# Continuous space in LQG

• Eh
In summary, loop quantum gravity is a quantum theory of geometry where space is represented as a lattice of discrete loops. However, when the wave function is added in, the geometry of the network of loops is seen in terms of probability. While space remains discrete from a classical viewpoint, the wave function is continuous. This means that within a given volume, there are an infinite number of possible states for the loops to be in. The geometrical properties of space, such as volume or area, are still discrete but their spectrum of possible values is also discrete.

#### Eh

I'm wondering how the discrete space in LQG is effected when it becomes a quantum field. In any given volume, you normally could find a continuous amount of intersecting field lines. In LQG, those lines or loops) are discrete, and space is basically a lattice of sorts. So in that case, there would be no continuous space. But what happens when the wave function is added in?

Since these loops do not comprise a static background in which matter and energy move about, and are dynamic, any change in energy with a given volume will necessarily change the local geometry. Since the distribution of energy can only be seen in terms of probability, I'm thinking that the geometry of the network of loops could also only be seen in terms of probability. So while space would be discrete from a classic viewpoint, the wave function itself would be continuous.

Is this the case?

Firstly, loop quantum gravity IS a quantum theory of geometry (Did you not know that the "Q" in LQG stands for "quantum"?). Secondly, space in LQG is topologically continuous, only it's geometrical properties like volume or area are discrete. For example, topologically, a sphere in LQG is just an ordinary sphere. However, the spectrum of possible values of it's area is discrete.

Yes, I know it's a quantum theory. I was just wondering how probability would effect a classic concept of volumes in a lattice. In other words, within a given volume, is there still an infinite number of possible states for the loops to be in?

I'm not very familiar with the workings of quantum field theory, so my question may seem a little vague or off the mark.

## 1. What is continuous space in LQG?

Continuous space in LQG (loop quantum gravity) refers to the idea that space is not made up of discrete building blocks or atoms, but rather is a continuous, smooth fabric. This is in contrast to other theories, such as string theory, which propose that space is made up of tiny discrete units.

## 2. How is continuous space in LQG different from traditional ideas of space?

Traditional ideas of space, based on classical physics, assume that space is infinitely divisible and continuous. However, LQG suggests that at the smallest scales, space is actually made up of discrete units, called quanta, which have a finite size. This has implications for our understanding of the fabric of space and how it behaves.

## 3. What evidence supports the idea of continuous space in LQG?

There is currently no direct experimental evidence for the existence of continuous space in LQG. However, LQG is a mathematically consistent theory that has been able to make predictions and provide solutions to some long-standing problems in theoretical physics, such as the black hole information paradox. Additionally, some observations, such as the discrete nature of certain physical quantities, lend support to the idea of discrete space at the smallest scales.

## 4. What are the implications of continuous space in LQG for the concept of infinity?

The concept of infinity is a fundamental aspect of traditional ideas about space. However, in LQG, the discrete nature of space at the smallest scales means that there is a finite limit to how small space can be divided. This has implications for our understanding of infinity and how it may or may not apply to the fabric of space.

## 5. How does continuous space in LQG relate to the concept of spacetime?

In LQG, spacetime is still considered to be a fundamental concept, but it is not a smooth, continuous fabric as traditionally thought. Instead, it is made up of discrete quanta of space and time. This has implications for our understanding of the fabric of the universe and how it behaves at the smallest scales.