Related papers: Destructuring Physics: A functional derivation of …
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
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…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
The central idea of this work is the concept of prespace, a hypothetical structure that is postulated to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the implications…
We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…
The time separation function (or Lorentzian distance function) is a fundamental object used in Lorentzian geometry. For smooth spacetimes it is known to be lower semicontinuous, and in fact, continuous for globally hyperbolic spacetimes.…
The research effort reported in this paper is directed, in a broad sense, towards understanding the small-scale structure of spacetime. The fundamental question that guides our discussion is ``what is the physical content of spacetime…
On a scientific meta-level, it is discussed how an overall understanding of the physical universe can be built on the basis of well-proven theories, observations, and recent experiments. In the light of almost a century of struggle to make…
Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…