"Marika Taylor, professor of theoretical physics at Southampton University and a former student of Hawking’s, said: “Understanding the microscopic origin of this entropy – what are the underlying quantum states that the entropy counts? – has been one of the great challenges of the last 40 years."
(The Guardian.)
Does the interrogative "what" 'ask' about noun (noun-like) thing(s) or does it 'ask' about adjectvally described information modifying "the underlying quantum states that the entropy counts" in "what are the underlying quantum states that the entropy counts??
g. e. asking for an identification or explanation of a noun-like thing.
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It is essentially similar to e.g. "What is that strange smell?", i.e. asking for an identification or explanation of a noun-like thing.
what are the underlying quantum states that the entropy counts?
I'd go along with what GPY says.
In grammatical parlance, we'd call this the specifying sense of "be" (as opposed to the ascriptive one), which seeks to identify the predicand – here, the "underlying quantum states ...".
So the answer would have the form of a noun phase, not an adjective one.