Related papers: Extracting a Paradox by the Roots
Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does…
The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
The dynamics of a quantum system undergoing frequent measurements (quantum Zeno effect) is investigated. Using asymptotic analysis, the system is found to evolve unitarily in a proper subspace of the total Hilbert space. For spatial…
The evolution of a quantum system is supposed to be impeded by measurement of an involved observable. This effect has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum…
Although Bolzano's concept of the continuum has gradually evolved, the basis remained the same: the continuum as an infinite class of points arranged in such a way that the so-called \emph{Bolzano completeness} holds. Bolzano realized over…
The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
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…
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…
The inconsistencies involved in the foundation of set theory were invariably caused by infinity and self-reference; and only with the opportune axiomatic restrictions could them be obviated. Throughout history, both concepts have proved to…
The mechanism responsible for the emergence of chaotic behavior has been identified analytically within a class of three-dimensional dynamical systems which generalize the well-known E.N. Lorenz 1963 system. The dynamics in the phase space…