Related papers: Space as relation
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…
Understanding the emergence of a tangible 4-dimensional space-time from a quantum theory of gravity promises to be a tremendously difficult task. This article makes the case that this task may not have to be carried. Space-time as we know…
While it remains the staple of virtually all cosmological teaching, the concept of expanding space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the…
I show that, by the same criteria that led to Galilean and Special Relativity and gauge symmetries, there is no way to identify a unique set of observables that give the structure of space or spacetime. In some sense, space is lost in the…
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…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations,…
In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
In this contribution to FQXi's essay contest 2018, I suggest that it is sometimes a step forward to reverse our intuition on "what is fundamental", a move that is somewhat reminiscent of the idea of noncommutative geometry. I argue that…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
Rovelli's relational interpretation of quantum mechanics tells us that the description of a system in the formalism of quantum mechanics is not an absolute, but it is relative to the observer itself. The interpretation goes further and…
It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its…
Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts…