Abstract
Abstract:
Ontologically, classical measurements are understood as revelatory of facts representing the state of a physical system, such that these facts (evaluated observables) always have well-defined values whether measured or not. Quantum measurements, by contrast, are understood as generative of novel facts representing novel states of a physical system. Furthermore, unlike classical measurements, the actualization of a novel measurement outcome event representing the state of a quantum system can be predicted only probabilistically, and only relative to a particular Boolean measurement context of a selected observable—a local context whereby the universe, represented by a global state vector, is decomposed into “system,” “measuring apparatus,” and “environment” with their respective state vectors. The probability valuations can be affirmed only retrodictively, after a measured result has been registered by the corresponding measuring apparatus. Given these aspects of quantum mechanical measurement, it follows that: [1] If every measurement outcome event is both contextual and novel, as posited in both Whiteheadian and relational realist philosophy; and [2] one presupposes that the asymmetrical order of causal relation and the asymmetrical order of logical implication are always aligned and jointly operative in not only physics but every conceivable instantiation of human reason; then any ontological interpretation of quantum mechanics requires a framework of logical causality by which local measurement outcome events (i.e., ‘facts’) can be coherently and consistently related globally. Relational realism, as a Whiteheadian speculative philosophical program, posits precisely such a framework—a mereotopological structure, formalized mathematically via a category-sheaf theory and Grothendieck topology, by which Boolean-contextualized facts are internally related in quantum mechanics.