Related papers: A Physics of Bounded Metric Spaces
After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the Deformed Minkowski space lead…
Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
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…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering…
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…
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…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces. Our new definition based only on distance properties allows us also to deal with discrete spaces.…
A gravity theory without masses can be constructed in Minkowski spaces using a geometric Minkowski potential. The related affine spacelike spheres can be seen as the regions of the Minkowski spacelike vectors characterized by a constant…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…
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…
Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…
The traditional Minkowski distances are induced by the corresponding Minkowski norms in real-valued vector spaces. In this work, we propose novel statistical symmetric distances based on the Minkowski's inequality for probability densities…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum measurements can lead to an effective…