Periodin kahdentuminen

Prof. Ari Lehto          In English

Periodin kahdentuminen

Epälineaarisilla dynaamisilla systeemeillä on perusperiodia kahdentava ominaisuus. Jos perusperiodiksi valitaan luonnonvakioista saatava Planckin aika, niin kahdentumisilmiö tuottaa uusia periodeja, joita vastaavat fysikaaliset suureet (esim. energia) ilmenevät tarkasti aineen stabiileissa rakenteissa ja ominaisuuksissa alkaen alkeishiukkasista ja päättyen avaruudessa esiintyviin rakenteisiin. Sama mekanismi synnyttää alkeisvarauksen Planckin varauksesta, joka myös saadaan luonnonvakioista.

Ari Lehto, Period-Doubling as a Structure Creating Natural Process

La Nuova Critica, Special Issue 63-64, ISSN 1824-9663 (2016), Scientific Models and a Comprehensive Picture of Reality, pp. 91-115. VIDEO.

Protonin ja neutronin rakenteet, neutriino

Planckin energia voidaan laskea joko Planckin massasta tai elektroni-positroniparin lepoenergiasta. Periodin kahdentumisilmiö tuottaa jälkimmäisestä Planckin energiasta tarkat ennusteet sekä protonin että neutronin lepoenergioille, magneettisille momenteille ja periodiavaruuden rakenteille.

Neutriino näyttää syntyvän luonnollisella tavalla neutronin hajotessa, ja sen rakenne ja pyörimisliikemäärä ovat samat kuin elektronilla (tai positronilla), josta puuttuu sähkövaraus. PFS seminaari 22.2.2016, Ari Lehto 

Ari Lehto, On the Planck Scale and Properties of Matter

Special Issue: Quantum Vacuum, Fundamental Arena of the Universe: Models, Applications and Perspectives. Vol. 2, No. 6-1, 2015, pp. 57-65.doi: 10.11648/j.ijass.s.2014020601.17. Full PDF paper
Period doubling, or a frequency halving sequence, is a common property of nonlinear dynamical systems. Period can be related to other physical quantities, e.g. length, energy and temperature, which obtain the corresponding doubling/halving behavior. It is found that physical properties of natural phenomena, systems and elementary particles can be derived directly from the Planck time, taken as the fundamental period. Analysis of experimental data suggests that the period doubling process takes place in three and four internal degrees of freedom. It is further found out that long term stability complies with the stability condition of nonlinear dynamical systems. A theory of period doubling in 1/r-type nonlinear systems with three and four internal degrees of freedom is presented.

Ari Lehto, Elementary particle classification

Periodin kahdentumisilmiö jakaa alkeishiukkaset luokkiin, jotka vastaavat Standardimallin luokitusta. Tunnetut alkeishiukkaset ryhmittyvät sen mukaan, kuinka monta periodin kahdentumista (=energian puolittumista) on tapahtunut Planckin energiasta alkaen. Massa-energia systeemeihin tarvitaan kolme sisäistä vapausastetta (dimensiota) ja sähkömagneettisiin systeemeihin neljä, mistä seuraa bipolaarisuus. Kvarkkihypoteesia ei tarvita. Ari Lehto, elokuu 2015.

Valittuja julkaisuja ja esityksiä periodin kahdentumisesta

Ari Lehto, On the Planck Scale and Structures of Matter NPA Conference, Storrs, University of Connecticut, May 25-29, 2009
Full text/pdf, Presentation slides ppt/pdf 
Abstract: Invariant properties and structures of matter are modeled by internal period-like degrees of freedom. Invariance then means periods, which remain unaltered over time. Period doubling is a phenomenon common to nonlinear dynamical systems. In this model the doubling process is generalized into multiple dimensions and utilized to bring about sub-harmonic frequencies, which generate decreasing energies and increasing sizes. It is assumed that period doubling takes place at the Planck scale, and therefore the Planck units are used as reference. The sub-harmonics can be converted into several other physical quantities by well known physical relations. A certain class of sub-harmonics is stable and the elementary electric charge (squared), rest energies and magnetic moments of the electron-positron and proton-antiproton pairs are shown to belong to this class. It is suggested that the structure of the Solar system results from period doubling, too. 

Ari Lehto, On the Planck Scale and Properties of Matter, Nonlin. Dyn. 55, 279-298 (2009)
Abstract: Invariant and long-lived physical properties and structures of matter are modeled by intrinsic rotations in three and four degrees of freedom. The rotations are quantized starting from the Planck scale by using a nonlinear 1/r potential and period doubling - a common property of nonlinear dynamical systems. The absolute values given by the scale-independent model fit closely with observations in a wide range of scales. A comparison is made between the values calculated from the model and the properties of the basic elementary particles, particle processes, planetary systems, and other physical phenomena. The model also shows that the perceived forces can be divided into two categories: (1) force is always attractive, like in gravitation and (2) force is attractive or repulsive, like in electrostatics. 

Ari Lehto, Quantization of Keplerian Systems, (2006) 

Ari Lehto, Periodic Time and the Stationary Properties of Matter, Chin. J. Phys., Vol. 28, no. 3, June 1990 Ari Lehto, On (3+3)-Dimensional Discrete Space-Time University of Helsinki, Report Series in Physics, HU-P-236 (1984).
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