A Discrete Relational Framework Without Fundamental Time or Wave: Master Equation, Relational Book, and Quantum Measurement by Relational Selection

This preprint proposes a discrete relational framework indexed by the additive group (nZ,+), in which neither fundamental time, nor primitive dynamics, nor ontological randomness, nor a physical wave ontology is assumed. The global structure is described by a relational configuration (Ψ,R)(\Psi,R)(Ψ,R) constrained by a master equation of coherence, interpreted as an atemporal global constraint (no derivatives, no evolution law). The work introduces the notion of a “relational book”: events are assumed to be fully pre-inscribed in a negative branch of the index set, while the positive branch contains virtual events that become apparent only through a relational connection to their pre-inscribed symmetric counterparts. Within this setting, quantum measurement is reformulated as constrained relational selection/activation driven by the measurement device, with no wave collapse and no underlying wave propagation. The Born rule is reinterpreted as a relational compatibility density whose observed statistical regularities emerge from partial relational access to the global structure. The preprint also discusses interference “without waves” (e.g., double-slit scenarios) as a signature of global relational constraints, and includes a structural comparison with Everett (Many-Worlds), Bohmian mechanics, Relational Quantum Mechanics, and QBism.