The No Cloning Theorem versus the Second Law of Thermodynamics

Asher Peres' proof that a violation of No Cloning Theorem would imply a violation of the Second Law of Thermodynamics is shown not to take into account the algorithmic-information's contribution to the Thermodynamical Entropy of the semi-permeable membranes of Peres' engine.Comment: under submissio

Computability Superselection Rule and its physical explanation

Unfortunately, after an imprudent sumbission of the paper to the e-print archive, I discovered in it many serious mistakes. So I draw back it .Comment: I draw back the paper because it's wrong

A new kind of numbers, the Non-Dedekindian Numbers, and the extension to them of the notion of algorithmic randomness

A new number system, the set of the non-Dedekindian numbers, is introduced and characterized axiomatically. It is then proved that any hypercontinous hyperreal number system is strictly included in the set of the Non-Dedekindian Numbers. The notion of algorithmic-randomness is then extended to non-Dedekindian numbers. As a particular case, the notion of algorithmic randomness for the particular hyperreal number system of Non-Standard Analysis is explicitly analyzed.Comment: The third version differs from the second version in the correction of some lapse

The role of Topology in the classical geometric theories of gravitation

I withdraw the previous version of the paper since it contains conceptual and mathematical mistakes. I will soon replace it with a radically revised version

The mathematical role of (commutative and noncommutative) infinitesimal random walks over (commutative and noncommutative) riemannian manifolds in Quantum Physics

Anderson's nonstandard construction of brownian motion as an infinitesimal random walk on the euclidean line is generalized to an Hausdorff riemannian manifold. A nonstandard Feynman-Kac formula holding on such an Hausdorff riemannian manifold is derived. Indications are given on how these (radically elementary) results could allow to formulate a nonstandard version of Stochastic Mechanics (avoiding both the explicitly discussed bugs of Internal Set Theory as well as the controversial renormalization of the stochastic action). It is anyway remarked how this would contribute to hide the basic feature of Quantum Mechanics, i.e. the noncommutativity of the observables' algebra, whose structure is naturally captured in the language of Noncommutative Probability and Noncommutative Geometry. With this respect some preliminary consideration concerning the notion of infinitesimal quantum random walk on a noncommutative riemannian manifold, the notion obtained by the Sinha-Goswami's definition of quantum brownian motion on a noncommutative riemannian manifold replacing a continuous time interval with an hyperfinite time interval, is presented

The multihistory approach to the time-travel paradoxes of General Relativity: mathematical analysis of a toy model

With a mathematical eye to Matt Visser's multihistory approach to the time-travel-paradoxes of General Relativity, a non relativistic toy model is analyzed in order of characterizing the conditions in which, in such a toy model, causation occurs

The Aharonov-Anandan phase of a classical dynamical system seen mathematically as a quantum dynamical system

It is shown that the non-adiabatic Hannay's angle of an integrable non-degenerate classical hamiltonian dynamical system may be related to the Aharonov-Anandan phase it develops when it is looked mathematically as a quantum dynamical system.Comment: The hypothesis that M is compact and orientable is added in Theorem 2.

Classification of the automorphisms of the noncommutative torus among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones

Adopting the measure of quantum complexity, the quantum logical depth, previously introduced by the author the automorphisms of the noncommutative torus are classified among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones

There exist consistent temporal logics admitting changes of History

Introducing his Chronology Protection Conjecture Stephen Hawking said that it seems that there exists a Chronology Protection Agency making the Universe safe for historians. Without taking sides about such a conjecture we show that the Chronology Protection Agency is not necessary in order to make the Universe unsafe for historians but safe for logicians

Two spaces that already found their geometer in the thirties

Giorgio Parisi's recent speculations on the concept of continuous dimension (cond-mat/0207334) are compared with Von Neumann's serious work