiltonian formulation of GR in an attempt to apply canonical quantization; belief is that resultant Hilbert basis is spin network basis, and these spin networks provide the fundamental 3-d spatial structure [and these networks can be considered eigenstates of geometrically-interpreted operators]

Thus: space comes out as superposition of spin network eigenstates — i.e., no well-defined geometric properties

Nota bene: the sort of indeterm at issue here has to do specifically with the indeterm arising from requirement of diffeomorphism invariance

Question: when you have vel-dep coord transformations, you should work with a phasespace across time.  This would not be implement-able in a reduced phasespace of the sort proposed by Maudlin.  CW responds: neither Maudlin nor I claim this will lead to solution to the problem, but may alter the way we view it..

Maudlin claims indeterminism is phony.  But CW contests that ignoring indeterm as an artefact of representation doesn’t work if canonical QG is taken seriously.  Should it be taken seriously?, CW asks, pointing out that this question is itself a nontrivial issue

Maudlin suggests that maybe we fix the gauge and in this way remove indeterm.  Problem: this may work for certain cases, but all quantifiable properties will depend on gauge chosen and hence on selected representation, not on genuine physical content.  Thus, we’d need to justify gauge choice as physically motivated

A third option from Maudlin is to ‘quotient out’ indeterm– cut out mathematical surplus structure and get down to the True physical degrees of freedom.  E.g., reduced phase space

Problem: this is exactly what leads to the no-time problem in the first place, that is, fixing the gauge is what got us into this mess of no-change. 

Healey’s proposal might be understood as counterpart to Rovelli’s program of partial observables

Another reaction from Maudlin: ‘observables’ lack meaningful contact to that which is in fact observable. 

For those who wish to bite the bullet: two main issues must be dealt with. 1] how do we do physics without change? 2] how do we explain phenomenology of temporality?  -cf. Earman 2002a and problems for physicalists in dealing with these two issues.

Healey 2002, 2004: there can be B-series change in standard formulation of GR [can be diff properties at diff times].  Change can emerge from unchanging fund. reality — likewise in Hamiltonian formulation: just accept that physical content is not fully captured by Dirac observables.  Change must be characterize wrt frame of reference, and cannot be captured by fundamental properties which are by construction frame-indep

Philosophical options at the point: reject paradox [identify that which must be eradicated and how we can implement covariance in that case] or embrace paradox [explain emergence or appearance of change].

EITHER WAY: formidable challenges to be faced.  [read: come and play with us, philosophers!]

Change is just gauge, it’s redundant, it arises from the particular way we’ve chosen to represent our physical system[s].

How do we recover or unfreeze dynamics? How, in particular, can a physicalist explain change when the fundamental level is not changing– failure of supervenience? 

received interp of Hamiltonian: generator of dynamic evolution via Ham eqn. If Dirac observs have weakly vanishing Poisson brakcets with the Ham and are constants of the motion, THEN: there can be no change!  Even in minimal sense that physical quantities can have diff valus at diff times.  A wee bit of a problem…