General covariance vs. locality

In summary, the conversation was about an article written by S.carlip regarding quantum gravity. Carlip discussed the need for quantum gravity and the two ways of quantization of GR. In the section on the problems of quantum gravity, Carlip mentioned the issue of general covariance vs. locality and how diffeomorphism-invariant observables in general relativity are necessarily nonlocal due to active coordinate transformations "moving points" and not preserving quantities defined by their value at individual points. The individual asking for clarification did not understand this concept and was seeking an explanation.
  • #1
sadegh4137
72
0
hi
i read an article by S.carlip about quantum gravity, arXiv:gr-qc/0108040v1 ,
in this article carlip stated:
why we need quantum gravity
what's problems of quantum gravity
and two ways of quantization of GR.

I couldn't realize some clues in section of "the problems of quantum gravity"
one of them is
General covariance vs. locality that Carlip stated:
The fundamental symmetry of general relativity is general covariance (strictly speaking, diffeomorphism invariance), the lack of dependence of physical quantities on the choice of coordinates. Observables in quantum gravity should presumably respect this symmetry . But diffeomorphism-invariant observables in general relativity are necessarily nonlocal , essentially because active coordinate transformations “move points” and cannot preserve a quantity defined, by its value at individual points.


I can't understand this phrase
is it possible to explain it for me.
thanks
 
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  • #2
sadegh4137 said:
But diffeomorphism-invariant observables in general relativity are necessarily nonlocal, essentially because active coordinate transformations “move points” and cannot preserve a quantity defined, by its value at individual points.
No, I don't understand that remark either. Translations "move points", and so by this reasoning, translation invariance requires a nonlocal theory. :eek:
 

1. What is the difference between general covariance and locality?

General covariance is a principle in physics that states that the laws of nature should be expressed in a way that is independent of the chosen coordinate system. This means that the laws should remain the same, regardless of the specific reference frame used to describe them. On the other hand, locality is the principle that physical interactions can only occur between objects that are in close proximity to each other. This means that the effects of a physical interaction cannot propagate faster than the speed of light.

2. How do general covariance and locality relate to each other?

General covariance and locality are often seen as competing principles in physics. While general covariance suggests that the laws of nature should be expressed in a way that is independent of the chosen coordinate system, locality implies that there are restrictions on how these laws can be expressed. In other words, the principle of locality can limit the degree of general covariance that is possible in a given physical theory.

3. Can a theory be both generally covariant and local?

Yes, it is possible for a theory to be both generally covariant and local. In fact, this is a desirable quality for a physical theory to have, as it allows for consistent and accurate predictions to be made. However, achieving both of these qualities can be challenging, and some theories may prioritize one principle over the other.

4. Are there any examples of theories that violate either general covariance or locality?

Yes, there are some theories that violate either general covariance or locality. For example, the theory of general relativity violates the principle of locality, as it allows for the effects of gravity to propagate at speeds faster than light. On the other hand, some theories that attempt to explain quantum entanglement violate general covariance, as they require a preferred reference frame in order to make sense of the phenomenon.

5. How do general covariance and locality impact our understanding of the universe?

General covariance and locality are both important principles in physics that help us understand the fundamental laws that govern the universe. They provide a framework for developing and testing theories, and allow us to make accurate predictions about the behavior of physical systems. By understanding the relationship between these two principles, we can continue to expand our knowledge and understanding of the universe.

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