Is the lack of infinities in LQG due to quantization of volume and area?

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In summary, LQG does not have infinities in 4-dimensions due to the quantized nature of volume and area operators. This also leads to a natural UV cut-off. Rovelli's book is recommended for learning LQG, but there are also other complementary sources available. Thiemann's writing style may be more dense and may skip important background information.
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zetafunction
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Why NO infinities in LQG ??

what is the reason for LQG in 4-dimension to have NO infinities when doing calculations ?? , is it due to the fact that the VOlume and Area operators are Quantizied ?

then if VOlume and Area are Quantizied, there should be a MINIMUM or quantum of area or volume we can detect and hence there would be a natural UV Cut-off , is this correct ??

by the way , a GOOD book to learn LQG ??, i have notions of SR , GR and Quantum mechanics... thanks.
 
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Exactly, There's a quantum of area and a quantum of volume, and they are both hard physical predictions of the theory. One problem is, they are so tiny (order of square and cube of Planck length) that they don't have many physical consequences.

There's a good book on LQG by Rovelli (it's not very recent, 2004, I think?), if you have access to a scientific library, check it out ... our scientific library had it. If not, there used to be a draft version available online, check it out.
 
  • #4


Another major LQG textbook writer, please let me know if you disagree, I think Rovelli and Thiemann are complementary in their approaches
Introduction to Modern Canonical Quantum General Relativity
(this is available for free, Thiemann also has a slightly more recent but slightly more expensive Cambridge Monographs with the same title).
 
  • #5


humanino said:
Another major LQG textbook writer, please let me know if you disagree, I think Rovelli and Thiemann are complementary in their approaches
Introduction to Modern Canonical Quantum General Relativity
(this is available for free, Thiemann also has a slightly more recent but slightly more expensive Cambridge Monographs with the same title).

Thanks, humanino. I will revise the list of useful source links here
https://www.physicsforums.com/showthread.php?p=2493787#post2493787
so that it will include the link you suggest:
http://arxiv.org/abs/gr-qc/0110034
Introduction to Modern Canonical Quantum General Relativity (free 2001 draft version)
 
  • #6


Thiemann is probably smart and he knows what he's talking about, but I found his writing style remarkably dense, and he skips a lot of important background. Rovelli's text is written well enough that you can follow his logic all the way to the end of the book.
 

1. Why can't there be infinities in Loop Quantum Gravity (LQG)?

The main reason why infinities cannot exist in LQG is because it is based on the principle of discrete spacetime. This means that space and time are not continuous, but rather made up of tiny discrete units. As a result, there is a limit to how small a distance or time interval can be, preventing the occurrence of infinities.

2. How does LQG prevent singularities?

Singularities, which are points of infinite density and curvature, are a major problem in traditional theories of gravity. However, in LQG, the discrete nature of spacetime prevents the occurrence of singularities. Instead, the theory predicts that spacetime is made up of a network of interconnected loops, which can bend and stretch without reaching a point of infinite curvature.

3. Can LQG explain the phenomena of black holes?

Yes, LQG provides a framework for understanding the behavior of black holes. In this theory, the event horizon of a black hole is described as a network of interconnected loops that form the boundary of the black hole. The curvature of spacetime around the black hole is also described by these loops, providing a more detailed and consistent explanation of black holes.

4. Is there any experimental evidence for the predictions of LQG?

Currently, there is no direct experimental evidence for LQG. However, the theory has made several predictions that can be tested, such as the discrete nature of spacetime and the existence of a minimum length scale. There are also ongoing efforts to develop experiments that can test the predictions of LQG, such as the measurement of gravitational waves.

5. What are the major challenges in developing LQG as a theory of quantum gravity?

One of the major challenges in developing LQG is the issue of background independence. This means that the theory should not rely on a fixed background spacetime, but rather explain the emergence of spacetime from fundamental quantum entities. Another challenge is the lack of a complete mathematical framework for LQG, making it difficult to make precise predictions and calculations. However, ongoing research and advancements in the field are addressing these challenges.

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