Theory of Loop Quantum Gravity

[Lutz-F]

TL;DR

Some questions about LQG and the earliest periods of our universe

From the german Version of Carlo Rovellis book "La realtà non è come ci appare. La struttura elementare delle cose" I have learned about the theory of Loop Quantum Gravity that

• space and time arise through the interactions of gravitational quanta,
• the space quanta have discrete volume spectra,
• there is a lower limit for size,
• there is a repulsive force at minimum size (of space quanta?).

But in this book there was very few information about the consequences of the theory for the earliest periods of our universe. Just that calculations suggest a Big Bounce. In the Big Bang Theory, during the Planck era only the quanta of the primal force existed, but no specific gravitational quanta. Does that mean that space did not exist during the first epoch of our universe? At the end of the Planck era, the forces split into GUT force and gravitation. Was this the first time space was created? Did all the space quanta start with the minimum size based on the Planck length, and was the following process due to the repulsive force therefore similar to the second part of a Big Bounce?

Or on the other hand, are these theories mutually exclusive? But for me it's hard to understand that there should have been an infinite series of universes with Big Bounces as transitions. Because the infinite series seems to end with the accelerated expansion of our universe and so we would live in a very special cosmos that differs from all the others.

By the way: no space in the Planck epoch => no size => no initial singularity ?

 

[Lutz-F]

It's a pity that nobody knows about the LQG. Are there any arguments against this theory?

What I like about this theory and what I have read in Carlo Rovellis book:

• The theory has no arbitrary assumptions and is only based on general relativity, quantum mechanics and compatibility with the standard model.
• The theory is well-defined even without supersymmetric particles.
• The "simple" structure of all that exits: The whole world consists of overlapping covariant quantum fields.
• Singularities do not occur.

But Carlo Rovelli also wrote that so far there have only been circumstantial evidence, but no predictions that could be proved to be correct.

 

[atyy]

Are there any arguments against this theory?

In older approaches to try to define LQG, there was a problem with writing down a well-defined theory that satisfies the Hamiltonian constraint. These older approaches are called "canonical" LQG, because "canonical" is a term in physics relating to defining theories by a Hamiltonian.

A more recent approach is to try to define LQG using spin foams, which is often called "covariant" LQG. There have been proposal to define a theory, but it has been unclear whether these give rise to general relativity as an approximation in the appropriate regime. General relativity is our best current theory of gravity, so LQG must agree with general relativity in the appropriate regime. One example is the flatness problem. General relativity says that spacetime is curved, but some analyses suggested that the EPRL and FK spin foam proposals produce flat spacetime.

Here is some recent work trying to clarify the issue.

https://arxiv.org/abs/2011.14468
Discrete gravity dynamics from effective spin foams
Seth K. Asante, Bianca Dittrich, Hal M. Haggard
"Using a simple toy model, we will show that for path integrals with weakly imposed second class constraints, the semiclassical limit - $\bar{h} \rightarrow 0$ does not, in general, reproduce the classical dynamics. The flatness problem in spin foams is just one example of this more general issue.
A possible way to resolve this issue is to update the definition of the semiclassical limit."

https://arxiv.org/abs/2005.00988
Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
Muxin Han, Hongguang Liu
"Our result proves that the new path integral formulation has the correct semiclassical limit, and indicates that the reduced phase space quantization in LQG is semiclassically consistent. Based on these results, we compare this path integral formulation and the spin foam formulation, and show that this formulation has several advantages including the finiteness, the relation with canonical LQG, and being free of cosine and flatness problems."

 

[Lutz-F]

Thanks for your advice. I should have continued studying mathematics instead of economics...

So it seems that Carlo Rovelli has been a little bit vague and optimistic in describing the part of the theory that relates to the curvature of spacetime. He wrote in the above mentioned book that in the spin network a loop is formed by following the links from node to node back to the starting node. The direction of an arrow that has been moved in a loop provides information about the curvature of spacetime. The mathematics of the theory determines the curvature for each closed loop in the graph. This allows the curvature of spacetime and thus the strength of the gravitational field to be estimated.

I am curious how the LQG will develop further. And maybe I'll get some more information about LQG and the beginning of our universe too.

 

[bayakiv]

I am curious how the LQG will develop further.

It depends on how well the LQG learns to knit its loops. I would advise them to wind the loops on the Clifford torus.