Her conclusion: ACA seems to apply usefully to Rovelli’s concept of time.  A number of conceptual problems remain for his picture.

Now we’re considering Rovelli’s strategy for quantum gravity.

Spacetime is dynamical.  Like other dynamical fields, it must be quantum in nature.  Put together, these criteria lead us to demand a background-independent quantum field theory with a field that in some sense represents spacetime.

In particular, Rovelli wants to put time “on a par” with other physical variables.

He starts from relationist principles, according to which fundamentally there are only physical objects and space is nothing more than a relational property of them.

A question: doesn’t Rovelli think that spacetime is one of the dynamical objects as the theory, which doesn’t sound like a relational property of other objects?

Kon’s answer: this is Rovelli’s broader picture of spacetime, not his specifically quantum picture.

Rovelli’s “partial observable” for time is highlighted (a measurement of local succession of events).  Are there conceptual conflicts between this picture and Rovelli’s commitment to relationism?  Not necessarily, since we might understand succession in purely relational terms.

But since observations occur at an instant, this particular temporal concept must be privileged, so it’s not clear that time is “on an equal footing” with space and other physical variables.

A question: how is time different from space in this way?

Kon: being at a particular place is defined by being at a particular instant.  But she can see the point—perhaps spatial relations could provide a framework for defining temporal ones in a similar way.

A question from Mattingly: why should we care about whether conceptual analysis applies to other theories if we have QG, presumably the best theory?

K’s answer: the idea of “best scientific theory” is problematic.  We need an account that can make sense of the way different theories share concepts.

Her Alternative (ACA) to Jackson:

1. Identify theories being examined.  For folk theories, we consult our intuitions, for scientific theories we consult our best interpretation of them, making sure to treat multiple different theories as parts of a conceptual network.

2. Determine what role “time” plays in the whole network.  Do its roles in different theories clash, or exhibit redundancy or irrelevancy?  If so, we must either eliminate the concept or ‘engage in metaphysics.’ (to quote Jackson)

3. Integrate an analysis of *folk time* with our analysis of time in physics.

Applying Jackson’s CA to time.  An assumption for simplicity’s sake: the present is the only feature constitutive of folk time.  (We’re analyzing the folk concept of “the present.”)

This works great with Lorentzian relativity, Kon’s first example.  We can keep the concept of “the present.”  In relativity this concept gets eliminated.  Looks like the right result!

But the problem with Jackson’s JCA: we can’t just read metaphysics off a scientific theory the way Jackson assumes.

In an improved account of CA, we should look for three desiderata:

1. Don’t problematically read scientific concepts off a theory

2. Apply to more than one scientific theory

3. Include an analysis of folk time rather than just eliminating the concept

For Jackson, a concept is the meaning of a term.  For him, a concept’s structure and reference is fixed by its theoretical role (a descriptivist model rather than a “causal reference” model).  J uses conceptual analysis to solve the “location problem” — the problem of reconciling the phenomena with one’s fundamental ontology (locating the world in the fundamental stuff).

Two steps:

1. Find out the referents of upper-level terms (establish our shared “folk theory” via reflection on linguistic intuitions).  This tells us the theoretical role of the upper-level concepts (e.g. “water”).

2. Determine whether statements involving the concept to be analyzed are entailed by lower-level descriptions of reality.  (If not, we can eliminated the concept.)  Example: our folk concept of water as potable liquid can be reconciled with our theoretical entity H2O, so we have “located” water in H2O.

Kon notes that Jackson assumes the lower-level description should come from our best scientific theory.

Kon directs interested parties to http://newagendasstudyoftime.wordpress.com

Kon would like to apply the method of conceptual analysis to the concept of time in physics, along the way providing an alternative to Frank Jackson’s picture of analysis which is better suited to QG than Jackson’s.

Fletcher: The Hauptvermutung seems not to offer a derivation of GR from CST, but it would provide an explanation of some sort for the usefulness of continuum spacetime as an approximation to the causal set-theoretic reality.

We also need a way of measuring differences in causal structure (like a “metric” on how causally different spacetimes are).  The most venerable existing proposal has a number of problems.  In particular, they only work for spacetimes defined on the same manifold.

A newer proposal due to Bombelli: Compare isometry classes of spacetimes according to the probability of getting the causal set if n points are selected at random from one of the spacetimes.  As a calculational problem, this is extremely hard.  Moreover, it only works for finite spacetimes.  There hasn’t been much progress with this problem.

Another proposal depends on the notion of Hausdorff distance between two subsets of a metric space.  Gromov generalized this to a distance between metric spaces, corresponding to the minimum possible Hausdorff distance when the two spaces are embedded in any larger space.  But can this be extended to Lorentzian manifolds?

A Lorentzian definition of Gromov-Hausdorff distance is proposed, but it is not clear how good a job it will do of providing good approximate agreement on observables for “nearby” spacetimes.

Perhaps the requirement that an embedding exist is too strong.  There are many small causal sets that cannot be embedded into a relativistic spacetime.  Small perturbations of a set should not change whether we count it as embeddable, but this will not hold if we require exact embeddings.  So we look instead for embeddings of a coarse–grained causal set, where a coarse-graining is a causal set that could have arisen with high probability from a Bernoulli deletion.

It’s not clear that deletion can be understood as a sort of “averaging” of a causal set.  One doesn’t normally do statistical mechanics by ignoring some atoms entirely; rather we pay attention to larger-scale variables.

A better option may be to use a Bernoulli process to identify vertices on adjacent elements of the set, but this is not easy.

Deleting too many points makes the task of embedding too easy.  So the embedding density should be set by the observables we’re interested in, and how many points can be deleted while still approximating them accurately.

A question from the audience: are we only asking about the connection between an “eigenstate” of a causal set and a classical spacetime.  Fletcher agrees that for present purposes, this is the question he’s interested in.  The concern is that perhaps the only workable way to approximate a spacetime is with a superposition of causal sets.  Fletcher agrees that this is an important problem but would like to focus on a more tractable one.