Role and Scope of Dynamical Invariants in Physical Problems: Interpretation and Applications

J. R. Ray

Isaac Wilhelm

Abstract I propose an account of probability in the Everett interpretation of quantum mechanics. According to the account, probabilities are objective chances of centered propositions. As I show, the account solves a number of problems concerning the role of probability in the Everett interpretation. It also challenges an implicit assumption, concerning the aim and scope of fundamental physical theories, that is made throughout the philosophy of physics literature.

Erik Axelkrans

The measurement problem is commonly taken to indicate a fundamental conflict betweenthe linear, unitary dynamics of quantum mechanics and the definite outcomes observed inmeasurement processes. Standard responses typically resolve this tension by modifying thedynamics, enriching the ontology, or revising the interpretation of the quantum state.In this paper, we analyze the measurement problem from a projection-based perspectivein which quantum evolution and measurement outcomes are associated with ontologicallydistinct effective descriptions defined by incompatible invariance requirements. Within thisframework, quantum mechanics is characterized by unitary invariance and coherent superpo-sition, whereas measurement records are defined by definiteness, stability, and reproducibil-ity. The measurement problem arises when these distinct projection structures are implicitlyidentified or required to coexist within a single effective description.By analyzing measurement as a transition between such projections, we show that theappearance of wavefunction collapse does not require a physical dynamical process. Instead,collapse emerges as a necessary structural consequence of projecting a quantum descriptiononto a measurement domain that enforces different invariance constraints. This accountpreserves the formal structure and empirical success of quantum mechanics while motivatinga restrained ontological reading of its elements.More broadly, the analysis situates the measurement problem within a general patternin which foundational paradoxes arise at the boundaries between effective descriptions. Inthis sense, the resolution proposed here does not introduce new physics, but clarifies theontological scope and limits of quantum-mechanical description.

Jan von Plato

Eberhard Zeidler

Sebastian Fortin

Decoherence has acquired a central role in the foundations of quantum mechanics and in various debates in philosophy of physics by providing an explanation for the suppression of interference and the emergence of quasiclassical behavior in open systems. However, it is sometimes attributed a broader philosophical scope than is effectively warranted by the formalism, particularly with regard to the measurement problem and the classical limit. This paper critically examines such scope through a simplified reconstruction of the standard formalism of environment-induced decoherence. It is argued that the decohered state corresponds to an improper mixture and, therefore, does not constitute an effective replacement for collapse nor solve the measurement problem. In addition, an operational interpretation in terms of “as if” and the preferred basis problem are analyzed, revealing conceptual tensions associated with the identification of robust states. The paper concludes with a call for prudence regarding the philosophical use of decoherence in foundational discussions.