Relativistic Situations Research Articles

Students’ preinstructional reasoning with the speed of light in relativistic situations

Special relativity theory (SRT) has recently gained popularity as a first introduction to “modern” physics thinking in upper level secondary physics education. A central idea in SRT is the absolute speed of light, with light propagating with uniform speed relative to the reference frame of the observer. Previous research suggests that students, building on their prior understandings of light propagation and relative motion, develop misunderstandings of this idea. The available research provides little detail on the reasoning processes underlying these misunderstandings. We therefore studied secondary education students’ preinstructional reasoning about the speed of light in a qualitative study, probing students’ reasoning through both verbal reasoning and drawing. Event diagrams (EDs) were used as a representational tool to support student reasoning. Results show that students productively use EDs to reason with light propagation. In line with previous research, we found two alternative reference frames students could use for uniform light propagation. Most students show a flexibility in their use of reference frame: They not only evaluate light propagation in their preferred frame of reference, but also relative to other frames. Some students experienced conflict between an alternative reference frame and the speed of light and changed their reasoning because of that. This finding suggests promising directions for designing education.Received 8 May 2019DOI:https://doi.org/10.1103/PhysRevPhysEducRes.15.020123Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesScientific reasoning & problem solvingSpecial relativityPhysics Education Research

BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields

We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.

Deriving a unified equation for Doppler effect for any wave in any medium from Lorentz transformations

We use the Lorentz transformation equations to derive a unified equation for the Doppler effect–that can be used for any one-dimensional (sound, water, EM, etc.) wave in any medium. This unified equation includes the effects of motion, if present, of the medium relative to the observer as well as the relative velocity between the observer and the source. This master equation can be applied to both relativistic and nonrelativistic situations to recover the more familiar Doppler effect expressions and it clarifies that the Doppler equations given in standard textbooks for both sound and EM waves, are basically the same. The advantage of this unified equation is that it reduces the effort in solving complex problems. Basic knowledge of Lorentz transformations and their physical effects is enough to understand this derivation.

Primitive Variable Determination in Conservative Relativistic Magnetohydrodynamic Simulations

In nonrelativistic hydrodynamics and magnetohydrodynamics, conservative integration schemes for the fluid equations of motion are generally employed. The computed quantities, namely, the mass density, (vector) momentum density, and energy density, can readily be converted back into the primitive variables that define the problem, namely, the mass density, (vector) velocity, and thermal pressure. In practical terms, the primitive variables can be “peeled away” from the computed variables. In relativistic problems, however, the appearance of the Lorentz factor in the computed quantities dramatically complicates the problem owing to its near-singular dependence upon relativistic velocities. Conservative integration schemes for the hyperbolic partial differential equations of special relativistic magnetohydrodynamics (RMHD) yield estimates of the five conserved quantities that are related in a highly nonlinear way to the five primitive variables. We also observe that an equivalent set of five nonlinear equations emerges in describing the general relativistic magnetohydrodynamics problem. Conversion from the conserved quantities to primitive variables is the most computationally intensive part of the simulation, consuming almost all the computational effort. This paper presents a new algorithm for accurately and rapidly addressing this problem. We provide an analytic representation for this nonlinear system as a single equation in a single unknown. This equation lends itself to an iterative approach, emerging from its underlying physical and analytic properties, one whose convergence is rapid and sufficiently close to geometric that the Aitken acceleration scheme renders the iterations quadratically convergent. The new algorithm enjoys robust convergence properties that render it well-suited to parallel computing architectures. We show how our new scheme facilitates the rapid and accurate computation of solutions to the RMHD equations for moderate Lorentz factors as well as extreme relativistic situations that are observed in high-energy astrophysical objects, where the Lorentz factor can exceed $10^4$ and magnetic fields can exceed $10^{13}$ Gauss, and in laboratory plasmas associated with fusion research where very high velocities and magnetic fields are introduced.

Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

Electromagnetic Emission from Laser Wakefields in Magnetized Underdense Plasmas

A wakefield driven by a short intense laser pulse in a perpendicularly magnetized underdense plasma is studied analytically and numerically for both weakly relativistic and highly relativistic situations. Owing to the DC magnetic field, a transverse component of the electric fields associated with the wakefield appears, while the longitudinal wave is not greatly affected by the magnetic field up to 22 Tesla. Moreover, the scaling law of the transverse field versus the longitudinal field is derived. One-dimensional particle-in-cell simulation results confirm the analytical results. Wakefield transmission through the plasma-vacuum boundary, where electromagnetic emission into vacuum occurs, is also investigated numerically. These results are useful for the generation of terahertz radiation and the diagnosis of laser wakefields.

Electromagnetic wave propagation in general relativistic situations: A general solution of the problem

[1] The exact full-wave modeling and computation of the electromagnetic signals propagating through curved space-time is important from theoretical and practical aspects (e.g., for satellite positioning systems). In this paper a general solution method is presented for these problems. Beside this, it is demonstrated that the Method of Inhomogeneous Basic Modes is a natural consequence of Maxwell's equations in the general relativity.

Relativistic and Quantum Revisions of the Multisource Thermal Model in High-Energy Collisions

The multisource thermal model is revised for relativistic and quantum situations. It is shown that the quantum effect can be neglected due to a very small result. The distributions of particle momenta, momentum components, transverse momenta, kinetic energies, and velocities in both the classical and relativistic situations are presented to give comparisons.

A Relativistic Model of Fluids Motion

The paper suggests a relativistic model of fluids motion combining the conventional formulation of therelativistic fluid mechanics with the “Maxwell’s formulation” of equations of the relativistic flow field,following from application of the 4D formalism in deducing Maxwell’s equations with the 4-potential replacedby the 4-momentum flux. The model is formulated to demonstrate a possibility of an alternative interpretation ofviscosity effects in non-relativistic and relativistic situations. The model complements also the similarities inmathematical formulation of fluid mechanics and electrodynamics addressed in different contexts.

Derivation of the relativistic ‘proper-time’ quantum evolution equations from canonical invariance

Based on (1) the spectral resolution of the energy operator; (2) the linearity of correspondence between physical observables and quantum self-adjoint operators; (3) the definition of conjugate coordinate–momentum variables in classical mechanics; and (4) the fact that the physical point in phase space remains unchanged under (canonical) transformations between one pair of conjugate variables to another, we are able to show that , the proper-time rest-energy transformation matrices, are given as aexp(−iEsts/ℏ), from which we obtain the proper-time rest-energy evolution equation . For special relativistic situations this equation can be reduced to the usual dynamical equations, where t is the ‘reference time’ and E is the total energy. Extension of these equations to accelerating frames is then provided.

Current-voltage and kinetic energy flux relations for relativistic field-aligned acceleration of auroral electrons

Abstract. Recent spectroscopic observations of Jupiter's "main oval" auroras indicate that the primary auroral electron beam is routinely accelerated to energies of ~100 keV, and sometimes to several hundred keV, thus approaching the relativistic regime. This suggests the need to re-examine the classic non-relativistic theory of auroral electron acceleration by field-aligned electric fields first derived by Knight (1973), and to extend it to cover relativistic situations. In this paper we examine this problem for the case in which the source population is an isotropic Maxwellian, as also assumed by Knight, and derive exact analytic expressions for the field-aligned current density (number flux) and kinetic energy flux of the accelerated population, for arbitrary initial electron temperature, acceleration potential, and field strength beneath the acceleration region. We examine the limiting behaviours of these expressions, their regimes of validity, and their implications for auroral acceleration in planetary magnetospheres (and like astrophysical systems). In particular, we show that for relativistic accelerating potentials, the current density increases as the square of the minimum potential, rather than linearly as in the non-relativistic regime, while the kinetic energy flux then increases as the cube of the potential, rather than as the square.

