Area spectrum in Simplex Gravity

In summary, the conversation discussed the concept of the hydrogen atom spectrum and how it relates to a question in modern theoretical physics regarding the area spectrum in Simplicial Quantum Gravity. The approach of dynamical triangulation has recently generated a 4D world, leading to speculation that space may be discrete in a certain way. The next major question in quantum gravity is to calculate the spectra of geometric operators, such as area and volume. This has already been done in Loop gravity, with the area eigenvalues being fractional multiples of the basic Planck area. The question now is whether the same results can be derived in Simplex quantum gravity.
  • #1
marcus
Science Advisor
Gold Member
Dearly Missed
24,775
792
talking about the hydrogen atom spectrum (energy levels)
reminds me of an outstanding question in modern theoretical physics

What is the area spectrum in Simplicial Quantum Gravity?"

SQG is Ambjorn's name used interchangeably for the dynamical triangulation approach to quantum gravity.

computer simulations using this approach recently
generated a 4D world (the Ambjorn Jurkiewicz Loll paper that Baez was talking about)

so Simplex Gravity works or so it appears, there is still plenty to check.

this means a major question, maybe the next big question in quantum gravity, is to calculate the spectra of the geometric operators, area and volume

like roughly 100 years ago Bohr realized the energy and angular momentum in the electron orbit were discrete and he made a discrete (quantum step) model of it and calculated what colors light

and now Ambjorn (and Loll and others) are guessing space is discrete in a certain way and modeling it with a swarm of simplices
(a simplex is the analog of triangle in more than 2 dimensions)
and those people or colleagues should be able to derive
a discrete spectrum of the (not energy this time but) area operator

this has already been done in Loop gravity
it turns out that the area eigenvalues are various fractional multiples of the basic Planck area (fractions and the like, some square roots too but basically simple)
so naturally one wonders if doing it in Simplex quantum gravity gives the same eigenvalues.
 
Last edited:
Physics news on Phys.org
  • #2
That's the big question.
 
  • #3


The area spectrum in Simplex Gravity, also known as Simplicial Quantum Gravity, is a topic of great interest in modern theoretical physics. This approach to quantum gravity involves modeling space as a swarm of simplices, or geometric shapes, and using computer simulations to generate a 4D world. One of the major questions in this field is to calculate the spectra of geometric operators, such as area and volume. This is similar to how Bohr's model of the atom revealed the discrete energy and angular momentum levels of the electron orbit, which then allowed for the calculation of light colors.

Ambjorn, Loll, and others have made significant progress in this area, and it is believed that the area operator in Simplex Gravity will also have discrete eigenvalues, similar to those found in Loop Gravity. These eigenvalues are expected to be fractional multiples of the basic Planck area, with some additional simple factors. Further research and simulations are needed to confirm this and to fully understand the implications of the area spectrum in Simplex Gravity.

Overall, the study of the area spectrum in Simplex Gravity is an exciting and ongoing area of research in modern theoretical physics. It has the potential to provide a deeper understanding of the fundamental structure of space and time, and could potentially lead to new insights and developments in the field of quantum gravity.
 

1. What is the concept of area spectrum in Simplex Gravity?

The area spectrum in Simplex Gravity is a fundamental concept that relates to the quantization of space. It suggests that the area of a surface can only take on discrete values, rather than being continuous. This idea is derived from the theory of Loop Quantum Gravity.

2. How does the area spectrum relate to the discreteness of space?

The area spectrum in Simplex Gravity suggests that space is not continuous, but rather made up of discrete units. This means that there is a smallest possible unit of space, and all other areas are multiples of this unit. This concept challenges the traditional view of space as a continuous and infinitely divisible entity.

3. What implications does the area spectrum have for our understanding of gravity?

The area spectrum in Simplex Gravity has significant implications for our understanding of gravity. It suggests that space is not a passive backdrop for matter, but rather an active and dynamic structure. This means that gravity is not simply a force between masses, but rather a manifestation of the geometry of space.

4. How is the area spectrum related to black holes?

The area spectrum in Simplex Gravity has been used to study the properties of black holes. It has been suggested that the event horizon of a black hole, which is the point of no return for anything that falls in, is quantized. This means that the area of the event horizon can only take on discrete values, similar to the area spectrum of space.

5. Is there any evidence for the area spectrum in Simplex Gravity?

Currently, there is no direct evidence for the area spectrum in Simplex Gravity. However, it is a concept that is actively being studied and researched by scientists. Some theoretical calculations using the theory of Loop Quantum Gravity have shown promising results that support the idea of quantized space. Further research and experiments are needed to confirm the existence of the area spectrum in Simplex Gravity.

Similar threads

  • Quantum Interpretations and Foundations
Replies
5
Views
815
Replies
6
Views
1K
  • Quantum Physics
Replies
2
Views
1K
  • Quantum Physics
2
Replies
69
Views
4K
  • Beyond the Standard Models
Replies
4
Views
3K
  • Beyond the Standard Models
Replies
11
Views
2K
  • Beyond the Standard Models
Replies
5
Views
2K
Replies
3
Views
931
  • Beyond the Standard Models
Replies
14
Views
3K
Back
Top