Why an infinitely measuring apparatus in gravity is not possible? In the discussion of the amplituhedron paper (arXiv:1312.2007), there is the following discussion in paragraph 14.outlook (page 28):

Quantum mechanics forces us to divide the world in two pieces - an
  infinite measuring apparatus and a finite system being observed. However for any
  observations made in a finite region of space-time, gravity makes it impossible to
  make the apparatus arbitrarily large, since it also becomes heavier, and collapses the
  observation region into a black hole.

Can one elaborate this point? Is this related to coordinate invariance?
 A: I hope that somebody familiar with this research will contribute so that we all learn something.
I found the following , it is in a separate column like a comment:

Locality and unitarity are the central pillars of quantum field theory, but as the following thought experiments show, both break down in certain situations involving gravity. This suggests physics should be formulated without either principle.
Locality says that particles interact at points in space-time. But suppose you want to inspect space-time very closely. Probing smaller and smaller distance scales requires ever higher energies, but at a certain scale, called the Planck length, the picture gets blurry: So much energy must be concentrated into such a small region that the energy collapses the region into a black hole, making it impossible to inspect. “There’s no way of measuring space and time separations once they are smaller than the Planck length,” said Arkani-Hamed. “So we imagine space-time is a continuous thing, but because it’s impossible to talk sharply about that thing, then that suggests it must not be fundamental — it must be emergent.”
Unitarity says the quantum mechanical probabilities of all possible outcomes of a particle interaction must sum to one. To prove it, one would have to observe the same interaction over and over and count the frequencies of the different outcomes. Doing this to perfect accuracy would require an infinite number of observations using an infinitely large measuring apparatus, but the latter would again cause gravitational collapse into a black hole. In finite regions of the universe, unitarity can therefore only be approximately known.

So what this tells me: They are pushing working concepts from quantum mechanics to the limits, i.e. unitarity and locality. In contrast to the conclusion in the first paragraph quoted here "This suggests physics should be formulated without either principle"  I would say that it suggests that in the limits new concepts must be employed that will merge consistently with the well validated concepts of quantum mechanics.
Our experience is that physics mathematical models have a region of validity where the mathematics describes nature. Taking the mathematics to the limits and finding contradictions is what gave rise and actually discovered the quantum mechanical underlying framework. It may well be once gravity is quantized in a unified theory with the standard particle physics model, the paradox will evaporate. If not, it will signify that we have reached the region of validity of quantum mechanics. Its principles are fine for its region of validity.
A: It is like the interesting proposition in simulation hypothesis which paraphrased goes, if we could create a computer simulation to understand reality it would be the approximate size and age of the current entire universe.
