Arguments with non-objectivists about reality and epistemology often boil down to some sort of assertion that "reality is not absolute, and quantum mechanics proves it"! I believe that this arises from popular beliefs about QM, primarily based on the Copenhagen Interpretation of QM.
As Greg Perkins notes, there are facts known about QM and then there are various interpretations of those facts. Which known interpretation, if any, is consistent with the facts of reality as understood by Objectivism?
UPDATE: To clarify the question, note that I am not asking Objectivists to advocate for a particular scientific theory. Obviously, only scientists can and should do that, based on the scientific method. What I am asking for is an identification of an interpretation of QM that is consistent with the philosophical axioms of Objectivism. Interpretations of QM are rightly the domain of philosophers. For example, Wikipedia states:
The main reason for this question is that when an armchair physicist tells me his subjective or intrinsic interpretation of the world is correct, and "QM proves it", it would be nice to point to an interpretation of QM that does nothing of the sort, if indeed any such currently exists. Relevant XKCD comics may be even better :)
As xkcd points out, most appeals to quantum mechanics (outside the domain of actual physics) are nonsense.
On a more serious note, a proper understanding of Objectivism does not warrant dictating specific scientific theories. That would require specialized experimental and theoretical knowledge that philosophy cannot provide. The only thing that Objectivism can do is to rule out a few particularly egregious ideas that contradict the philosophical axioms. These bad ideas include any of the following:
For example, the von Neumann-Wigner interpretation would be rejected by Objectivism because this interpretation claims a role for human consciousness in determining reality.
Other interpretations may also violate the axioms, but in a more subtle way. A detailed study of these other interpretations would be needed before making a judgment.
By the way, the most popular interpretation among physicists, the Copenhagen interpretation, is often misunderstood as giving a role for the observer's mind. It actually gives a special role to the act of measurement, which involves a macroscopic measuring device which is assumed to be classical. This interpretation has been criticized for reasons that are not unique to Objectivist thinking. Specifically, the Copenhagen interpretation makes an ad hoc division between the classical and quantum worlds, whereas we should expect a consistent theory to explain measuring devices as quantum entities, too.