Livine/Terno Geometry from Information

f-h

There's no discussion of this recent paper yet as far as I can see:

Pasting from Marcus' Intuitive content thread:

http://arxiv.org/abs/gr-qc/0603008
Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
Etera R. Livine, Daniel R. Terno
27 pages, 12 figures

"After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose to probe the structure of a surface through the analysis of the coarse-graining and renormalisation flow(s) of its area. We further introduce a procedure to coarse-grain spin network states and we quantitatively study the decrease in the number of degrees of freedom during this process. Finally, we use these coarse-graining tools to define the correlation and entanglement between parts of a spin network and discuss their potential interpretation as a natural measure of distance in such a state of quantum geometry."


This touches on many issues we discussed in the Baez thread. Careful, Kea, anyone else, any comments?

f-h

Why do I like this paper. First of all I find the often implicit assumption in LQG that the elementary excitations labeled by spin-networks carry a completely unambiguous geometrical interpretation questionable.

By proposing a way how the geometric concepts arise from the pregeometric information (I hope this word isn't overloaded to much?) in the spin networks this point is clarified, and the precise additional information/assumptions needed to get geometry becomes visible.

In doing so it might become clear what additional structures next to geometric ones, might arise.

Finally a notion of coarse graining will be imperative to find potential (semi-)classical behaviours in Spin Networks.

marcus

Good initiative F-H
BTW the second author Daniel Terno was a student of the late Asher Peres. Terno has co-authored several papers IIRC with Peres. Yesterday and today I was citing the "Einstein Podolsky Rosen and SHANNON" paper of Peres. Rosen was Peres' PhD thesis advisor at princeton. Shannon founded Information Theory, Peres helped to establish Quantum information theory. Terno just recently moved from Haifa Technion to Perimeter, where he has collaborated on several things with Livine including this. This sketch of connections is meant to help indicate where Terno is coming from.

marcus

To make this a little bit more specific, here is a sample exerpt from page 23 of the Livine Terno paper

----quote Livine Terno---
Our goal is to understand the (quantum) metric defined by a spin network state, without referring to any assumed embedding of the spin network in a (background) manifold.

We support the basic proposal that a natural notion of distance between two vertices (or more generally two regions) of that spin network is provided by the correlations between the two vertices induced by the algebraic structure of the spin network state.

Two parts of the spin network would be close if they are strongly correlated and would get far from each other as the correlations weaken. Our set-up is as follows. We consider two (small) regions, A and B, of the spin network. The distance between them should be given by the (quantum) metric outside these two regions. Thus we define the correlations (and entanglement) between A and B induced by the rest of the spin network. This should be naturally related to the (geodesic) distance between A and B.

A first inspiration is quantum field theory on a fixed background. Considering a (scalar) field phi for example, the correlation phi(x)phi(y) between two points x and y in the vacuum state depends (only) on the distance d(x, y) and actually decreases as 1/d(x, y)^2 in the flat four-dimensional Minkowski space-time. Reversing the logic, one could measure the correlation phi(x)phi(y) between the value of a certain field phi at two different space-time points and define the distance in term of that correlation.

Indeed just as the correlations in QFT contain all the information about the theory and describes the dynamics of the matter degrees of freedom, we expect in a quantum gravity theory that the correlations contained in a quantum state to fully describe the geometry of the quantum space-time defined by that state. Another inspiration is the study of spin systems, in condensed matter physics and quantum information [14, 15, 21]. Such spin systems are very close mathematically and physically to the spin networks of LQG...
---endquote---

I have bolded some words and broken their text into bite-size paragraphs so I can understand it easier

marcus

this is a long shot.

do the ideas in this paper have any connection with Garrett's (audaciously speculative )new paper

this Livine Terno, which F-H flagged, wrestles with the majorly undefined notion of "coarse-graining"

Garrett's paper confronts the idea of "action"

the most necessary ideas that nobody can do work without are always the most undefinable, it seems---and so, in exasperation, one ventures out on limbs

I'm game, and will venture slightly: "action" is what washes away when you coarse-grain. Naaaah!

anyway, read Garrett's new paper. it is far-out, but I think interesting

http://www.physicsforums.com/showthread.php?t=119029

Mike2

In the ongoing search to deduce physics from logical principles, we have that the action integral is minimized along the geodesic. This hints at a geometrical reason for physical properties. But why a geodesic? Now it may be that the least information of a system accurs along the geodesic. Other paths would be less probable and provide too much information.

How's that for going out on a limb?

marcus

It is good for going out on a limb. Personally I like what you are saying.

I am not sure one can deduce fundamental descriptions of nature from logical principles but I dont want to say anything about that general question---it is offtopic. If it HEURISTICALLY works for you to pursue that line then that is fine.

selfAdjoint

Could you do a Feynmann (or a Huygens ) from this and have the too-much info paths cancel out, leaving only the geodesic? Might require complex information, or anyway some kind of phase so you could have out-of-phase cancellation. So the real info would also be the minimum.