Related papers: Zeno's Paradoxes. A Cardinal Problem 1. On Zenonia…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed. The first part of the paper investigates a periodicity…
Miller's 1937 splitting theorem was proved for pairs of cardinals $(\n,\rho)$ in which $n$ is finite and $\rho$ is infinite. An extension of Miller's theorem is proved here in ZFC for pairs of cardinals $(\nu,\rho)$ in which $\nu$ is…
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of…
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…
There is no single canonical polynomial-time version of the Axiom of Choice (AC); several statements of AC that are equivalent in Zermelo-Fraenkel (ZF) set theory are already inequivalent from a constructive point of view, and are similarly…
The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
No quantitative theory describing all physical phenomena can be made if any arbitrary standard spacetime structure is assumed. This statement is a consequence of transforming the Peano arithmetic axioms into sentences with a physical…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
We study the measurement process by treating classical detectors entirely quantum mechanically. As a generic model we use a point-contact detector coupled to an electron in a quantum dot and tunneling into the continuum. Transition to the…
This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. Deviations from classical trajectories are calculated and evolution of the…
Wolfram's Principle of Computational Equivalence (PCE) implies that universal complexity abounds in nature. This paper comprises three sections. In the first section we consider the question why there are so many universal phenomena around.…
In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
This article proves the Riemann hypothesis, which states that all non-trivial zeros of the zeta function have a real part equal to 1/2. We inspect in detail the integral form of the (symmetrized) completed zeta function, which is a product…
Zonotopes are studied from the point of view of central symmetry and how volumes of facets and the angles between them determine a zonotope uniquely. New proofs are given for theorems of Shephard and McMullen characterizing a zonotope by…
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our…
In the celebrated Theaetetus 147d3-e1 passage Theodorus is giving a lesson to Theaetetus and his companion, proving certain quadratic incommensurabilities. The dominant view on this passage, expressed independently by H. Cherniss and M.…
Gravitation has posed a puzzle and a problem for many decades. Attempts to unify it with other fundamental interactions have failed. These problems and puzzles have been underscored by the likes of Witten and Weinberg. We survey this and…