Calculation of flat galactic rotation curves from de Broglie’s double solution theory for wave mechanics

Louis de Broglie suggested in 1927 a double-solution theory for wave mechanics [1] based on the Lorentz invariant Klein-Gordon equation. This excellent candidate for unification of quantum and gravitational theories was not viable at that time, but it may be revived now taking into account three elements that were not available to de Broglie: (1) dark matter fluid, (2) explicit introduction of atomism at the foundations of physical theory and the concomitant discrete mathematical limits [2, 3], and (3) new mathematical solutions for the Klein-Gordon equation discovered by one of us in the mid-1990s [4], which leads to quantized and other novel forces explicitly described in general for the first time at the Q2C meeting of the APS in April 2020. Present paper is a straightforward calculation of galactic rotation curves predicted by our model to obtain the physical conditions that explain flat profiles reported in literature. References: [1] Louis de Broglie (1927) “The five-dimensional universe and wave mechanics” (in French, “L’univers a cinq dimensions et la mécanique ondulatoire”), Le Journal de Physique et le Radium, series VI, 8(2) 65–73. “Comment” by O. Klein, ibid 242–243. “Response” by L. de Broglie, ibid 244. [2] Hector A. Munera (1986) “Properties of discrete electrostatic systems”, Nature 320(6063) 597–600. [3] Hector A. Munera (2018) “Unified fluid and field theory solves long standing controversies”, 20th Annual International Conference on Education, Athens Institute for Education and Research (ATINER), 20–22 May 2018, Athens, Greece, paper published as ATINER Conference Paper Series EDU2018-23XX. [4] Hector A. Munera and Octavio Guzmán (1997) “New explicit nonperiodic solutions of the homogeneous wave equation”, Foundations of Physics Letters 10(1) 31–41.