Related papers: The Origin of a Metric
In applications of mechanics, including quantum mechanics, we often consider complex systems, where complete solutions of the underlying "fundamental" equations is both impractical and unnecessary to describe appropriate observations…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
The existence of a median-type ternary operation on a metric space is known to have a number of implications for the geometry of the space. For such operations, if two of the three arguments coincide, they also coincide with the output of…
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The truncated moment problem consists of determining whether a given finitedimensional vector of real numbers y is obtained by integrating a basis of the vector space of polynomials of bounded degree with respect to a non-negative measure…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
A generalized view of Duality is offered as a bridge between physical sciences and the more abstract philosophical dimensions bordering on mysticism. To that end several examples of duality are first cited from from conventional physics…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
The perception-related origins of physical measures and standards are considered within the framework of the general observer theory. The impact of observer characteristics on the development of observer-centric physics, physical concepts…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
We discuss the applicability of the programme of decoherence -- emergence of approximate classical behaviour through interaction with the environment -- to cases where it was suggested that the presence of symmetries would lead to exact…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
In this note we reconsider linearised metric perturbations in the one-brane Randall-Sundrum Model. We present a simple formalism to describe metric perturbations caused by matter perturbations on the brane and remedy some misconceptions…
We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions -- allowing…
Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…