Why General Relativity is non-renormalizable quantum theory?

In summary, the conversation discussed the concept of renormalization in physics and how it relates to nonrenormalizable theories such as Einstein gravity and the four fermi theory. It was noted that these theories can still be effective at low energy scales and may have a UV completion at high energies. The concept of renormalizability was also applied to quantum field theories, with the example of the standard model of particle physics mentioned.
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tatanacevedo
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Hello

I have not understand this.
 
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Because the simplest term you can write down in gravity (the Einstein Hilbert action in curved space time) is the Ricci scalar which allows you to see that the scaling dimension of Newton's constant in 4d is -2. This means it is irrelevant under the RG flow and flow to strong coupling at high energies. If you tried to renormalize, you would see that you could no get rid of divergences with a finite number of counter terms.

However, when theories are non-renormalizable they can viewed as an effective theory at the appropriate energy scale, so even though Einstein gravity is nonrenormalizable, it works just fine at low energy scales. We just don't know what the full theory is.

Another example of a nonrenormalizable theory is the four fermi theory. However, it turns out this is just an effective theory which has a UV completion. So it is not really nonrenormalizable if you consider that it contains other things at high energies.
 
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  • #3
Note also that quantum field theories in general are not renormalizable either. They have to meet certain stringent conditions to be renormalizable that can be summarized as having a reduction from infinite dimensional group symmetries to their finite dimensional closed subgroups. Then similarly to what was commented in the previous post one obtains a low energy efective theory that works fine like the standard model of particle physics , so the parallelism with the case in GR is clear.
 
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FAQ: Why General Relativity is non-renormalizable quantum theory?

1. What is General Relativity and why is it considered a non-renormalizable quantum theory?

General Relativity is a theory of gravity that describes the behavior of objects in the presence of massive bodies. It is considered a non-renormalizable quantum theory because it breaks down at extremely small length scales, such as near the center of a black hole, where quantum effects become significant. This means that the equations of General Relativity cannot be used to accurately describe these extreme conditions and must be combined with quantum mechanics.

2. How does General Relativity differ from quantum mechanics?

General Relativity and quantum mechanics are two of the most successful theories in physics, but they are fundamentally different. General Relativity is a classical theory that describes the behavior of matter and energy on large scales, while quantum mechanics is a theory that describes the behavior of matter and energy on a microscopic level. General Relativity does not take into account the principles of quantum mechanics, such as the uncertainty principle, which leads to the non-renormalizability of the theory.

3. What are the consequences of General Relativity being non-renormalizable?

The non-renormalizability of General Relativity has significant consequences for our understanding of the universe. It means that we do not have a complete theory that can accurately describe the behavior of matter and energy in all situations. It also makes it difficult to reconcile General Relativity with other fundamental theories, such as quantum mechanics, and has led to the search for a more comprehensive theory of gravity, such as a theory of quantum gravity.

4. Can General Relativity be made renormalizable?

There have been attempts to make General Relativity renormalizable, such as the theories of quantum gravity, but so far, these attempts have not been successful. Some scientists believe that a complete theory of quantum gravity is necessary to make General Relativity renormalizable, while others believe that General Relativity will always be non-renormalizable due to the fundamental differences between classical and quantum theories.

5. How does the non-renormalizability of General Relativity impact our understanding of the universe?

The non-renormalizability of General Relativity has a major impact on our understanding of the universe. It means that there are still many unanswered questions about the behavior of matter and energy in extreme conditions, such as near the center of a black hole or during the Big Bang. It also highlights the need for a more complete theory of gravity that can reconcile General Relativity with quantum mechanics and potentially provide a more unified understanding of the universe.

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