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Register a new userFractal properties in fundamental force coupling constants, in atomic energies, and in elementary particle masses
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Authors
Boris Tatischeff
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Using the discrete-scale invariance theory, we show that the coupling constants of fundamental forces, the atomic masses and energies, and the elementary particle masses, obey to the fractal properties.
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In this article the concept of mass is analyzed based on the special and general relativity theories and particle (quantum) physics. The mass of a particle (m=E(0)/c^2) is determined by the minimum (rest) energy to create that particle which is invariant under Lorentz transformations. The mass of a bound particle in the any field is described by m<E80)/c^2 and for free particles in the non-relativistic case the relation m=E/c^2 is valid. This relation is not correct in general, and it is wrong to apply it to the radiation and fields. In atoms or nuclei (i.e. if the energies are quantized) the mass of the particles changes discretely. In non-relativistic cases, mass can be considered as a measure of gravitation and inertia.
We discuss the fundamental constants of physics in the Standard Model and possible changes of these constants on the cosmological time scale. The Grand Unification of the strong, electromagnetic and weak interactions implies relations between the time variation of the finestructure constant and of the QCD scale. An experiment in quantum optics at the MPQ in Munich, which was designed to look for a time variation of the QCD scale, is discussed.
A contribution is presented to the study of hadron spectroscopy through the use of fractals and discrete scale invariance implying log-periodic corrections to continuous scaling. The masses of mesons and baryons, reported by the Particle Data Group (PDG), are properly fitted with help of the equation derived from the discrete-scale invariance (DSI) model. The same property is observed for the mass ratios between different particle species. This is also the case for total widths of several hadronic species. Each fitted parameter, as a function of the hadronic masses, displays the same distribution for all hadronic species. Several masses of still unobserved mesons and baryons are tentatively predicted.
The fractal property stipulates that the same physical laws apply for different scales of a given physics. This property is applied to particles and nuclei, in order to study the possibility to use it to help for determination of unknown spins of some particles or excited nuclei levels.
In this article we reconsider the old mysterious relation, advocated by Dirac and Weinberg, between the mass of the pion, the fundamental physical constants, and the Hubble parameter. By introducing the cosmological density parameters, we show how the corresponding equation may be written in a form that is invariant with respect to the expansion of the Universe and without invoking a varying gravitational constant, as was originaly proposed by Dirac. It is suggest that, through this relation, Nature gives a hint that virtual pions dominante the content of the quantum vacuum.
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