Gravity and Quantum Mechanics don’t play nice together. Since Einstein’s time, we have two towering theories that have defied all attempts by some very smart people to be reconciled. The Standard Model, built on the foundations of quantum mechanics, has been spectacularly successful. It allows the treatment of masses acquired from the binding energies, and, if the Higgs boson confirmation pans out, accounts for the elemental rest masses - but it does not capture gravity. (The current mass generation models that involve gravity are all rather speculative at this point.)
Einstein’s General Relativity has been equally successful in explaining gravity as innate geometric attributes of space and time itself. It has survived every conceivable test and made spectacular predictions (such as gravity lenses).
On the surface this dysfunctional non-relationship between the two major generally accepted theoretical frameworks seems very puzzling. But it turns out that the nature of this conundrum can be described without recourse to higher math (or star-trek like animations with a mythical sound-track).
Much has been written about the origin of this schism: The historic struggle for the interpretation of Quantum Mechanics, with Einstein and Bohr being the figureheads of the divided physics community at the time. Mendel Sachs (who, sadly, passed away recently) drew the following distinction between the philosophies of the two fractions:
[The Copenhagen Interpretation views] Schroedinger's matter waves as [complex] waves of probability. The probability was then tied to quantum mechanics as a theory of measurement - made by macro observers on micro-matter. This view was then in line with the positivistic philosophy, whereby the elements of matter are defined subjectively in terms of the measurements of their properties, expressed with a probability calculus. [...] Einstein's idea [was] that the formal expression of the probability calculus that is called quantum mechanics is an incomplete theory of matter that originates in a complete [unified] continuous field theory of matter wherin all of the variables of matter are 'predetermined'.
These days, the Copenhagen Interpretation no longer reigns supreme, but has some serious competition: E.g. one crazy new kid on the block is the Many World Interpretation. (For an insightful take on MWI I highly recommend this recent blog post from Scott Aaronson).
But the issue goes deeper than that. No matter what interpretation you favor, one fact remains immutable: Probabilities will always be additive, mathematically they behave in a linear fashion. This, despite its interpretative oddities, makes Quantum Mechanics fairly easy to work with. On the other hand, general relativity is an intrinsically non-linear theory. It describes a closed system in which the field, generated by gravitating masses, propagates with finite speed and, in a general, non-equilibrium picture, dynamically affects these masses, in turn rearranging the overall field expression. (Little wonder Einstein's field equations only yield to analytical solutions for drastically simplified scenarios).
There is no obvious way to fit Quantum Mechanics, this linear peg, into this decidedly non-linear hole.
Einstein considered Quantum Mechanics a theory that would prove to be an approximation of a fully unified field theory. He spent his last years chasing after this goal, but never achieved it. Mendel Sachs claims to have succeeded where he failed, and indeed presents some impressive accomplishments, including a way to derived the quantum mechanics structure from extended General Relativity field equations. What always struck me as odd is how little resonance this generated, although this clearly seems to be an experience shared by other theoretical physicists who work off the beaten path. For instance, Kingsley Jones approaches this same conundrum from a completely different angle in his original paper on Newtonian Quantum Gravity. Yet the citation statistic shows that there was little up-take.
One could probably dedicate an entire blog speculating on why this kind of research does not break into the mainstream, but I would rather end this with the optimistic notion that in the end, new experimental data will hopefully rectify this situation. Although the experiment on a neutral particle Bose-Einstein condensate proposed in Kingsley Jones' paper has little chance of being performed unless there is some more attention garnered, other experiments to probe the domain where gravity and quantum mechanics intersect get a more lofty treatment: For instance this paper was featured in Nature although its premise is probably incorrect. (Sabine Hossenfelder took Nature and the authors to task on her blog - things get a bit acrimonious in the comment section).
Nevertheless, it is encouraging to see such a high profile interest in these kinds of experiments, chances are we will get it right eventually.
Kingsley Jones (who's 1995 paper paper I referenced above) has a new blog entry that reflects on the historic trajectory and current state of quantum mechanics. I think it's fair to say that he does not subscribe to the Many World Interpretation.