Two Principles of Quantum Gravity in the Condensed Matter Approach

This is restricted from 3 principles for the sake of time.

D.O.: Isn’t a boundary less fundamental than something that’s not a boundary?

EK: No. This is the container view again.

MS: Are you happy for both to be equally fundamental? Are all grades of fundamentally equivalent?

EK. Yes. [Rest of answer lost]

JB: In EM, holonomies are non-local and vastly overcomplete. Fundamental meaning sub-ontic? If we resist your view, it is in part that we believe that dimension is background for everything else we do in physics.

EK. But need to cash out why that is difficult. Prima facie, we can cope with indeterminate dimensionality.  Why must it be determinate? Doesn’t quantum gravity do away with the container view entirely?

NH: One of the things relevant to T duality is that both of the duals predict that the space is large. States in either dual have an interpretation in terms of dual processes.  It doesn’t matter which you choose. Is this similar to AdS/CFT? What would beings who live in either of these spaces experience?

KH: If we define things functionally/structurally then plausible that we only live in one.

DB: Suppose the correct theory of our world is dual to boundary CFT.  Say I ostend to dimensions, then I’ve fixed what I mean and the theory on the boundary is just a notational variant. 

EK: Any such theory will require us to identify my experiences within the theory. Are there principled reasons to prefer one description to the other?.

But what about fundamentality?  Can we use our previous criteria?

If equivalence is precise, hard to ground claims of superiority. But one could be more revealing w.r.t. structure of underlying [CW: Or overlying?] theory.  However, the usual claim is that duality implies equivalence.  The moral of this talk is that differences in dimensionality don’t need to have physical significance.

Distinguish between dimensionality of physical degrees of freedom and spacetime. Note that d.o.f. don’t disappear, they are just translated into a different form.

If we accept that we can have distinct representations of the same situation anyway then duality is less puzzling.

To the questions in good time!

Back to AdS/CFT. Which theory represents spacetime accurately? The target metric in string theory (or at least a non-compactified version) plays a pretty traditional role in spacetime.

CFTs are invariant under conformal transformations of the metric.  This means that the thing that might represent ST is the equivalence class of metric conformally equivalent to Minkowski.

Does a spacetime with only conformal structure even represent spacetime? No inertial structure. Geodesics, even, are not invariant under conformal transforms.  Thus the structure is not a candidate for representing phenomenological spacetime.

Giant insects!?  [any notion of being larger or smaller at stake]

Brian Pitts: Are these the same point? If nothing were massive, conformal structure would be all we need.

EK: Sure, but not exactly the same point.

Which version of EM correctly describes spacetime?

They both seem to do a fairly good job.

Which offers a more fundamental picture?

By identifying gauge-related classes of bundles we arrive at the holonomies. Both descriptions describe the same (non-ST) degrees of freedom.

Questions EK doesn’t understand (heading off objections to aforementioned controversial views?)

Q. Is the (e.g) fibre bundle space a *real* *physical* space?

A. It can represent physical d.o.f, sure. But what of it? It’s a mathematical space.

Q: Where does the stuff of the universe *really* *live*?!

A: You are pushing a metaphor too far, give it up. 

We tend to have the view that spacetime and dynamical symmetries should match. (e.g. Earman).  But in GR it is not quite clear to say how this should go.

The roles we care about will be filled by an object if it provides (locally) preferred inertial co-ords. (Brown, more or less).

Thus we can interrogate a theory to see if it has such an object.

What is the arena in which physical reality unfolds? (From Albert)  That is what is at stake.

But EK will be questioning this approach.

1. Which is more fundamental?

Do they have different domains? Cope better with closely related cases?

2. Which objects represent space-time role?

EK: this is to be functionally determined (one of those controversial claims).

Contrast `functional kind’ with `compositional kind.’  We specify functional role and then look for what instantiates that role in the theory.

Take it for granted that AdS/CFT correspondence holds.  What are the realist interpretational options?

1. Bulk theory is reality.

2. Boundary theory is reality

3. Both represent the same reality?

How do we make sense of 3?