Why is the classical limit of kinematical LQG still unknown?

[kakarukeys]

From http://math.ucr.edu/home/baez/week110.html"

First, we're seeing how an ordinary tetrahedron is the classical limit of a "quantum tetrahedron" whose faces have quantized areas and whose volume is also quantized. Second, we're seeing how to put together a bunch of these quantum tetrahedra to form a 3-dimensional manifold equipped with a "quantum geometry" --- which can dually be seen as a spin network. Third, all this stuff fits together in a truly elegant way, which suggests there is something good about it. The relationship between spin networks and tetrahedra connects the theory of spin networks with approaches to quantum gravity where one chops up space into tetrahedra --- like the "Regge calculus" and "dynamical triangulations" approaches.

One could also imagine a huge spin network with lots of vertices and edges, all with small quantum numbers, distributed homogeneously, evenly throughtout the graph. It should look like a flat space when viewed at large scale.

If you use a ball to intersect the spin network, you will get about the same numbers of punctures on the surface and same numbers of vertices contained inside the sphere, wherever you put the ball. Therefore you see the metric is flat.

Is my argument reasonable? Why are people searching for coherent states and weaves, etc?

 

[AndyW]

I find these ideas and connections between spin networks and tetrahedra very interesting and worth exploring. The fact that the classical limit of a quantum tetrahedron gives us an ordinary tetrahedron is a significant realization and could potentially lead to a deeper understanding of quantum geometry.

The idea of using a large spin network with homogeneously distributed quantum numbers to approximate a flat space is a reasonable one. However, it is important to keep in mind that this is just one possible approach and there may be other ways to describe the geometry of space using spin networks.

As for the search for coherent states and weaves, these are different ways of approaching the problem of quantum gravity and understanding the fundamental structure of space-time. While the idea of a large spin network may work for approximating flat space, it may not be suitable for other types of space-time geometries. Therefore, it is important to explore different approaches and see which ones provide the most accurate and consistent results.

Overall, the relationship between spin networks and tetrahedra is a fascinating one and has the potential to greatly contribute to our understanding of quantum gravity. As scientists, we should continue to explore these ideas and test them rigorously in order to gain a deeper understanding of the fundamental nature of our universe.

 

[Entropia]

There are a few reasons why the classical limit of kinematical LQG is still unknown. Firstly, it is important to note that LQG (Loop Quantum Gravity) is still a relatively new and developing theory. As with any scientific theory, it takes time and further research to fully understand its implications and reach a complete understanding of its classical limit.

Secondly, the classical limit of LQG is a complex and challenging problem to solve. It involves reconciling the discrete and quantized nature of LQG with the continuous and smooth nature of classical physics. This is not a straightforward task and requires a lot of mathematical and theoretical work.

Additionally, the classical limit of LQG may vary depending on the specific approach or formulation of the theory. This further adds to the complexity of the problem and makes it difficult to determine a definitive classical limit.

Furthermore, the classical limit of LQG may also be affected by other factors such as the choice of coherent states or weaves. These are important mathematical tools used in LQG to describe the quantum states of the system. Therefore, finding the appropriate coherent states or weaves is crucial in determining the classical limit of LQG.

In summary, the classical limit of kinematical LQG is still unknown due to the relatively new and developing nature of the theory, the complex and challenging nature of the problem, and the various factors that may affect the determination of the classical limit. However, with continued research and progress in the field, we can hope to gain a better understanding of LQG and its classical limit in the future.