> Quatom mechanics doesn't really have a concept of space-time

The Standard Model of Particle Physics incorporates the Poincaré group, which is the isometry group of the flat spacetime of Special Relativity, so it has an exact concept of spacetime built right into the formulation.

Quantum mechanics and Special Relativity were unified in the 1920s by Dirac. Solutions for some curved spacetimes came not much later, and are now taught in several textbooks. The problem is that we don't have a general solution for quantum mechanics on arbitrary curved spacetimes (and some curved spacetimes are known to make quantum field theories insoluble with current methods).

I refer you to my sibling comment https://news.ycombinator.com/item?id=24877746 for more details.

> (by design) just an approximation of the still unknown theory of quantum gravity

Kind-of. It is manifestly an approximative approach because the equation includes "mean" angle-brackets around the stress-energy tensor, which, speaking roughly, indicate that the curvature is generated by the averaged value of the stress-energy generated by the quantum field(s) are used, rather than an exact value at each and every infinitesimal point in the solution. This "classicalizes" the source term of the classical curvature, erasing quantum effects.

It is not really in the strictest sense an approximation to a theory of quantum gravity, however any candidate quantum gravity theory had better explain results from semiclassical gravity that find some support in astronomical observations.

Contrasting approaches -- like canonical quantum gravity -- "quantumize" the metric, leaving the source term fully quantum mechanical and non-averaged, and results from such approaches also find some support in astronomical observations. These are arguably approximations to a full theory of quantum gravity since one can cast them as a series of terms similar to a Taylor series; the problem is that the set of such terms appears to grow without bounds as one takes energy-momentum into the "ultraviolet" regime (UV ~ extreeeeeemely high energy-momentum densities). Worse, the relative weight of the contribution of some of the far-from-leading-order terms grow stronger in the UV limit, so not only can't we just ignore them, we also can't apply perturbative renormalization. Fortunately this probably only happens inside black hole event horizons and near the big bang, one of which is probably not observable, and the other of which is at high enough individual energies that the Standard Model doesn't predict results even if their collective mutual gravitation (and the contribution of dark matter and other energy-densities) could be factored out.

> we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity

We can calculate the effects of a boost, even an ultraboost, on particles with mutually-entangled properties just fine thanks to the Poincaré invariance baked into post-Dirac relativistic quantum mechanics. If you were flying past from an entanglement experiment in deep space at ultrarelativistic speeds, one could predict your observed redshift (etc) of the entangled properties exactly with no worries. (If you were flying radially to or from an Earthbound experiment at ultrarelativistic speeds you might want to incorporate some corrections from the https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... for greater accuracy. The post-Newtonian expansion leading-order corrections attributable to Earth's gravity will not be large; linearized gravity is enough. Errors from the next-to-leading-order corrections will not be measurable with current technology, and we can brute force calculate at least next-to-next-to-leading order corrections, which is good enough for accelerating down towards the surface of a neutron star, like the material that is blown onto the Hulse-Taylor binary members.