# How do unitarity and locality break in theories involing gravity?

In the science-pop article A Jewel at the Heart of Quantum Physics https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/, there is a footnote, with the following claims:

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.

1. Breaking of locality:

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.

1. Breaking of unitarity:

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 the graviational theories the notion of locality seems to be obscured, because due to the ability to perform diffeomophisms the position is not an invariant notion. From this paragraph, I would think, that it is meant something like $$\Delta E \cdot\Delta t \sim \hbar$$, and we take the scale to be $$M_{pl}$$ - but in the ordinary QFT we have the same uncertainty principle, derived from quantum mechanics.

And the second statement I do not really understand. In the quantum mechanics we assume, that our evolution is governed by a unitary opertator of form $$e^{i H t}$$, where $$H$$ is a hamiltonian - some hermitian operator. In the theories with gravity, because of the time reparametrisation, the notion of Energy and Hamiltonian also becomes more subtle, but how to connect it with the statement in the paragraph?

I would strongly appreciate if someone shed light on this statements