Related papers: The Origin of a Metric
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
Quantum sensing is one of the arenas that exemplifies the superiority of quantum technologies over their classical counterparts. Such superiority, however, can be diminished due to unavoidable noise and decoherence of the probe. Thus,…
Let $K$ be a convex body in Euclidean space ${\mathbb R}^d$, and let a translation invariant, locally finite Borel measure on the space of hyperplanes in ${\mathbb R}^d$ be given. For $\delta\ge 0$, we consider the set of all points $x$ for…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…
Consider a set represented by an inequality. An interesting phenomenon which occurs in various settings in mathematics is that the interior of this set is the subset where strict inequality holds, the boundary is the subset where equality…
In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
Discussions surrounding the nature of the infinite in mathematics have been underway for two millennia. Mathematicians, philosophers, and theologians have all taken part. The basic question has been whether the infinite exists only in…
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…
Every physical measuring needs a finite, different from zero measurement time and provides information in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results…
The ether can "explain" certain questionable "quantum realities" in which single, isolated photons form a diffraction pattern in a two-slit apparatus; and, similarly, single, isolated electrons form a diffraction pattern in the equivalent…
We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we…