Operational Approach to the Topological Structure of the Physical Space

Abstract

axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and topology in a fully operational manner. Curiously enough, primitive concepts such as points, spaces, straight lines, planes are all defined within our formalism. Our construction breaks down with the usual literature, as our axioms have deep connection with nature. Besides that, we hope this operational approach could also be of pedagogical interest.

A Categorical View on the Principle of Relativity

“…One way of seeing this is the fact that the set of accessible events for each frame of reference is different. Moreover, the construction of the physical space we did in previous works seems to also point in this direction [11,18].…”

“…After this brief intro concerning Operationalism, let us review how one can build the notion of a frame of reference, and together with it, the one of space. All the details can be found in [11]. The first observation is that there exists around us bodies whose distance between any two arbitrary and distinct points does not change with time.…”

“…Hence, we can conclude that change of references is only attainable when the two are connected by a boost. This inference is even clearer when we adopt an operational approach to construct underlying notions, such as the central one of a frame of reference [11], which shall be revised in the next Section.…”