Sabine Hossenfelder wrote a blog post about the information loss paradox, pretty much repeating standard arguments made in this debate. Among them the following:

"Physicists are using quantum field theory here on planet Earth to describe, for example, what happens in LHC collisions. [..] in principle black holes can be created and subsequently annihilated in any particle collision as virtual particles. This would mean then [..] we’d have no reason to even expect a unitary evolution."

As I said, this is a standard argument, but I have a problem with it:

In any experiment we can do, e.g. at the LHC, the energy of such a virtual black hole would be well below the Planck mass, i.e. far from the quasi-classical limit where the information loss problem is discussed.

In which sense can any particle fall into a microscopic b.h. with a radius much smaller than the Planck length, if its wavelength is much larger? So in which sense would a virtual b.h. pose an information loss problem?

We have to assume that the mass of an off-shell virtual b.h. could be arbitrarily large, but its contribution to any S-matrix element would be strongly suppressed (at least exponentially) for energies much larger than the collision energy, which is well below the Planck mass. Therefore its contribution would for all practical purposes be unmeasurable.

added later: Without a full theory of quantum gravity (and even string theory does not know how to handle black holes yet, see e.g. fuzzballs and firewalls vs. ER=EPR) we can only make some basic estimates.

There are estimates of proton decay due to virtual black holes and the expected lifetime is about 10

^{45}years - a factor 10

^{11}higher than what we could currently detect.

But I think even those estimates are too low if information loss requires a black hole of mass > m

_{Planck}(if the surface area is indeed quantized black holes with a small mass m < m

_{Planck}may not even exist). Wick rotation suggests that the contribution of a massive black hole m > m

_{Planck}to any Feynman diagram would be suppressed by a factor exp(-k

^{2}) or exp(-(m/E)

^{2}) if E is the energy of the collision.

Btw the same exponential factor shows up in a different estimate, suppressing the production of black holes even for large collision energies E.

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