A Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church's Undecidability and Godel's Incompleteness

In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.Comment: 13 pages, no figure

There is Neither Classical Bug with a Superluminal Shadow Nor Quantum Absolute Collapse Nor (Subquantum) Superluminal Hidden Variable

In this work we analyse critically Griffiths's example of the classical superluminal motion of a bug shadow. Griffiths considers that this example is conceptually very close to quantum nonlocality or superluminality,i.e. quantum breaking of the famous Bell inequality. Or, generally, he suggests implicitly an absolute asymmetric duality (subluminality vs. superluminality) principle in any fundamental physical theory.It, he hopes, can be used for a natural interpretation of the quantum mechanics too. But we explain that such Griffiths's interpretation retires implicitly but significantly from usual, Copenhagen interpretation of the standard quantum mechanical formalism. Within Copenhagen interpretation basic complementarity principle represents, in fact, a dynamical symmetry principle (including its spontaneous breaking, i.e. effective hiding by measurement). Similarly, in other fundamental physical theories instead of Griffiths's absolute asymmetric duality principle there is a dynamical symmetry (including its spontaneous breaking, i.e. effective hiding in some of these theories) principle. Finally, we show that Griffiths's example of the bug shadow superluminal motion is definitely incorrect (it sharply contradicts the remarkable Roemer's determination of the speed of light by coming late of Jupiter's first moon shadow).Comment: 15 pages, no figure

CEPTC_{E}PT Symmetry of the Simple Ecological Dynamical Equations

It is shown that all simple ecological, i.e. population dynamical equations (unlimited exponential population growth (or decrease) dynamics, logistic or Verhulst equation, usual and generalized Lotka-Volterra equations) hold a symmetry, called $C_{E}PT$ symmetry. Namely, all simple ecological dynamical equations are invariant (symmetric) in respect to successive application of the time reversal transformation - $T$, space coordinates reversal or parity transformation - $P$, and predator-prey reversal transformation - $C_{E}$ that changes preys in the predators or pure (healthy) in the impure (fatal) environment, and vice versa. It is deeply conceptually analogous to remarkable $CPT$ symmetry of the fundamental physical dynamical equations. Further, it is shown that by more accurate, "microscopic" analysis, given $C_{E}PT$ symmetry becomes explicitly broken.Comment: 11 pages, no figure

Population Dynamics of Children and Adolescents without Problematic Behavior

In this work we suggest a simple mathematical model for the dynamics of the population of children and adolescents without problematic behavior (criminal activities etc.). This model represents a typical population growth equation but with time dependent (linearly decreasing) population growth coefficient. Given equation admits definition of the half-life time of the non-problematic children behavior as well as a criterion for estimation of the social regulation of the children behavior.Comment: two pages, no figure

A Simple Solution of the Lotka-Volterra Equations

In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this solution, exponents of the corresponding Lotka-Volterra variables have simple, time polynomial form. When approximation order tends to infinity obtained approximate solution converges toward exact solution in some finite time interval.Comment: 6 pages, no figure

From Quantum To Classical Dynamics: A Landau Continuous Phase Transition With Spontaneous Superposition Breaking

Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein that there is a Landau continuous phase transition from the exact quantum dynamics to the effectively classical one, occurring via spontaneous superposition breaking (effective hiding), as a special case of the corresponding general formalism (Bernstein). Critical values of the order parameters for this transition are determined by Heisenberg's indeterminacy relations, change continuously, and are in excellent agreement with the recent and remarkable experiments with Bose condensation. It is also shown that such a phase transition can sucessfully model self-collapse (self-decoherence), as an effective classical phenomenon, on the measurement device. This then induces a relative collapse (relative decoherence) as an effective quantum phenomenon on the measured quantum object by measurement. We demonstrate this (including the case of Bose-Einstein condensation) in the well-known cases of the Stern-Gerlach spin measurement, Bell's inequality and the recently discussed quantum superposition on a mirror a la Marshall et al. These results provide for a proof that quantum mechanics, in distinction to all absolute collapse and hidden-variable theories, is local and objective. There now appear no insuperable obstacles to solving the open problems in quantum theory of measurement and foundation of quantum mechanics, and strictly within the standard quantum-mechanical formalism. Simply put, quantum mechanics is a field theory over the Hilbert space, the classical mechanics characteristics of which emerge through spontaneous superposition breaking.Comment: 32 page

The Simplest Determination of the Thermodynamical Characteristics of Schwarzschild, Kerr Andreissner-Nordstrom Black Hole

In this work, generalizing our previous results, we determine in an original and the simplest way three most important thermodynamical characteristics (Bekenstein-Hawking entropy, Bekenstein quantization of the entropy or (outer) horizon surface area and Hawking temperature) of Schwarzschild, Kerr and Reissner-Nordstrom black hole. We start physically by assumption that circumference of black hole (outer) horizon holds the natural (integer) number of corresponding reduced Compton's wave length and use mathematically only simple algebraic equations. (It is conceptually similar to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie relation.)Comment: 5 pages, no figure

A "Quasi-Rapid" Extinction Population Dynamics and Mammoths Overkill

In this work we suggest and consider an original, simple mathematical model of a "quasi-rapid" extinction population dynamics. It describes a decrease and final extinction of the population of one prey species by a "quasi-rapid" interaction with one predator species with increasing population. This "quasi-rapid" interaction means ecologically that prey species behaves practically quite passively (since there is no time for any reaction, i.e. defense), like an appropriate environment, in respect to "quasi-rapid" activity of the predator species that can have different "quasi-rapid" hunting abilities. Mathematically, our model is based on a non-Lotka-Volterraian system of two differential equations of the first order, first of which is linear while second, depending of a parameter that characterizes hunting ability is nonlinear. We compare suggested "quasi-rapid" extinction population dynamics and the global model of the overkill of the prehistoric megafauna (mammoths). We demonstrate that our "quasi-rapid" extinction population dynamics is able to restitute successfully correlations between empirical (archeological) data and overkill theory in North America as well as Australia. For this reason, we conclude that global overkill theory, completely mathematically modelable by "quasi-rapid" extinction population dynamics can consistently explain the Pleistocene extinctions of the megafauna.Comment: 11 pages, no figure