I have a number of problems with relational quantum mechanics (RQM), perhaps foremost being how promising RQM seems at first to be compared to how I think it ends up fairing! In trying to retain too many desiderata one generally wants out of physical theories whilst “answering” or “resolving” seemingly paradoxical aspects of quantum theory, RQM ends up being largely incoherent. In this way it is not dissimilar to the kinds of approaches advocated by the founders of quantum theory that Rovelli took inspiration from. Bohr, for instance, tried to retain classical conceptions and indeed classical physics itself by more or less insisting that quantum theory had to be understood as a complement to the classical world we experience and attempting to recast seeming paradoxes into dualistic, complementary pictures that full apart all too easily. Heisenberg did likewise, but was more concerned with recovering rather than retaining classicality via the requirement of a classical cut.
Rovelli’s starting inspiration appears to be from the (classical) theories of relativity and the way in which these forced us to consider differences in observations as resulting necessarily from different “perspectives” (i.e., reference frames) that are rendered into a single coherent one when properly understood. But this is merely inspiration. Quantum mechanics, whatever else it may be, is a statistical theory used to calculate probabilities. Physical states encode information about preparation procedures and (together with the “observables”/operators) the probabilities associated with specific kinds of measurement outcomes given these preparations. Rovelli is quite clear about the priority that should be given to the probabilities encoded in the quantum formalisms. But exactly because of this statistical nature of quantum “systems” and the probabilistic nature of their “physical” variables, there is little or nothing akin to the kinds of observable-dependent quantities we find in relativity. There is all the difference in the world between quantities that differ depending upon extrinsic reference frames one associates with them and the intrinsic physical properties associated with physical systems and/or their states.
To tease out how this is so, it might be best to make some comparisons with other interpretations of QM and their issues.
The central problems of RQM can be, albeit overly simplistically, traced back to attempts to retain a realist, (mostly?) local, “ontological” interpretation of quantum theory (as a complete theory) without privileged observers, unobserved variables, or unobserved “worlds”.
These problems can rather easily seen (again simplistically as well as fairly naively) if one considers how RQM differs from the many-worlds interpretation (MWI) on the one hand and epistemic approaches such as QBism on the other. The MWI also assumes a realist stance and, like RQM, does not privilege any observer. It does this by rejecting the projection postulate or the collapse of the wavefunction. The result of these starting assumptions (and without further assumptions such as the hidden variables of Bohmian mechanics) is that every outcome of “measurement” or interaction must be realized, and we only observe particular outcomes because we find ourselves in a “branch” or “world” in which that particular outcome is realized.
The central problem with the many-worlds approach (apart from prioritizing a radically Copernican perspective in which we would opt to imagine countless and constantly emerging worlds rather than grant some privileged position to observers) is probabilities.
Imagine for a moment the probabilities associated with a coin toss. There are two outcomes. Assuming a fair coin, then we can assign 50/50 odds. Now imagine a quantum system prepared and measured in some experiment such that there are at least two possible outcomes. If, as in the case of a fair coin (or fair dice roll, or fairly dealt hands of cards, etc.), the distribution is uniform, deriving the probability distributions needed to use quantum theory without the Born rule and collapse is mostly straightforward.
But now imagine a biased coin rather than a fair one. Further, imagine that we do not know the actual probabilities apart from the fact that they are no longer 50/50. To figure out the probabilities, we need only to toss the coin many times and tally up the relative frequencies. This is what is done in QM in practice in order to determine the actual probabilities associated with measurements. And in general, probabilities of measurement outcomes in QM are not uniform.
For the MWI, this is a serious problem. The MWI assumes the actual realization of all possible outcomes and explains the fact that we only ever observe a single outcome by positing the “many-worlds” for which it is named: all outcomes occur, but in each “world” only one is realized and we always find ourselves in one of these.
Now go back to the biased coin and imagine that instead of obtaining heads or tails, each coin toss results in two “worlds”, one in which “heads” is observed and the other in which “tails” is. We can no longer calculate the probable outcomes, because we cannot observe (or even make much sense out of) the biased probabilities. Each toss results in a “heads” world and a “tails” world, so what would it mean for such a toss to have odds 70/30, or 80/20, or anything other than 50/50? This issue only gets more complicated with more realistic situations in theoretical and applied quantum mechanics.
Now we go back to RQM. RQM rejects both unobserved worlds and unobserved variables, the two most discussed, well-known, and perhaps most popular of the ontological, realist interpretations. Yet it too is a realist approach, which does not rely on consciousness or similar mechanisms to explain why quantum systems evolve according to dynamics that only hold if we don’t look. So how are such problems explained? By making everything an observer and all measured outcomes objectively real
for that observer. The crucial component is the idea that measurements, probabilities, and indeed physical properties and facts about reality itself are all products of interactions among systems and relative to these. Thus interactions in RQM plays a role analogous to that of worlds in the MWI.
But here’s the rub: if facts are relative and the real properties of real systems given by variables that are likewise relative to relative states of the relative observers, the it isn’t at all clear that RQM actually explains anything or gives anything like a coherent account of how seeming paradoxes of quantum theory are to be resolved except by fiat. In this way it is not clear how RQM can be seen to offer anything to quantum foundations or to our understanding, as it can avoid basically any kind of no-go theorem or experimental test just because it uses the same quantum formalism and declares the observed results to be relatively true for ill-defined systems with “real” but theoretically unobservable properties. RQM “resolves” the extended Wigner’s friend by declaring that observer’s cannot consider their own state and thus Wigner’s friends outcome is “real” for the friend and the contrary and conflicting outcome Wigner finds “real” for Wigner. If the “friend” is a cat, then the only thing that forbids a dead cat from being found to be alive by Wigner is that the outcome of the quantum-mechanical poisoning apparatus the cat “observes” to have released the poison via decay or to not have released is not an interaction Wigner takes part in.
The crucial component to the Wigner’s friend version of the Schrödinger cat paradox is to give a version in which, rather than a clearly distinct macroscopic state that somehow “collapses” to a living or a dead cat upon observation, one has a friend who can say what the outcome of measurement was. There is a conflict between the state assignment of Wigner’s friend demanded by the formalism and that which it demands from Wigner. In its extended from, the problem is made testable (and has been in several experimental realizations) and rendered more problematic still. But these problems are “avoided” by RQM simply by stating that there is no problem with Wigner’s “facts” being in contradiction to his “friends” because dead friends tell no tales. How is this a better approach than that offered by Bohr and Heisenberg? How is it more coherent? Superior? What does it offer for those in quantum foundations to build off of or deepen our understanding of?
At least in the MWI, a lot of productive work has resulted in attempts to derive the Born rule without appealing to collapse (in fact, a lot of this work was taken from QBism or ended up used by QBists). In operational quantum mechanics, we can explore e.g., the implications of the most generalized models of measurement or what so-called “classical” toy models or theories either yield the same results as found in quantum theory or else point to crucial differences (such as the non-commutativity of quantum observables compared to their classical counterparts). Bohmian mechanics began as a clear counter-example to von Neumann’s original no-go theorem and offered a great deal of inspiration for e.g., understanding potentials in QM among other things.
In general, other well-known interpretations (no matter how distasteful I find them) have managed to yield productive results in the form of theorems proven, experiments proposed, or at least acknowledging the cost payed in terms of e.g., Bohmian nonlocality with its superfluous ontology, the vast and increasing unobservable worlds of the MWI, the approximate nature of an ultimately incomplete theory for those who reject quantum theory as fundamental, etc. RQM seems to offer relatively little beyond that which textbook quantum mechanics is based off of.
