Toward an Axiomatic Pregeometry of Space-Time

2006

The sixteen papers collected in this volume are expanded and revised versions of talks delivered at the Second International Conference on the Ontology of Spacetime, organized by the International Society for the Advanced Study of Spacetime (John Earman, President) at Concordia University (Montreal) from 9 to 11 June 2006. Most chapters are devoted to subjects directly relating to the ontology of spacetime. This book starts with four papers that discuss the ontological status of spacetime and the processes occurring in it from a point of view that is first of all conceptual and philosophical. The focus then slightly shifts in the five papers that follow, to considerations more directly involving technical considerations from relativity theory. After this, Time, Becoming and Change take centre stage in the next five papers. This book ends with two excursions into relatively uncharted territory: a consideration of the status of Kaluza-Klein theory, and an investigation of possible rel...

2009

Modern physics, via the standard model with Higgs mechanism and string theory for example, has supplied ether-like models and emergent general relativity scenarios that substantially weaken the usual defense of orthodox relativity and abstract, relational space-time in general. Over a dozen arguments in support of relativism against space-substances are discussed. It is not known whether perceived space-time is fundamental or due to a condensed state or string theoretical membrane. Emergent relativity indicates perhaps a whole tower of more fundamental space-times. Whether space is best described as a thing, an emergent phenomenon, or instead Kant's necessary, a priori pre-condition of the possibility of all phenomena, depends on which space-time is under consideration. Nevertheless, space-time is *fundamentally* abstract relational. This is supported by throughout acknowledging as well as illustrating the value of space-substance models, yet still keeping firm in refusing them on the deepest level. The gist is that even while refusing, physics and philosophy gain more from ether concepts than from plainly refusing them.

Journal of Philosophy, 1996

If two different authors use the words "red," "hard," or "disappointed," no one doubts that they mean approximately the same thing.... But in the case of words such as "place" or "space"...there exists a far-reaching uncertainty of interpretation.-Albert Einstein' T Nhere is supposed to be a problem concerning the metaphysics of space and time (or space-time), which, following Lawrence Sklar,2 goes by the name the substantivalist-relationist controversy. What is presumably at stake is whether we should be realists in some suitably robust sense about space and time (space-time), or whether no such entities exist over and above the objects and events of the material world. Insofar as this question is intended to have anything to do with physics, I shall argue that it is no longer a meaningful one. In the course of its development, physical theory simply lost touch with the categories necessary for the original formulation of the problem. One might, of course, seek judicious criteria for projecting old categories onto new terrain. Part of my project is to explain why, given the relevant historical developments, one should be skeptical that there is any such natural or preferred projection in this case. The other part is to make evident that the current controversy reduces to verbal disputes occasioned by arbitrary preference for one manner of projection over another. I. AN EINSTEIN "PUZZLE" * Work on this was supported by National Science Foundation grant # SBR-9310561. Frank D6ring was most kind to proof the translations from German. I would also like to thank Peter Achinstein and Steve Gimbel for helpful comments on an earlier draft. I am grateful to the Albert Einstein Archives at the Hebrew University ofJerusalem for granting permission to quote from the Einstein papers. ' "Forward," to Max Jammer, Concepts of Space (New York: Dover, 1993, 3rd ed.), p. xiv. 2 Space, Time, and Spacetime (Berkeley: California UP, 1974).

2006

In the aftermath of the rediscovery of Einstein’s hole argument by Earman and Norton (1987), we hear that the ontological relational/substantival debate over the status of spacetime seems to have reached stable grounds. Despite Einstein’s early intention to cast GR’s spacetime as a relational entity a la Leibniz-Mach, most philosophers of science feel comfortable with the now standard sophisticated substantivalist (SS) account of spacetime. Furthermore, most philosophers share the impression that although relational accounts of certain highly restricted models of GR are viable, at a deep down level, they require substantival spacetime structures. SS claims that although manifold spacetime points do not enjoy the sort of robust existence provided by primitive identity, it is still natural to be realistic about the existence of spacetime as an independent entity in its own right. It is argued that since the bare manifold lacks the basic spacetime structures –such as geometry and inert...

2001

Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded ''geometric judgments'' from certainty and contributed, by this, to isolate the foundation of Mathematics from other disciplines. After the success of the logical approach, it is time to broaden our foundational tools and reconstruct, also in that respect, the interactions with other sciences. The way space (and time) organize knowledge is a cross-disciplinary issue that will be briefly examined in Mathematical Physics, Computer Science and Biology. This programmatic paper focuses on an epistemological approach to foundations, at the core of which is the analysis of the ''knowledge process'', as a constitutive path from cognitive experiences to mathematical concepts and structures.

The intention of this paper is that of proposing a method of approaching the problem of spacetime ontology that is, at least at the beginning, independent from the previous ones concerning the "Hole Argument": to propose an approach based on the possibility of describing the gravitational field at three distinct levels. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now no longer "visible" in terms of its autonomous degrees of freedom, but it is analyzable through three levels: a first one, called the potential level, a second one, known as the connections level and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part" of the metric field. It is then shown how to this last level it is possible to establish a "primitive level of objectivity" of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor.

2011

My application is for two mutually reinforcing projects. The first is to show that the structure of space essentially determines the dynamics of space, which in turn determines the physcial properties of time. This will be done by completing my program for the relational derivation of classical dynamics from the fewest possible axioms. In particular, only scale-invariant (angledetermining) structure of space is presupposed. Much of the structure of spacetime usually taken as fundamental is thereby shown to be emergent.

Handbook of the Mathematics of the Arts and Sciences, 2021

Our relation to phenomenal space has been largely disregarded, and with good motivations, in the prevailing foundational analysis of Mathematics. The collapse of Euclidean certitudes, more than a century ago, excluded ''geometric judgments'' from certainty and contributed, by this, to isolate the foundation of Mathematics from other disciplines. After the success of the logical approach, it is time to broaden our foundational tools and reconstruct, also in that respect, the interactions with other sciences. The way space (and time) organize knowledge is a cross-disciplinary issue that will be briefly examined in Mathematical Physics, Computer Science and Biology. This programmatic paper focuses on an epistemological approach to foundations, at the core of which is the analysis of the ''knowledge process'', as a constitutive path from cognitive experiences to mathematical concepts and structures.

Space and Time, 2013

In the paper the Space – Time problem is considered as it is seen in the informational conception (“the Information as Absolute conception”) comparing with a number of existent physical and philosophical approaches. Since the conception is rigorously grounded (for the conception the existence, the truth, the self-consistence and the completeness of are proven), the notions “Space” and “Time” – which cannot be deduced from physics itself since are Meta-physical notions – obtain reasonable elucidation that is presented in the paper. Key words: space, time, Matter, special relativity, informational model, arrow of time, time flow PACC: 0330, 0455, 0170 PACS : 01.70.+w, 03.30.+p, 04.80.Cc