More important, in a book with hundreds of pages of philosophizing about human nature, there’s no mention of evolution; in a book obsessed with “physics,” there’s no evidence of any acquaintance with relativity, quantum mechanics, or pretty much anything else about physics. (When Stadler starts talking about particles approaching the speed of light, Dagny impatiently changes the subject.) It’s an interesting question whether Rand outright rejected the content of modern science; maybe we’ll pick up that debate in the comments section. But another possibility—that Rand was simply indifferent to the sorts of things an Einstein, Darwin, or Robert Stadler might discover, that she didn’t care whether they were true or not—is, to my mind, hardly more defensible for a “philosopher of reason.”
The book, however, is not obsessed with physics, or even "physics." Physics is featured as the hero's profession. The validity of relativity or quantum mechanics is just not relevant to the book's theme, which may count as another possibility for why such matters were not addressed in it.
It is likely that, were she asked, Ayn Rand would have responded that she could not judge the validity of modern theories of physics because she did not have the requisite expertise. In fact that is how she did reply when asked about the theory of evolution, even while being an atheist and an admirer of science generally. It makes no sense to conclude from the fact that she was not an expert, and that she was honest enough to withhold judgment, that she was "simply indifferent."
But independently of Ayn Rand's knowledge of the subject, it's a legitimate question: even though Objectivism doesn't take positions on the validity of particular scientific theories, are the metaphysics and epistemology of Objectivism in fact consistent with quantum mechanics and relativity?
The question is not well-posed, however, because these theories have each been interpreted in startlingly different ways. I would argue that some more-or-less mundane reformulation of relativity, concerning such issues as the meaning of the concept "entity" and whether space or spacetime or "the metric" can be said to exist as a substance, does not run afoul of any aspect of Objectivism. However, I am not much interested in this question, because for non-philosophical reasons (e.g., the non-locality exhibited in Bell experiments) I believe relativity is best taken as an effective theory, with no metaphysical claims to make about the ultimate nature of space and time.
Quantum mechanics is a more interesting subject. It is clear that insofar as quantum mechanics was interpreted (more accurately: forced into a mold) by Bohr or Heisenberg or multitudes of popular accounts, there is a clear conflict with Objectivist metaphysics. Objectivism holds that the external world exists independently of consciousness. The way the measurement postulate of quantum theory is usually presented, at least when it is done forthrightly without the waving of hands, consciousness is asserted as some irreducible object with direct causal power in the external world.
Does this mean that Objectivism would logically entail the rejection of quantum mechanics? No. David Bohm's interpretation of quantum mechanics, for instance, obviates any subjectivism. Against the usual understanding of the physical processes involved in measurement, consciousness has no fundamental role to play in Bohm's theory and, to paraphrase John Bell, we may actually contemplate objects to be a certain way in reality, independently of us, rather than just to be observed to be so. In fact if you want a perspective on quantum mechanics from someone upholding metaphysical realism--the aspect of Objectivism relevant here--John Bell is a perfect example.
What Bell called the "unprofessionally vague" formulation of quantum mechanics adopted by the mainstream of its practitioners, I would go marginally further to call unscientific and ultimately the product of a campaign by Bohr and his followers to transplant certain then-fashionable philosophic ideas into the foundations of physics.
That the residue of Bohr's silly philosophy has lingered for 80 years on the scientific project of understanding the quantum world is a shame on the physicists who have always, down-deep rejected this play-philosophy but have never wanted to risk being thought overly philosophical or pedantic for raising the issue. Indeed the virus of quantum subjectivism thrived by virtue of another philosophic microbe that was simultaneously unleashed against the immune system of the host: the methodological doctrine of positivism.
It was an effective combination. First, here, take this dose of the-moon-isn't-there-when-you're-not-looking. It's making you sick? Well you shouldn't be dwelling on these metaphysical issues, which don't mean anything anyway, so just swallow it, shut up, and calculate like a good little boy.
The orthodoxy has loosened its grip over the past two decades, but the cultural damage within physics has been significant. The effect is that Bohm's theory, while offering such a simple, direct alternative to vagueness and subjectivity, and while perhaps gaining ground since Bell's own endorsement, is currently not even the most popular among alternative interpretations. I suspect the reason for this is the psychological fall-out from physicists' historical acceptance of Bohr's ideas. Once one has given credence to such silly metaphysical claims, it is hard to just admit it was all a needless house of cards.
Instead we have the rise of things like the consistent histories or many worlds interpretations, which to their credit seem to have been motivated by a desire to dispense with subjectivism, but ultimately fail to accomplish their goal without the adoption of similarly radical philosophic positions. Many worlds, in particular, winds up solving the measurement problem (the failure to infer anything about measurement outcomes from the Schrodinger equation without ad hoc postulates) by baldly denying the reality of whichever one distinct measurement outcome we observe. It is asserted instead that despite our perceptions all potential outcomes actually occur, and that it is merely our narrow consciousness that, for some inexplicable reason, fixes itself to a single random one.
In other times the vacuousness of such an explanation would have served to disqualify it from serious consideration. But in the aftermath of Bohr's obscurantism, its roundaboutness in comparison to a simple alternative is felt as a mark of profundity. Bohm's theory has some other objections of a more technical nature leveled against it, which I think are all wrong and am glad to discuss, but I suspect this psychological factor is the real source of its limited acceptance.
At one time this contentious legacy was more-or-less confined to a basement in the house of modern physics, from which the youth were barred by the pad-lock of positivism. Normal physicists were busy with the work of understanding new discoveries about the most basic interactions of elementary particles and the fascinating properties exhibited when large numbers of them got together. As these new discoveries in the former area have been cut off to a slow trickle, and as the old ones have virtually all been accounted for by the triumphant standard model of particle physics, attention has shifted to certain neglected but foundational matters of principle in order to further unify our theories of nature and to amplify and exploit the peculiar phenomena of the quantum world. As a result it was necessary to re-enter that old basement.
The troubling development of particle physics since the early 80s has demonstrated how such foundational matters are of more consequence than the positivists would like to admit, but I'll postpone additional commentary for now.