Relativity and View Effects

Relativity has been based on the implicit assumption that it would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. An object has no speed limit due to gravitation but it is limited in speed with electromagnetism. Inertial behavior is examined. The equivalence principle does not introduce gravitation to General Relativity. Relativity impacts the energy formula of electromagnetism using the Lorentz factor which also introduces view effects that are optical illusions with no impact on energy.

Fast Particle Acceleration in Three-dimensional Relativistic Reconnection

Magnetic reconnection is invoked as one of the primary mechanisms to produce energetic particles. We employ large-scale 3D particle-in-cell simulations of reconnection in magnetically dominated (σ = 10) pair plasmas to study the energization physics of high-energy particles. We identify an acceleration mechanism that only operates in 3D. For weak guide fields, 3D plasmoids/flux ropes extend along the z-direction of the electric current for a length comparable to their cross-sectional radius. Unlike in 2D simulations, where particles are buried in plasmoids, in 3D we find that a fraction of particles with γ ≳ 3σ can escape from plasmoids by moving along z, and so they can experience the large-scale fields in the upstream region. These “free” particles preferentially move in z along Speiser-like orbits sampling both sides of the layer and are accelerated linearly in time—their Lorentz factor scales as γ ∝ t, in contrast to γ ∝ t in 2D. The energy gain rate approaches ∼eE rec c, where E rec ≃ 0.1B 0 is the reconnection electric field and B 0 the upstream magnetic field. The spectrum of free particles is hard, dN free / d γ ∝ γ − 1.5 , contains ∼20% of the dissipated magnetic energy independently of domain size, and extends up to a cutoff energy scaling linearly with box size. Our results demonstrate that relativistic reconnection in GRB and AGN jets may be a promising mechanism for generating ultra-high-energy cosmic rays.

Coherent Emission in Pulsars, Magnetars, and Fast Radio Bursts: Reconnection-driven Free Electron Laser

We develop a model of the generation of coherent radio emission in the Crab pulsar, magnetars, and fast radio bursts (FRBs). Emission is produced by a reconnection-generated beam of particles via a variant of the free electron laser mechanism, operating in a weakly turbulent, guide field-dominated plasma. We first consider nonlinear Thomson scattering in a guide field-dominated regime, and apply it to explain emission bands observed in Crab pulsar and in FRBs. We consider particle motion in a combined field of the electromagnetic wave and the electromagnetic (Alfvénic) wiggler. Charge bunches, created via a ponderomotive force, Compton/Raman scatter the wiggler field coherently. The model is both robust to the underlying plasma parameters and succeeds in reproducing a number of subtle observed features: (i) emission frequencies depend mostly on the scale λ t of turbulent fluctuations and the Lorentz factor of the reconnection-generated beam, ω ∼ γ b 2 ( c / λ t ) —it is independent of the absolute value of the underlying magnetic field. (ii) The model explains both broadband emission and the presence of emission stripes, including multiple stripes observed in the high frequency interpulse of the Crab pulsar. (iii) The model reproduces correlated polarization properties: the presence of narrow emission bands in the spectrum favors linear polarization, while broadband emission can have an arbitrary polarization. (iv) The mechanism is robust to the momentum spread of the particle in the beam. We also discuss a model of wigglers as nonlinear force-free Alfvén solitons (light darts).

The eMERLIN and EVN View of FR 0 Radio Galaxies

We present the results from high-resolution observations carried out with the eMERLIN UK-array and the European VLBI network (EVN) for a sample of 15 FR 0s, i.e., compact core-dominated radio sources associated with nearby early-type galaxies (ETGs), which represent the bulk of the local radio galaxy population. The 5 GHz eMERLIN observations available for five objects exhibit sub-mJy core components and reveal pc-scale twin jets for four out of five FR 0s once the eMERLIN and JVLA archival visibilities data are combined. The 1.66 GHz EVN observations available for 10 FR 0s display one- and two-sided jetted morphologies and compact cores. The pc-scale core emission contributes, on average, to about one tenth of the total extended radio emission, although we noted an increasing core contribution for flat-/inverted-spectrum sources. We found an unprecedented linear correlation between the pc-scale core luminosity (∼1021.3–1023.6 W Hz−1) and [O III] line luminosity, generally considered as proxy of the accretion power, for a large sample of LINER-type radio-loud low-luminosity active nuclei, all hosted in massive ETGs, which include FR 0s and FR Is. This result represents further evidence of a common jet–disc coupling in FR 0s and FR Is, despite then differing in kpc-scale radio structure. For our objects and for other FR 0 samples reported in the literature, we estimated the jet brightness sidedness ratios, which typically range between one and three. This parameter roughly gauges the jet bulk Lorentz factor Γ, which turns out to range from 1 to 2.5 for most of the sample. This corroborates the scenario that FR 0s are characterized by mildly relativistic jets, possibly as a result of lower-spinning black holes (BHs) than the highly spinning BHs of relativistic-jetted radio galaxies, FR Is.

