The Planck length and the constancy of the speed of light in five dimensional space parametrized with two time coordinates

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant; the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe

Cross sections and modelling results for TGF- and positron spectrum produced by a negative stepped lightning leader

We model the energy resolved angular distribution of TGFs and of positrons produced by a negative lightning leader stepping upwards in a thundercloud. First we present our new results for doubly differential cross sections for Bremsstrahlung and pair production based on the triply differential cross-sections of Bethe and Heitler. Other cross sections in literature and databases do not cover the appropriate energy range or do not apply to the small atomic numbers of nitrogen and oxygen or do not resolve both energies and emission angles of emitted photons or positrons. Second we have extended the Monte Carlo model of Chao Li towards relativistic electron energies, and we have included the new cross sections as well as Compton scattering of photons and photo ionization. We will present the angular resolved spectrum of TGFs and positrons of stepped negative leaders and compare it with results of other authors

Production mechanisms of leptons, photons, and hadrons and their possible feedback close to lightning leaders

It has been discussed that lightning flashes emit high-energy electrons, positrons, photons, and neutrons with single energies of several tens of MeV. In the first part of this paper we study the absorption of neutron beams in the atmosphere. We initiate neutron beams of initial energies of 350 keV, 10 MeV, and 20 MeV at source altitudes of 4 km and 16 km upward and downward and see that in all these cases neutrons reach ground altitudes and that the cross-section areas extend to several km2. We estimate that for terrestrial gamma-ray flashes approximately between 10 and 2000 neutrons per ms and m2 are possibly detectable at ground, at 6 km, or at 500 km altitude. In the second part of the paper we discuss a feedback model involving the generation and motion of electrons, positrons, neutrons, protons, and photons close to the vicinity of lightning leaders. In contrast to other feedback models, we do not consider large-scale thundercloud fields but enhanced fields of lightning leaders. We launch different photon and electron beams upward at 4 km altitude. We present the spatial and energy distribution of leptons, hadrons, and photons after different times and see that leptons, hadrons, and photons with energies of at least 40 MeV are produced. Because of their high rest mass hadrons are measurable on a longer time scale than leptons and photons. The feedback mechanism together with the field enhancement by lightning leaders yields particle energies even above 40 MeV measurable at satellite altitudes

Streamer propagation in the atmosphere of Titan and other N2:CH4 mixtures compared to N2:O2 mixtures

Streamers, thin, ionized plasma channels, form the early stages of lightning discharges. Here we approach the study of extraterrestrial lightning by studying the formation and propagation of streamer discharges in various nitrogen-methane and nitrogen-oxygen mixtures with levels of nitrogen from 20% to 98.4%. We present the friction force and breakdown fields Ek in various N2:O2 (Earth-like) and N2:CH4 (Titan-like) mixtures. The strength of the friction force is larger in N2:CH4 mixtures whereas the breakdown field in mixtures with methane is half as large as in mixtures with oxygen. We use a 2.5 dimensional Monte Carlo particle-in-cell code with cylindrical symmetry to simulate the development of electron avalanches from an initial electron-ion patch in ambient electric fields between 1.5Ek and 3Ek. We compare the electron density, the electric field, the front velocities as well as the occurrence of avalanche-to-streamer transition between mixtures with methane and with oxygen. Whereas we observe the formation of streamers in oxygen in all considered cases, we observe streamer inceptions in methane for small percentages of nitrogen or for large electric fields only. For large percentages of nitrogen or for small fields, ionization is not efficient enough to form a streamer channel within the length of the simulation domain. In oxygen, positive and negative streamers move faster for small percentages of nitrogen. In mixtures with methane, electron or streamer fronts move 10-100 times slower than in mixtures with oxygen; the higher the percentage of methane, the faster the fronts move.Comment: 34 pages, 11 figures, 1 tabl