Related papers: The Constructivist's Programme and the Problem of …
For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite…
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics,…
Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
The distinction between a theory's kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a…
This study addresses the often underestimated importance of physical dimensions and units in the formal reconstruction of physical theories, focusing on structuralist approaches that use the concept of ``species of structure" as a…
Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set…
We consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
The formulation of a relativistic dynamical problem as a system of Hamilton equations by respecting the principles of Relativity is a delicate task, because in their classical form the Hamilton equations require the use of a time…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
We present here an abstract notion of structure consisting of propositions and realizers (which we call PR-structures) giving rise to set based contravariant functors taking values in the category of sets endowed with binary relations. We…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
At present we have only the very successful but phenomenological Einstein geometrical modelling of the spacetime phenomenon. This geometrical model provides a `container' for other theories, in particular the quantum field theories. Here we…
Inertia has long been treated as the paradigm of natural motion. This paper challenges this identification through the lens of General Relativity. Drawing on Norton (2012)'s distinction between idealisation and approximation and analysing…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of general relativity, published in 1972, purports to build up the kinematical structure of that theory from only axioms which have indubitable empirical content. It is, therefore,…