Sabine Hossenfelder recently discussed various gedanken experiments showing that "semiclassical gravity" can't be a consistent description of Nature:
Backreaction on Eppley-Hannah's thought experiment
Backreaction on this and Page-Geilker's thought experiment
While she admits that "semiclassical gravity" can't be right for various theoretical reasons, she still irrationally criticizes the two thought experiments above. In this inconsistent treatment of hers, she seems to misunderstand that the very purpose of gedanken experiments is to give us those "theoretical reasons" to know that Nature can't work in certain ways.
Now, I must tell you what we mean by
"semiclassical gravity". Quite generally, the adjective
"semiclassical" in physics means that certain parts of the physical system are being treated in the framework of quantum mechanics; others are treated using classical physics. If the two parts influence each other (in both directions), this is really an inconsistent approach, as I will discuss, and it doesn't make sense to develop the "semiclassical approach" too accurately.
In particular, the term "semiclassical approximation" is often applied to electrons in an external potential. The potential, e.g. the electrostatic potential induced by the atomic nuclei, is assumed to be a source of classical external forces. This is justifiable as an approximation because the nuclei are much heavier, and therefore "more classical", than the electrons and the same comment applies to the field they exert.
However, such a treatment automatically denies the existence of virtual photons etc. so it can't possibly be right at the quantum (loop) level. Only the leading quantum effects influencing the electron, those proportional to \(\hbar^1\), may be considered in this treatment. That's why the first quantum corrections to classical physics, e.g. one-loop diagrams in various quantum field theories, are often called "semiclassical" as well; some people view "semiclassical" and "one-loop" to be synonyms. The WKB approximation is a typical example of a semiclassical treatment in non-relativistic quantum mechanics.
In the context of gravity, people use the term "semiclassical gravity" either as a legitimate approximation that is aware of its limitations; it's the approximation that was used e.g. by Stephen Hawking to derive the thermal radiation emitted by black holes. Alternatively, some people use the term "semiclassical gravity" as a proposed "hybrid" quantum-classical picture of physics. Reasons why this idea is wrong will occupy the rest of this blog entry.