'Particles' and 'waves' as understood by temporal concept analysis

Abstract

A qualitative mathematical framework for a granular representation of relational information about general objects, as for examples particles, waves, persons, families, institutions or other systems in discrete or continuous "space-time" is introduced. That leads to a common description of particles and waves in physics, such that the intuitive physical notion of "wave packet" can be captured by the mathematical notion of a general object or a packet in a spatio-temporal Conceptual Semantic System. In these systems particles and waves are defined as special packets. It is proved, that "classical objects" and "classical waves" can be represented as, respectively, particles and waves in spatio-temporal Conceptual Semantic Systems. The underlying mathematical framework is Formal Concept Analysis and its subdiscipline Temporal Concept Analysis. That allows for describing continuously fine or arbitrarily coarse granularity in the same conceptual framework. The central idea for a "symmetric" description of objects, space, and time is the introduction of "instances" representing information units of observations, connecting the granules for objects, space, and time. © Springer-Verlag 2004.