Conventionality and Relationality in Relativistic Space-Time

The Journal of Philosophy, 1996

Philosophy of Science

We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this underdetermination occurs. Three of the five formulations of conventionalism will be found to fail. Two are found to open up new interesting problems for researchers in the foundations of general relativity. In all five cases, our analysis explores the interplay between geometric identities, symmetry, conformal structure, and the dynamical content of physical theories with the conventionalism dialectic deployed as a tool of explication, clarification, and exploration.

2017

The text proposes some directions of research, as based on previous works made by the author. Our purpose is to discuss the contribution of general relativity to the epistemology of space and time, in the context of a relational, and not substantial, rationality. General relativity brings us the important idea (of a relational nature) that space and time do not constitute a scene external to phenomena, but that, on the contrary, the phenomena themselves, in the first place the phenomenon of gravitation, are responsible for assessing the corresponding variables. However, this contribution does not make us progress on the "mystery" of time, that remains conceptually separated from space, even though, since the relativity theory, the values of space and time variables are related. Encouraged by general relativity, we must go further and express more strongly the link between the concepts of space and time, and their identity of substance. The relational approach must extend t...

International Journal of Modern Physics D, 2011

Starting from scientific ontology, we expose a materialistic relational theory of space-time, that carries out the program initiated by Leibniz, and provides a protophysical basis consistent with any rigorous formulation of General Relativity. Space-time is constructed from general concepts which are common to any consistent scientific theory and they are interpreted as emergent properties of the greatest assembly of things, namely, the world. * Facultad de Ciencias Astronómicas y Geofísicas -Universidad Nacional de La Plata, ARGENTINA.

Erkenntnis, 1995

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to knowing subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing, but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of successives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemannian space-time.

2011

1. Some remarks on Weyl’s Principle 2. The two approaches at the foundations of standard models 3. Deductive and constructive axiomatizations 4. Constructive axiomatization and relationism 5. Space and substratum in de Sitter models

The relativists have not understood the geometry of Einstein's gravitational field. They have failed to realise that the geometrical structure of spacetime manifests in the geometrical relations between the components of the metric tensor. Consequently, they have foisted upon spacetime quantities and geometrical relations which do not belong to it, producing thereby, grotesque objects, not due to Nature, but instead, to faulty thinking. The correct geometry and its consequences are described herein.

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemmanian space-time.