Related papers: A Note on Fuzzy Space And Topology
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…
The Hamiltonian defines the dynamical properties of the universe. Evidence from particle physics shows that there is a different version of the Hamiltonian for each direction of time. As there is no physical basis for the universe to be…
This lecture provides us with Newtonian approaches for the interpretation of two puzzling cosmological observations that are still discussed subject : a bulk flow and a foam like structure in the distribution of galaxies. For the first one,…
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly…
Shortly the vacuum component of the Universe from the geometry point of view and from the point of view of the standard model of physics of elementary particles is discussed. Some arguments are given to the calculated value of the…
In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore…
A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the…
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…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
We show that the previously introduced concept of distance on statistical spaces leads to a straightforward definition of differential entropy on these statistical spaces. These spaces are characterized by the fact that their points can…
The widely accepted description of the present cosmic acceleration and the neutrino oscillations in terms of a cosmological constant and neutrino masses, respectively, seems conceptually not very satisfactory. From a phenomenological…
Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly…
In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…
Revolutionary advances in both theory and technology have launched cosmology into its most exciting period of discovery yet. Unanticipated components of the universe have been identified, promising ideas for understanding the basic features…
We consider the incompressible two-dimensional Euler equation in the plane in the case when its initial vorticity is the characteristic function of a bounded open set. We show that the travel distance grows linearly for most of fluid…
What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making…
One of the greatest achievements of twentieth century physics is the discovery of a very close link between the microcosm and the macrocosm. This follows from the two basic principles of quantum mechanics and relativity, the uncertainty…