Re: [Philweb] Ist Unendlichkeit endlich darstellbar?

Hi Rat Frag, um die Teilbarkeit (und inwieweit Unendlichkeit endlich darstellbar ist) geht es in dem Papier "Alternative Interpretations of Classical Physics“ genauer und deshalb hatte ich sie ins Spiel gebracht und die Zusammenfassung der beiden Autoren bereits mitgeteilt. Wenn Du nicht bei Planck stehen bleiben willst, lohnt sich die Lektüre, zumal die meisten Referenzen ebenfalls frei verfügbar sind. Die diskreten Teilchenorte sind die „hidden variables“ der modernen und das Kontinuum der reellen Zahlen die der klassischen Physik. Der eigentliche Durchbruch in die „Moderne Physik“ gelang bereits Boltzmann und Planck folgte lediglich widerwillig seinen Vorgaben. Dazu könntest Du vorab den Artikel "Ludwig Boltzmann - A Pioneer of Modern Physics“ von Dieter Flamm lesen, der folgende Zusammenfassung gibt: „In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus broke with the classical prejudice, that fundamental laws have to be strictly deterministic. Even Max Planck had not been ready to accept Boltzmann's statistical methods until 1900. With Boltzmann's pioneering work the probabilistic interpretation of quantum mechanics had already a precedent. In fact in a paper in 1897 Boltzmann had already suggested to Planck to use his statistical methods for the treatment of black body radiation. The second pioneering step towards quantum mechanics was Boltzmann's introduction of discrete energy levels. Boltzmann used this method already in his 1872 paper on the H-theorem. One may ask whether Boltzmann considered this procedure only as a mathematical device or whether he attributed physical significance to it. In this connection Ostwald reports that when he and Planck tried to convince Boltzmann of the superiority of purely thermodynamic methods over atomism at the Halle Conference in 1891 Boltzmann suddenly said: `I see no reason why energy shouldn't also be regarded as divided atomically’.“ https://arxiv.org/abs/physics/9710007 <https://arxiv.org/abs/physics/9710007> Es grüßt, Ingo