“But the two masses come from very different places.” Yes that was the old view, which yet may be proven right according to Clark.
“Another way of stating the equivalence principle is to say that these two masses are always numerically exactly the same.” The equivalence principle is a map between paradigms. It is a statement in the classic paradigm pushing you into the GR paradigm in which the meaning becomes a tautology (x=x) and thus not even a physical principle.
The early 20th century brought two new physics paradigms—GR and QM which supplanted the ‘classic paradigm’. This article is the most accessible that I recall to explain the tension between the two, without doing violence to either. I argue here that the Clark adopts the QM paradigm in arguing against the GR paradigm. This is slightly unfair. See a clever and ironic quote by Magueijo that captures the mess.
Some recent commentator has recently written that it is perhaps unprecedented that some unification (i.e. simplification) in physics, or science in general, once grasped, been found to be wrong. Some philosopher’s famous example was the realization that the morning star and the evening star were both ‘Venus’. (I think that this realization is pre-historic.)
“Yet there is no obvious reason why this correspondence should be so.” This is a classic paradigm statement. Clark uses the classic paradigm; that’s fair. There is an explanation in the GR paradigm.
“All the other forces of nature are transmitted between bodies by physical, if ethereal, quantum particles.” This is the QM paradigm. Paraphrasing Clark: this is “still our best stab at explaining the mysterious stability of atoms”. It is, nonetheless, the QM paradigm.
“If we want to find some bigger, better theory that can unify gravity with the other forces that dictate the world’s workings, the equivalence principle cannot stay. We must either unmask this coincidence — or radically rethink how physics can progress from here.” I agree with the second sentence but not the first.
“The electromagnetic force, for example, is transmitted between bodies with electrical charge by the exchange of the massless particles called photons.” QM paradigm again. GR has a nifty set of fields that explain this force too. Einstein was disappointed that his equations did not require the electromagnetic field—he had to add them to his equations. To my limited taste those extra terms fit perfectly in the stress energy tensor.
Clark quotes Gripaios “Any theory of quantum gravity must violate the equivalence principle at some level,”. I think that this is so if gravity is to be explained in QM, but I see no headway towards duplicating the successful and novel predictions of GR and I see a notable lack of interest in this task.
“They point out that whether or not Einstein was right about there being no gravity, just inertia, no one has yet come up with a convincing explanation of inertia.” Inertia is to me a pleasing primitive of GR. Every theory has its primitives. Where better to start?
Clark goes on to describe attempts to unite these theories and interesting proposed empirical tests of the equivalence principle.