Relativistic velocity addition from the geometry of momentum space

With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

Laser–Accelerated Plasma–Propulsion System

In this paper, the laser-accelerated plasma–propulsion system (LAPPS) for a spacecraft is revisited. Starting from the general properties of relativistic propellants, the relations between specific impulse, engine thrust and rocket dynamics have been obtained. The specific impulse is defined in terms of the relativistic velocity of the propellant using the Walter’s parameterization, which is a suitable and general formalism for closed–cycle engines. Finally, the laser-driven acceleration of light ions via Target Normal Sheath Acceleration (TNSA) is discussed as a thruster. We find that LAPPS is capable of an impressive specific impulse Isp in the 105 s range for a laser intensity I0≃1021W/cm2. The limit of Isp≲104 s, which characterizes most of the other plasma-based space electric propulsion systems, can be obtained with a relatively low laser intensity of I0≳1019W/cm2. Finally, at fixed laser energy, the engine thrust can be larger by a factor 102 with respect to previous estimates, making the LAPPS potentially capable of thrust-power ratios in the N/MW range.

Synchrotron mechanism of X-ray and gamma-ray emissions in lightning and spark discharges

X-ray and γ-ray emissions observed in lightning and long sparks are usually connected with the bremsstrahlung of high-energy runaway electrons. Here, an alternative physical mechanism for producing X-ray and gamma-ray emissions caused by the polarization current and associated electromagnetic field moving with relativistic velocity along a curved discharge channel has been proposed. The existence of fast electromagnetic surface waves propagating along the lightning discharge channel at a speed close to the speed of light in vacuum is shown. The possibility of the production of microwave, X-ray and gamma-ray emissions by a polarization current pulse moving along a curved path via synchrotron radiation mechanism is pointed out. The existence of long tails in the power spectrum is shown, which explains observations of photon energies in the range of 10–100 MeV in the terrestrial gamma-ray flashes, as well as measured power spectrum of laboratory spark discharge.

Baryogenesis via relativistic bubble walls

We present a novel mechanism which leads to the baryon asymmetry generation during the strong first order phase transition. If the bubble wall propagates with ultra-relativistic velocity, it has been shown [1] that it can produce states much heavier than the scale of the transition and that those states are then out of equilibrium. In this paper, we show that this production mechanism can also induce CP-violation at one-loop level. We calculate those CP violating effects during the heavy particle production and show, that combined with baryon number violating interactions, those can lead to successful baryogenesis. Two models based on this mechanism are constructed and their phenomenology is discussed. Stochastic gravitational wave signals turn out to be generic signatures of this type of models.

Nuclear Processes in Dark Interstellar Matter of H(0) Decrease the Hope of Migrating to Exoplanets

It is still generally assumed that interstellar travel will be possible after purely technical development and thus that mankind can move to some suitable exoplanet when needed. However, recent research indicates this not to be the case, since interstellar space is filled with enough ultradense hydrogen H(0) as stable condensed dark matter (Holmlid, Astrophysical Journal 2018) to make interstellar space travel at the required and technically feasible relativistic velocities (Holmlid et al, Acta Astronautica 2020) almost impossible. H(0) can be observed to exist in space from the so-called extended red emission (ERE) features observed in space. A recent review (Holmlid et al., Physica Scripta 2019) describes the properties of H(0). H(0) gives nuclear processes emitting kaons and other particles, with kinetic energies even above 100 MeV after induction for example by fast particle (spaceship) impact. These high particle energies give radiative temperatures of 12000 K in collisions against a solid surface and will rapidly destroy any spaceship structure moving into the H(0) clouds at relativistic velocity. The importance of preserving our ecosystem is pointed out, since travel to suitable exoplanets may be impossible. The possibilities of instead clearing interstellar space from H(0) are discussed, eventually providing tunnels suitable for relativistic interstellar transport. Finding regions with low intensity of ERE could even be a way to identify space-cleaning activities and thus to locate earlier space-travelling civilizations.

Relativistically invariant Bohmian trajectories of photons

Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity, the relativistic velocity addition rule. Our new velocity equation can be operationally defined in terms of weak measurements of momentum and energy. We finally propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

Synchrotron mechanism of X-ray and gamma-ray emissions in lightning and spark discharges

X-ray and γ-ray emissions observed in lightning and long sparks are usually connected with the bremsstrahlung of high-energy runaway electrons. Here, an alternative physical mechanism for producing X-ray and gamma-ray emissions caused by the polarization current and associated electromagnetic field moving with relativistic velocity along a curved discharge channel has been proposed. The existence of fast electromagnetic surface waves propagating along the lightning discharge channel at a speed close to the speed of light in vacuum is shown. The possibility of the production of microwave, X-ray and gamma-ray emissions by a polarization current pulse moving along a curved path via synchrotron radiation mechanism is pointed out. The existence of long tails in the power spectrum is shown, which explains observations of photon energies in the range of 10-100 MeV in the TGF, as well as measured power spectrum of laboratory spark discharge.

Derivations of Time Dilation using Two Different Lorentz-Type Transformations

The Lorentz transformation (LT) of Einstein's Special Theory of Relativity (STR) leads to the prediction of time dilation and length contraction in moving rest frames. In addition, the relativistic velocity transformation (RVT) is derived from the LT by simply taking the ratios of its space and time coordinates, and this in turn guarantees satisfaction of Einstein's light-speed constancy postulate. The Global Positioning Transformation (GPS-LT) is similar to the LT but differs from it in a significant way, namely it does not lead to the space-time mixing characteristic of the LT. The way in which time dilation is derived from both transformations is compared and it is shown that only the GPS-LT is self-consistent with respect to this key prediction of relativity theory

Apparent superluminal velocities and random walk in the velocity space

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes.

Improved and simplified design of the relativistic helitron resonator

One of the main trends in microwave electronics is the ultra-large power production. The electron stream energy is converted inside vacuum systems, where the key moment is increasing output power of microwave devices, which is possible only when using more and more powerful electron streams. Increasing electron stream power is possible due to either enhancing the carried currents or as a result of increasing the electron energy. Given the law that connects currents and voltages in electronic systems operating when the current is limited by a spatial charge, the production of ultra-high-power electron flows is associated with the usage of relativistic velocity electrons, i. e. approaching the light speed. Likewise, at present, relativistic electrovacuum devices (traveling-wave lamps and backward-wave lamps) use magnetic focusing for linear relativistic streams, which prevents the implementation of simple superconducting electrodynamic systems, because highfrequency metal superconductivity disappears in constant magnetic fields. Meanwhile, simplified ultra-highpower superconducting device structures can significantly increase the device energy due to the strong ohmic loss reduction, which just limits the device energy, destroying the working electrodynamic system surface by increasing power or pulse duration of the generator. The article outlines the modernized design of a new-type microwave generator – the relativistic helitron. The paper considers a simpler coaxial resonator design, obtained by using the supercritical narrowing of the inner conductor radius by the Hn1l mode of the electromagnetic field, rather than a coaxial resonator with notch filters.