Related papers: The continuum problem and reality
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
The off-site continuums are proposed for the cosmological models of the galaxies and the Universe. It is shown that many visual properties of galaxies and the Universe may be described on frames of the off-site continuums methodology. In…
The hypothesis of quantum self-interference is not directly observable, but has at least three necessary implications. First, a quantum entity must have no less than two open paths. Second, the size of the interval between any two…
In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to…
According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of…
Quantum coherence is a fundamental characteristic to distinguish quantum systems from their classical counterparts. Though quantum coherence persists in isolated non-interacting systems, interactions inevitably lead to decoherence, which is…
It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations,…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer's consciousness into quantum theory of measurements. Most naturally this is achieved in the…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD.…
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…
The aim of this work is to show how Einstein's quantum hypothesis leads immediately and necessarily to a departure from classical mechanics. First we note that the classical description and predictions are in terms of idealized measurements…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…