Mark’s going to try to get a handle on the mystery of background independence (henceforth BI) – try to understand how we can think about it in classical field theories, and identify QG analogues to these. He’s not going to try to tell us why and whether we should care about BI.

Question about connection with observables and diffeomorphisms. Replies never used diff talk. Rejects invariance in favor of covariance. See Trautmann: need actual points, and never move them alone, only individuated by fields. 

Is main idea that we introduce points? No. Doesn’t introduce them primitively. Thinks active diffs don’t make much sense: like building a building, seeing you don’t need it, and knocking it down.

Accused of adding points and having more information. Responds that you only get them after the fact. But what if have two manifolds? Why? Question continues: moving points around gives same physical situation. Pitts: we all agree that points exist in GR, just not individuated until have the metric.

This was a confusing QA session. Not sure what the actual worry of the questions was. Butterfield tries to redirect from point type worries to the actual issue of whether we need to coordinate the constraints in order to generate gauge transformations. 

I could not really follow Dittrich’s point. If anyone is reading this, perhaps that can be filled in here.

Argument at length about the connection between phase space and observables generally. Chair cut it off.

Pitts tells us that perhaps there is no coherent notion of Bergmann observables. On the other hand we can tell what Dirac observables are supposed to be – so his conception can be fixed. 

So Pitts gets Earman’s fondness for Hamiltonian formulation and Maudlin’s desire for change to live happily together. Should have been obvious, he says, because Lagrangian and Hamiltonian formulations should be equivalent.

Result: Change is having no time-like Killing field, and we can get that in homogeneous GR.

What about GR? Is the situation analogous? Can we find a combination of constraints that behave nicely?

Does generate a normal coordinate transformation? no

What about . no

So not a gauge transformation. Uncoordinated effort does not generate gauge transformation.

Many examples follow of first-class constraints that do not generate gauge transformations.

Bergmann and Anderson 1951 say sometimes one needs to take a Poisson bracket of a velocity term. Their motivation is unclear. For Pitts it is necessary to make all of this stuff go through.

Get a bad physical change with a secondary first-class constraint.

Can we find a team effort? Yes by combining the primary and secondary first-class constraints.

Now possibility of change re-emerges in GR. Not exactly clear from this, but at least door open.

What goes wrong here? Dirac makes an error in his book – forgetting about the hidden secondary constraint living inside transformed Hamiltonian. Then this error widely propagated in the literature.

Can find the root of much trouble on page 21 of Dirac’s book.

Can do some pretty easy tests in classical electrodynamics (em) and just find out. Can show by direct calculation that first class constraint does not, generally, generate a gauge transformation. 

And how has this not been noticed?!?

Confusion seems to arise out of failure of associating between Hamiltonian and Lagrangian formulations.

What is link between first-class constraints and gauge freedom? Team effort or individual? two answers in literature: Bergmann and Anderson argue for former. And that’s correct. G comes from constraints acting in concert. Latter is wrong says Pitts. Can see this by looking at the actual Poisson brackets to find out whether commuting with Hamiltonian entails making no physical change – i.e. generates a gauge transformation.