The X-ray plateau phase of gamma-ray burst originating from an expanding shell with a Lorentz factor of a few tens

Gamma-ray bursts (GRBs) are one of the most energetic explosions known in the Universe and are also known to have the most relativistic jets, with initial expansion Lorentz factors of $100< \Gamma_i <1000$ \cite{KP91, Fenimore+93, WL95, LS01, ZLB11, Zou+11, Racusin+11}. Many of these objects have a plateau in their early X-ray light curves (up to thousands of seconds) \cite{Nousek+06, OBrien+06, Zhang+06, Liang+07, Srinivasaragavan+20}. In this phase, the X-ray flux decreases much slower than theoretically expected \cite{MR93} which has puzzled the community for many years. Here, we show that the observed signal during this phase in both the X-ray and the optical bands is naturally obtained within the classical GRB “fireball” model, provided that (i) the initial Lorentz factor of the relativistically expanding jet is of the order of a few tens, rather than a few hundreds, as is often cited in the literature, and (ii) the expansion occurs into a medium-low density “wind” with density typically 3-4 orders of magnitude below the expectation from a Wolf-Rayet star \cite{CL99}. Within this framework, the end of the “plateau” phase (the beginning of the regular afterglow) marks the transition from the coasting phase to the self-similar expansion phase, which follows the scaling laws first derived by Blandford \& McKee.\cite{BM76}. This result therefore implies that the long GRB progenitors are either (i) not Wolf-Rayet stars, or (ii) the properties of the wind ejected by these stars prior to their final explosion are very different than the properties of the wind ejected at earlier times. This result shows that the range of Lorentz factors in GRB jets is much wider than previously thought, and bridges an observational ‘gap’ between mildly relativistic jets\cite{Ghisellini1993} inferred in active galactic nuclei, $\Gamma_i\lesssim 20$, to the much higher Lorentz factors, $\Gamma_i\lesssim 1000$ inferred in a few extreme GRBs\cite{Racusin+11}.

Relativity and View Effects

Relativity has been based on the implicit assumption that it would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. An object has no speed limit due to gravitation but it is limited in speed with electromagnetism. Inertial behavior is examined. The equivalence principle does not introduce gravitation to General Relativity. Relativity impacts the energy formula of electromagnetism using the Lorentz factor which also introduces view effects that are optical illusions with no impact on energy.

Relativity and View Effects

Relativity has been based on the implicit assumption that it would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. An object has no speed limit due to gravitation but it is limited in speed with electromagnetism. Inertial behavior is examined. The equivalence principle does not introduce gravitation to General Relativity. Relativity impacts the energy formula of electromagnetism using the Lorentz factor which also introduces view effects that are optical illusions with no impact on energy.

MATHEMATICAL EXPANSION OF SPECIAL THEORY OF RELATIVITY ONTO ACCELERATIONS

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

Relativity and View Effects

Relativity has been based on the implicit assumption that electromagnetism would exclusively describe interactions. Relativistic view effects are included as well, and they act with no force and no energy exchanges. The Ehrenfest paradox is solved. View effects specific to each point of view are the solution. The calculation of the deflection of light by the sun explains in detail why the deflection angle must be almost double the value obtained with Newton’s laws. The compatibility of General Relativity with the new interpretation is discussed. View effects cannot impact total energy. An object has no speed limit due to relativity but can be limited due to other causes. Inertial behavior is examined. Inertial masses are redundant, but this does not introduce gravitation to General Relativity. Relativity impacts the energy formula of electromagnetism using the Lorentz factor which also introduces view effects that are optical illusions with no impact on energy.