But in a paper recently published in Science Advances, we show that in the micro-world of atoms and particles that is governed by the strange rules of quantum mechanics, two different observers are entitled to their own facts.
So long as the empirical results are in accordance with known, objective facts (actual "facts") which are, thanks to the objective nature of quantum theory, independent of any individual observer or experiment.
The best that can ever be said of any test of reality that claims to have demonstrated the subjective nature of reality empirically is that we cannot trust the claim.
Experiments that are designed and implemented outside of the mind (as opposed to thought experiments) assume
a priori that there exists some observer-independent, external reality that we can agree about. In particular, one can easily dismiss any claim that any empirical test which showed the contrary could not possibly have done so: to demonstrate empirically that it is impossible to agree on objective facts about an experiment would mean that one has shown AT MOST that one cannot trust THE EXPERIMENT IN QUESTION! After all, any experiment including the one in question is done in the "real world" and perhaps most importantly the results are written up and disseminated
with the understanding that the experiment has actually shown something objective about which we can all, in principle, agree.
Put more simply still, this:
In other words, according to our best theory of the building blocks of nature itself, facts can actually be subjective.
is really a statement about the subjectivity of observations (as Wigner originally intended, although the researchers explicitly disagree with Wigner's original purpose which as was in part to emphasize the necessity and importance of consciousness or the conscious observer).
The claim that this or any research could show that quantum theory makes actual facts about the physical world subjective is an objective claim about the physical world that the authors are telling us cannot be said to be objectively true.
In short, the claim is self-defeating- "this statement is false".
Chris Fuchs and Asher Peres (along with a few others) have explored perhaps the most radical form of this kind of approach to quantum theory which they claim requires no interpretation (and that, in particular, their QBism or quantum Bayesianism is simply "quantum theory" itself). I've heard them present on this topic and talked to Fuchs (he works not far away from me). Fuchs perhaps especially has been trying to make it clear both to critics and to advocates that QBism, which holds quantum theory to be entirely a subjective probability calculus in which its users are given a formal framework that yields the best odds of predicting the results of experiments, is a realist approach. That is, he and most of the QBists believe that the subjective nature of quantum theory in no way stops quantum theory from being realist. Rather, it proposes a more comprehensive view of reality.
Regardless, even if one were to agree that quantum theory is inherently subjective in that it yields local, observer-dependent probabilities it does so via a universal, observer-external framework which can be tested (and has been for over a century) objectively.