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Non-Uniqueness of the Q-based Interpretation of Quantum Mechanics

Benjamin H. Feintzeig, William DeWitt

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

We consider Friederich’s recent Q-based interpretation of quantum mechanics. We argue that the interpretation is incomplete by providing distinct microdynamical models that give rise to the same bulk evolution of the Q-function. Since there are apparent foundational differences between the ostensibly distinct interpretations suggested by the different possible microdynamics, Friederich must either commit to a single microdynamics, or else provide some reason to consider the distinct microdynamical models as physically equivalent.

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We consider Friederich’s recent Q-based interpretation of quantum mechanics. We argue that the interpretation is incomplete by providing distinct microdynamical models that give rise to the same bulk evolution of the Q-function. Since there are apparent foundational differences between the ostensibly distinct interpretations suggested by the different possible microdynamics, Friederich must either commit to a single microdynamics, or else provide some reason to consider the distinct microdynamical models as physically equivalent.
Richard Healey and Simon Friederich have each advocated a pragmatist interpretation of quantum mechanics as a way to dissolve its foundational problems. The idea is that if the way quantum claims are used are concentrated on, the foundational problems of quantum mechanics cannot be formulated, and so do not require solution. Their central contention is that the content of quantum claims differs from the content of non-quantum claims, in that the former is prescriptive whereas the latter is descriptive. Healey also argues that claims about non-decoherent systems are largely devoid of content. Chapter 9 considers various objections to these claims, noting in particular the ways in which the application of pragmatism to quantum mechanics differs from previous examples of pragmatist ‘therapy.’ It concludes that a pragmatist dissolution of the foundational difficulties of quantum mechanics is promising, but requires fairly radical changes to our understanding of the content of propositions and the extent of physical explanation.
It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.
The article analyzes the principal interpretations of quantum mechanics from the standpoint of an original conception of informational realism. It is shown that these interpretations can be unified within an informational ontology in which fundamental status is accorded to informational invariants of quantum constraints that are common to all empirically equivalent interpretations of quantum mechanics. A distinction is proposed between two informational layers: epistemic information (measurement data and the updating of knowledge on their basis) and ontic information (invariant structures and constraints). The first layer varies across interpretations, whereas the second is preserved, which explains their experimental equivalence. The proposed informational ontology is compared with other realist approaches, and its advantages are formulated and argued for. It is shown that all the interpretations considered, despite often incompatible philosophical foundations and worldviews, are equally dependent on a certain set of informational invariants, which prove to be primary with respect to any particular interpretation. This can be explained either by the fact that a unified descriptive model of real physical processes at the quantum level is still unknown, or – as argued in the present article – by the claim that the fundamental level consists of informational constraints, and that different descriptions are equivalent, with their differences explained by distinct perspectives. The novelty and contribution of the article consist in proposing an operational definition of a falsifiable class of invariants and constraints on operations that are stable under changes of perspective; providing a unified translational vocabulary for interpretations in terms of the two informational layers; showing that their empirical equivalence is explained by the preservation of the same ontic layer; and formulating a criterion for distinguishing interpretations from alternative theories. Taken together, this allows informational ontology to be regarded as a meta-position with respect to these interpretations.
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationally-defined theories that contain "nonlinear boxes" and show that operational verifiability without superluminal signaling implies a split in the equivalence classes of preparation procedures. We conclude that any theory satisfying the above requirements is (a) inconsistent unless it contains distinct representations for the two different kinds of preparations and (b) incomplete unless it also contains a rule for uniquely distinguishing them at the operational level. We refer to this as the preparation problem for nonlinear theories. In addition to its foundational implications, this work shows that, in the presence of nonlinear quantum evolution, the security of quantum cryptography and the existence of other exotic effects remain open questions.