OE

The passage is trying to establish the difficulties that arise in trying to promote new ideas in the world of academia. The first blank is talking about something happening to potential growth in the field of physics. Since this thing is happening "in spite of immense intellect," we can infer that it must be negative. "Correlated" means connected. This word doesn't describe growth being inhibited or promoted, so it doesn't work. "Supplanted" means replaced. This answer does not make sense in the context of the question. We are left with "Antagonistic," which means "opposed to," or "hostile." Having factors that are "opposed" to growth makes sense.
The second blank is the end of a list that states the obstacles a progressive person would face. We want a word that completes this list. "Eminence" means renown. This doesn't continue the tone of the list. "Acquiescence" means compliance. This is of course the opposite of what we want. "Inscience" means "ignorance." Ignorance would function like "entrenched logic" and "petty careerism" in inhibiting society from accepting new ideas.