General covariance vs. locality

[sadegh4137]

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

 

[Bill_K]

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.