Abstract
A dense assembly of an equal number of two kinds of Planck masses, one having positive and the other one negative kinetic energy, described by a nonrelativistic nonlinear Heisenberg equation with pointlike interactions, is proposed as a model for a unified theory of elementary particles. The dense assembly of Planck masses leads to a vortex field below the Planck scale having the form of a vortex lattice, which can propagate two types of waves, one having the property of Maxwell's electromagnetic and the other one the property of Einstein's gravitational waves. The waves have a cutoff at a wavelength equal to the vortex lattice constant about ∼103 times larger than the Planck length, reproducing the GUT scale of elementary particle physics. The vortex lattice has a resonance energy leading to two kinds of quasiparticles, both of which have the property of Dirac spinors. Depending on the resonance energy, estimated to be ∼107 times smaller than the Planck energy, the mass of one of these quasiparticles is about equal to the electron mass. The mass of the other particle is much smaller, making it a likely candidate for the much smaller neutrino mass. Larger spinor masses occur as internal excitations, with a maximum of four such excitations corresponding to a maximum of four particle families. Other vortex solutions may describe the quark-lepton symmetries of the standard model. All masses, with the exception of the Planck mass particles, are quasiparticles for which Lorentz invariance holds, with the Galilei invariance at the Planck scale dynamically broken into Lorentz invariance below this scale. The assumed equal number of Planck masses with positive and negative kinetic energy makes the cosmological constant exactly equal to zero.
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References
Bopp, F. (1946).Zeitschrift für Naturforschung,1, 196.
Bopp, F. (1949).Zeitschrift für Physik,125, 615.
Delacrétaz, G.,et al. (1986).Physical Review Letters,56, 2598.
Gupta, S. N. (1954).Physical Review,96, 1683.
Hawking, S. W. (1978).Physical Review D,18, 1747.
Heisenberg, W. (1954).Zeitschrift für Naturforschung,9a, 292.
Heisenberg, W. (1957).Reviews of Modern Physics,29, 269.
Hönl, H. (1952).Ergebnisse der Exakten Naturwissenschaften,26, 291.
Hönl, H., and Papapatrou, A. (1939a).Zeitschrift für Physik,112, 512.
Hönl, H., and Papapatrou, A. (1939b).Zeitschrift für Physik,114, 478.
Landau, L. D., and Lifschitz, E. M. (1970).Theory of Elasticity, Pergamon Press, New York.
Landau, L. D., and Lifschitz, E. M. (1975).The Classical Theory of Fields, Pergamon Press, New York.
Laughlin, R. B. (1983a).Physical Review,27B, 3383.
Laughlin, R. B. (1983b).Physical Review Letters,50, 1395.
Nussinov, S. (1988).Physical Review D,38, 1606.
Pfister, H., and Schedel, C. (1987).Classical and Quantum Gravity,4, 141.
Redmount, L. A., and Wai-Mo Suen (1993).Physical Review D,47, R2163.
Schlayer, K. (1928).Zeitschrift für Angewandte Mathematik und Mechanik,8, 352.
Schrödinger, E. (1930).Sitzungsberichte der Preussichen Akademie der Wissenschaften. Physikalische-Mathematische Klasse, 416.
Schrödinger, E. (1931).Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse, 418.
Shupe, M. A. (1985).American Journal of Physics,53, 122.
Thomson, W. (1887).Philosophical Magazine,24, 342.
Von Weizsäcker, C. F. (1971).Die Einheit der Natur, Carl Hanser Verlag, Munich.
Weinberg, S. (1987). InElementary Particles and the Laws of Physics, Cambridge University Press, Cambridge, pp. 80ff.
Wheeler, J. A. (1968). InTopics in Nonlinear Physics, N. J. Zabusky, ed., Springer, New York, pp. 615ff.
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Winterberg, F. The Planck Aether model for a unified theory of elementary particles. Int J Theor Phys 33, 1275–1314 (1994). https://doi.org/10.1007/BF00670794
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DOI: https://doi.org/10.1007/BF00670794