New Markopolou/Smolin: Quantum Theory from Quantum Gravity

[marcus]

New Markopolou/Smolin: "Quantum Theory from Quantum Gravity"

http://arxiv.org./gr-qc/0311059

"Planck's constant turns out to be a derived quantity"

 

[marcus]

From Markopoulou and Smolin's new paper (posted yesterday, 18 November) "Quantum Theory from Quantum Gravity"

"The model is not intended to be realistic. Much more work needs to be done to understand whether the basic strategy uncovered here can lead a real physical theory..."

"...may, in a more realistic model, lead to predictions of a time dependence of h-bar that could falsify such a theory..."

The intriguing thing, to me, is that they start with nothing but a graph. No spacetime, no quantum mechanics. No labels on the graph---
nothing but this bare undirected graph. They show what extra assumptions go into deriving Schroedinger's equation and determining a value of Planck's constant.

The graph consists of a finite number of points and an adjacency matrix of zeros and ones. An abstract graph, in other words. When they want to discuss the low energy limit they embed the graph in R³. The N nodes of the graph become the locations of N particles and their positions obey a form of Schroedinger equation.
Planck's constant appears in this embedding process---both quantum mechanics and classical Newtonian dynamics appear, in effect, as limits of this graph model.

Since Planck's constant is generated by the model, they point out that the model itself (if developed further) could be falsified or disproved if it were discovered to predict a CHANGING value of Planck's constant---variation which could presumably be excluded or at least experimentally restricted within narrow bounds.

Very edgy---if that is the word. More and more I see these papers in which a simple graph plays a basic role. In Freidel and Livine the theory is developed on a graph and then one builds a kind of Hilbertspace limit by taking larger and larger graphs. As if by taking bigger and bigger graphs one could eventually get spacetime.
If I remember my Greek there is a book that begins
En Arche en ho Logos or something like that---substitute "Graphos"

 

[selfAdjoint]

Except that Graphos means something written. Maybe you want Web. En arche en to arachnion.

 

[selfAdjoint]

I have been reading the paper and I find that the emergence of the Schoedinger equation (in pretty much its operator form) is due to two features in their model:

1)The clash of topologies between the net (more or less the "taxicab topology") and that of the Riemannian space in which it is embedded in the low energy limit. They point this out as the principal source, but there is also

2) The stochastic behavior of some of the nodes. This behavior is essential because it is only this which allows them to bring in Nelson's "stochastic quantization".

I have Nelson's book, Quantum Fluctuations (Princeton Series in Physics, 1985) and his derivation takes place in the context of a set of points developing stochastically but interacting with a background field that evolves by a Lagrangian action. From the stochastic diffusion in this situation he derives his Schroedinger equation and his Planck's constant.

Thus it might be said that what this paper really does is provide a physically plausible (to us) instantiation of Nelson's model.

 

[ranyart]

Originally posted by marcus
http://arxiv.org./gr-qc/0311059

"Planck's constant turns out to be a derived quantity"

-----------------------------------------------------------

The model is not intended to be realistic. Much more work needs to be done to understand whether the basic strategy uncovered here can lead a real physical theory..."

I think this quote above..is the understatement of the year!

Great paper, and I do admire Fotini Markopoulou, the paper some years ago relating to the fact that the Universe is dependent/needs observers is one fine paper.