Related papers: The Origin of a Metric
This paper has been withdrawn by the author. In this short paper I present a new approach to the problem of measurement, based on the difference between language (reality) and meta-language (meta-reality). This way, it will be shown as the…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
The classical Cantor's intersection theorem states that in a complete metric space $X$, intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter approaches zero, has exactly one point. In this article, we…
The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation,…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…
The existence of various physical phenomena stems from the concept called asymptotic emergence, that is, they seem to be exclusively reserved for certain limiting theories. Important examples are spontaneous symmetry breaking (SSB) and…
The evolution of the luminosity distance in a contracting universe is studied. It is shown that for quite a lot of natural dynamical evolutions, its behavior is far from trivial and its value can even decrease with an increasing time…
The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…
We study Borel systems and continuous systems of measures, with a focus on mapping properties: compositions, liftings, fibred products and disintegration. Parts of the theory we develop can be derived from known work in the literature, and…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Process Physics models reality as self-organising relational or semantic information using a self-referentially limited neural network model. This generalises the traditional non-process syntactical modelling of reality by taking account of…
In this paper, we summarize the development of the concept of emergence in physical science and propose key concepts of emergence in the form of conjectures. Our conjectures are threefold: I. A system having a broken-symmetry in membership…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
We study properties of truncations in the dual and intertwining process in the monotone case. The main properties are stated for the time-reversed process and the time of absorption of the truncated intertwining process.
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising…
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized…
Let $ (X,d) $ be a metric space. We study a metric $ d_0 $ on $ X $ naturally derived from $ d $. If $ (X,d) $ is complete and locally compact, or if it is complete and $ (d_0)_0=d_0 $, then $ d_0 $ coincides with the length metric induced…