What is the physics behind GR's diffeomorphism invariance?

[atyy]

The third is subtler, and I don't know whether it is equivalent to the second, or not. It's something like "the indistinguishabilty of points".

I don't understand this well either, but here are some thoughts. It's usually said here that the hole argument says that observables must be relational in gravity. I don't understand this because I think observables must also be relational in special relativity, ie. relative to an inertial frame.

However, what is known is that in pure gravity, there are no gauge invariant local observables. Classically, this problem can be solved if matter is introduced, so that relational aspects of the matter distribution create local observables. There's a discussion of this around Eq 1.1 of http://arxiv.org/abs/gr-qc/9404053.

The quantum situation seems trickier, eg. http://arxiv.org/abs/hep-th/0106109, http://arxiv.org/abs/hep-th/0512200.