My friends and I are asking this question about the standard model and general relativity to put the discussion on a firmer footing:
Does some experiment show that the two theories contradict each other?
It is obvious that the two theories really do contradict each other - but only on paper. Their mathematical descriptions are not compatible and contradictory. In reality, it seems that no experiment contradicts these theories, and no experiment shows any contradiction between the two theories.
What is the exact status? Is there a discussion of this point somewhere?
(1) The incompleteness of either theory is clear and due to their different domains of application. But that does not show that they contradict each other. In nature, inertial and gravitational mass are equal; so letting something fall does not contradict the standard model. Just let the observer fall near the experiment, as a check.
(2) The mathematical formulations of the two theories do contradict each other, because general relativity is not probabilistic (e.g. the mass-energy tensor) whereas quantum theory is. But it seems that no experiment has observed the contradiction.
(3) Is there a thought experiment showing a contradiction?
(4) Any experiment (real or thought) confirming one theory and contradicting the other would qualify. In the meantime, a number of experts have confirmed to us that as of November 2022, no such experiment is known. Following the most recent reviews, general relativity and the standard model have no confirmed anomalies or exceptions. (Falling apples, quantum superpositions or double slit experiments do not qualify: they do not contradict the other theory.)