Related papers: Is time the real line?

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

Existence of arrow of time in our world may be easy explained if time has multifractal nature. The interpretation of nature of time arrow is made on the base of multifractal theory of time and space presented at works…

Various diagnostics of the emergence of an arrow of time in the bulk description of a holographic theory have been proposed, including the decay of some real time correlation functions and the appearance of type III$_1$ von Neumann algebras…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the…

It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…

We find ourselves in an extended era of entropy production. Unlike most other observations, the arrow of time is usually regarded as a constraint on initial conditions. I argue, however, that it primarily constrains the vacuum structure of…

The thermodynamic arrow-of-time problem is thought to be resolved by the observation that our universe initially was---and still is---far from equilibrium. The psychological arrow-of-time problem is often attributed the same resolution, but…

Scientific discussions of the arrow of time often get quite confusing due to highly complex systems they deal with. Popular literature then often coveys messages that tend to get lost in translation. The purpose of this note is to demystify…

This paper investigates the influence of extra dimensions on the nature of the arrow of time. We demonstrate that the observed arrow of time can be explained by the monotonic growth of the multidimensional manifold's volume. Unlike…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose…

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding…

Since the early days of the theory of electromagnetism and of gravity the idea of space, then space-time, as a sort of physical continuum hovered the scientific community. Actually general relativity shows the strong similarity that exists…

The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical systems seem to evolve in paths of…

As repeatedly emphasized by Einstein our knowledge of the structure of space and time is based entirely on inferences from observations of physical objects and processes. At the most fundamental level these objects and processes are…

Time is one of those issues about which many thinkers and scientists have tried to pronounce their finest thoughts, but the discourse about time has remained vague and often inconsistent. In this paper we put forward a conceptual framework…

The paper puts forward a conceptual framework in which the phenomenon of time can be presented and discussed in a proper way. We argue that change is ontologically and epistemologically a more basic phenomenon than time. Time is an abstract…

The continuum has been one of the most controversial topics in mathematics since the time of the Greeks. Some mathematicians, such as Euclid and Cantor, held the position that a line is composed of points, while others, like Aristotle, Weyl…

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…