Abstract
We build a model of time starting from the primitive concept of base-setB≡{α i |i∈I} of all physical systems, whose elements are called pre-particles α i . We assume thatB is a denumerably infinite set. Particles or bodies are represented by the subsets of the power setP (B) of the base-setB. A physical system is represented by a set of particles. We introduce the distinction between evolving and non-evolving particles, and assume that the former are represented by those subsets ofP (B) which are chains. Making use of the above concepts we define the state of a particle and the indicator of the state of a particle with respect to a given state of the same or another particle. Then we define in terms of indicators the concepts of instant, time-set, degenerate time-set, event, and clock. For the time related to a given clock one has a set in which the order relation is is in general not connected. Some theorems are proved.
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Garcia-Sucre, M. Time in a simple model of a physical system. Int J Theor Phys 12, 25–34 (1975). https://doi.org/10.1007/BF01884107
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DOI: https://doi.org/10.1007/BF01884107