Timotheus Riedel

Relational Quantum Mechanics posits that facts about the properties of physical systems are relative to other systems. As recently pointed out by Adlam, this gives rise to the question of the relationship between the facts that obtain relative to complex systems and the facts that obtain relative to their constituents. In this paper, I respond to Adlam’s discussion of what she calls the Combination Problem. My starting point is a maximally permissive default view according to which any collection of systems counts as a new system and composites inherit all facts that obtain relative to their constituents. Subsequently, I advance three main claims: First, that Adlam’s arguments in favour of a more restrictive approach are not compelling. Second, that even if they were, she is wrong to claim that a ‘tamed’ version of RQM with postulated links between perspectives is in a better position to support such a restrictive approach. And third, that the possibly most difficult aspect of the Combination Problem in fact pertains to the combination of quantum states and probabilities. While significant challenges for the permissive solution arise here, I argue that they are likely to arise for any plausible response to the Combination Problem. More tentatively, I propose a strategy to mitigate the difficulty based on the observer-dependence of relative quantum state assignments. Along the way, I address crucial foundational issues in Relational Quantum Mechanics, from cross-perspective communication to the link between relative facts and experiences to empirical adequacy.

Recent no-go theorems for absolute facts in single-world interpretations are widely considered the strongest arguments in favour of ‘quantum relativism’: interpretations according to which measurement results are observer-relative. In this paper, however, I show that relativist interpretations are themselves vulnerable to mathematically identical ‘revenge’ theorems, unless they assume a particularly radical form. To this end, a novel distinction between tame and feral varieties of quantum relativism is introduced, where a relativist interpretation counts as tame if and only if it postulates i) absolute facts about relative facts (absolute facts of second order) and ii) the possibility of communication across perspectives. While at first sight preferable to feral views, tame relativism turns out to be subject to revenge problems: arguments against absolute measurement outcomes can be modified and turned against absolute facts about which outcome a measurement has relative to a particular observer. This observation is developed in detail for the case of the ‘Local Friendliness’ EWF theorem. Moreover, it is shown to generalise to absolute facts about the facts that obtain relative to sequences of specified reference systems of arbitrary length. This suggests that only the most radical types of relativist interpretations have a hope of being motivated with recourse to EWF scenarios.

The idea that the dynamical properties of quantum systems are invariably relative to other systems has recently regained currency. Using Relational Quantum Mechanics (RQM) for a case study, this paper calls attention to a question that has been underappreciated in the debate about quantum relativism: the question of whether relativity iterates. Are there absolute facts about the properties one system possesses relative to a specified reference, or is this again a relative matter, and so on? It is argued that RQM (in its best-known form) is committed to what I call the Unrestricted Iteration Principle (UIP), and thus to an infinite regress of relativisations. This principle plays a crucial role in ensuring the communicability and coherence of interaction outcomes across observers. It is, however, shown to be incompatible with the widespread, conservative reading of RQM in terms of relations, instead necessitating the adoption of the more unorthodox notion of perspectival facts. I conclude with some reflections on the current state of play in perspectivist versions of RQM and quantum relativism more generally, underscoring both the need for further conceptual development and the importance of the iteration principle for an accurate cost-benefit analysis of such interpretations.