摘要:

We make a systematic analysis of the dual incursive model of the discrete harmonic oscillator. We derive its closed form solution, and identify its natural frequency of oscillation. We study its orbital stability, and the conservation of its total energy. We finally propose a superposed model that conserves energy with absolute precision, and exhibits a high degree of orbital stability. Within the conjecture that spacetime is discrete, the above results lead to the conclusion that discretization must be accompanied by anticipation, in order to guarantee orbital stability and energy conservation. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787311

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

The field of nonlinear dynamics focuses on function rather than structure. Evolution and brain function are examples. An equation for a brain, described in 1973, is explained. Then, a principle of interactional function change between two coupled equations of this type is described. However, all of this is not done in an abstract manner but in close contact with the meaning of these equations in a biological context. Ethological motivation theory and Batesonian interaction theory are reencountered. So is a fairly unknown finding by van Hooff on the indistinguishability of smile and laughter in a single primate species. Personhood and evil, two human characteristics, are described abstractly. Therapies and the question of whether it is ethically allowed to export benevolence are discussed. The whole dynamic approach is couched in terms of the Cartesian narrative, invented in the 17th century and later called Enlightenment. Whether or not it is true that a “second Enlightenment” is around the corner is the main question raised in the present paper. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787312

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

The aim of the theory of scale relativity is to derive the physical behavior of a non‐differentiable and fractal space‐time and of its geodesics (with which particles are identified), under the constraint of the principle of the relativity of scales. We mainly study in this contribution the effects induced by internal fractal structures on the motion in standard space. We find that the main consequence is the transformation of classical mechanics in a quantum mechanics. The various mathematical quantum tools (complex wave functions, spinors, bi‐spinors) are built as manifestations of the non‐differentiable geometry. Then the Schro¨dinger, Klein‐Gordon and Dirac equations are successively derived as integrals of the geodesics equation, for more and more profound levels of description. Finally we tentatively suggest a new development of the theory, in which quantum laws would hold also in the scale‐space: in such an approach, one naturally defines a new conservative quantity, named ‘complexergy’, which measures the complexity of a system as regards its internal hierarchy of organization. We also give some examples of applications of these proposals in various sciences, and of their experimental and observational tests. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787313

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In quantum mechanics, the three coordinate operators have each the set of real numers as eigen values. The problem of localization of a particle being linked to that of measurement of distance to a given point we can equivalently consider the “square distance operator”. The eigen‐values of the “square distance operator” acting on functions of position are the same as those of the Laplacian (multiplied by a negative constant involving h) acting on functions of momentum (Fourier transforms, involving h, of the function of position). We impose to these functions (as well as to the Fourier transform of the wave function) to vanish outside a compact and on its boundary. Consequently the above Laplacian has a discrete infinite spectrum of strictly positive eigen‐values which are also the eigen‐values of of the “square distance operator”. So their square roots are the observable values of distance with a minimum observable distance. Examples are given. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787314

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

A multivariate 4‐vector representation for space‐time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to theSU(3) ×SU(2)L×U(1) symmetry, and to particle structures and mass‐generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically‐symmetric distance‐dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator‐type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787315

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

The four (electro‐magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac‐Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables aregauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, theDirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement ofcausalitydictates the choice ofretardedsolutions at the classical level. However both the problems of the classical theory of the electron, leading to the choice of12(retarded + advanced) solutions, and the regularization of quantum field teory, leading to the Feynman propagator, introduceanticipatoryaspects. The determination of the relativistic Darwin potential as a semi‐classical approximation to the Lienard‐Wiechert solution for particles with Grassmann‐valued electric charges, regularizing the Coulomb self‐energies, shows that these anticipatory effects live beyond the semi‐classical approximation (tree level) under the form of radiative corrections, at least for the electro‐magnetic interaction.Talk and “best contribution” at The Sixth International Conference on Computing Anticipatory Systems CASYS’03, Liege August 11–16, 2003. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787316

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

We expose a conception of the physical universe based on acausal relations between fundamental elements with only a binary property. Relations occur following a stochastic process which describes universe evolution. Separations can be defined by the spinor null‐pole formula to define a possibly scale dependent geometry. The central unknown being the stochastic process, some properties can be inferred from macroscopic evidence, but some alternatives are opened for example to have a time model closer from the physical one accounting for example for the past‐present‐future distinction and the “depth of physical time”. Independent of considerations about the evolution process, some properties of the universe as a matter‐antimatter implied gemellarity automatically arises if the binary fundamental property is identified with charge polarity. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787317

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

A general line element and a general metric tensor are defined as functions of two parameters &agr; and &agr;′. The related Einstein’s field equations of a gravitational potential field in a vacuum, including parameter &Lgr;, have been derived. The parameters &agr; and &agr;′ are identified in a gravitational field by the solution of the Einstein’s field equations. Parallel with this, it has been find out that the so‐called cosmological constant &Lgr;, is not really constant, but a function of gravitational radius, &Lgr; = f(r). This discovery is very important, among the others, for cosmology. One of the consequences is the new form of the acceleration equation of the universe motion that can be attractive (negative) or repulsive (positive). According to the observations, the repulsive acceleration gives rise to accelerating expansion of the universe at the present time. The obtained solution of the diagonal line element can be applied in a very strong gravitational field. Besides, this solution gives the Ricci scalar equal to zero, R= 0. This is in an agreement with the current observation that our universe is flat. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787318

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Generally unicellular prokaryotes are considered the most fundamental form of living system. Many researchers include viruses since they commandeer cellular machinery in their replication; while others insist viruses are merely complex infective proteins. New biological principles are introduced suggesting that even the prion, the infectious protein responsible for transmissible spongiform encephalopathies, qualifies as the most fundamental form of life; and remains in general concordance with the six‐point definition of living systems put forth by Humberto Maturana and his colleagues in their original characterization of living organisms as a class of complex self‐organized autopoietic systems in 1974. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787319

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

System design and implementation targets operation in the future. Success depends on anticipation and timely response. Artificial systems are designed to emulate living organisms, but do they really do that? Does our existing image of a system reflect life? We have dissected widely held organizational concepts and misconceptions to try and establish the essential “anatomy” of a system. This paper reports our conclusions. “A system” implies unity: quantum‐mechanical “systems” are unified by entanglement; Newtonian ones are inescapably fragmented. A Newtonian system is not directly unified: we are inevitably a part of the system: the necessary entanglement is provided by our brains! We conclude that system unification is always through quantum‐mechanical entanglement. Artificial systems can never be both Newtonian and autonomous. Anticipation of future events requires multiply‐scaled models of the environment, created in the past for use in the future. These, must be united through entanglement into a system’s “anatomical” structure, in which anticipative processes unfold. We should not expect artificial systems to successfully emulate anticipatory organisms. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1787320

出版商:AIP    

年代:1904

数据来源: AIP