Static fluid cylinders and their fields: global solutions

The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of state of the fluid. In the case of a fluid admitting a non-vanishing density for zero pressure, it is shown that the cylinder's radius has to be finite. For incompressible fluid, the field equations are solved analytically for nearly Newtonian cylinders and numerically in fully relativistic situations. Various physical quantities such as proper and circumferential radii, external conicity parameter and masses per unit proper/coordinate length are exhibited graphically.

Relativistic invariant quantum entanglement between the spins of moving bodies

The entanglement between the spins of a pair of particles may change because the spin and momentum become mixed when viewed by a moving observer [R. M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002)]. In this paper, it is shown that, if the momenta are appropriately entangled, the entanglement between the spins of the Bell states can remain maximal when viewed by any moving observer. Based on this observation, a relativistic invariant protocol for quantum communication is suggested, with which the nonrelativistic quantum information theory could be invariantly applied to relativistic situations.

Exact relativistic treatment of stationary counterrotating dust disks: Physical properties

This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counterrotating disks of dust. We discuss the physical properties of a class of solutions to the Einstein equations for disks with constant angular velocity and constant relative density which was constructed in the first part. The metric for these spacetimes is given in terms of theta functions on a Riemann surface of genus 2. It is parametrized by two physical parameters: the central redshift and the relative density of the two counterrotating streams in the disk. We discuss the dependence of the metric on these parameters using a combination of analytical and numerical methods. Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the static limit which gives a solution of the Morgan and Morgan class and the limit of a disk without counterrotation. We study the mass and the angular momentum of the spacetime. At the disk we discuss the energy-momentum tensor, i.e., the angular velocities of the dust streams and the energy density of the disk. The solutions have ergospheres in strongly relativistic situations. The ultrarelativistic limit of the solution in which the central redshift diverges is discussed in detail: In the case of two counterrotating dust components in the disk, the solutions describe a disk with diverging central density but finite mass. In the case of a disk made up of one component, the exterior of the disks can be interpreted as the extreme Kerr solution.

Post-Newtonian approximation of the rigidly rotating disc of dust to arbitrary order

Using the analytic, global solution for the rigidly rotating disc of dust as a starting point, an iteration scheme is presented for the calculation of an arbitrary coefficient in the post-Newtonian (PN) approximation of this solution. The coefficients were explicitly calculated up to the 12th PN level and are listed in this paper up to the 4th PN level. The convergence of the series is discussed and the approximation is found to be reliable even in highly relativistic cases. Finally, the ergospheres are calculated at increasing orders of the approximation and for increasingly relativistic situations.

II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations:The general law of reflection

The general law of reflection concerns situations when the light ray undergoes a shift of frequency at the reflection point. For example, it governs reflection of light rays from a moving mirror (either in a vacuum or in a transparent medium), reflection from a motionless mirror coated with a layer of Raman-active molecules in the coherent-scattering regime, or external reflection of X-rays from the surface of a condensed matter sample, with partial dissipation of energy within the skin depth. The general law of reflection is derived from the extremum principle for propagation of variable-frequency light rays. It states that the angle of reflection depends not only on the angle of incidence but also on the frequency shift in the reflection point and dispersion of the refractive index of the medium in contact with the mirror. The compatibility of the general law of reflection and the special relativistic treatment of reflection is examined in detail. Applications of the new law of reflection are discussed in the special relativistic and the nonrelativistic regime. PACS Nos.: 42.15-i, 03.30+p

II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations:<BR>The general law of reflection

II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations:<BR>The general law of reflection

Quantum mechanics of charged-particle beam transport through magnetic lenses.

The quantum theory of charged-particle beam transport through a magnetic lens system with a straight optic axis, at the level of single-particle dynamics and disregarding spin (or, when nonzero, assuming it to be an independent spectator degree of freedom), is presented, based on the Schr\"odinger and Klein-Gordon equations in a form suitable for analyzing the paraxial and aberration aspects in a systematic way using a Lie algebraic approach. In the classical limit, the well known Lie algebraic treatment of the corresponding classical theory is obtained. As examples, quadrupole and axially symmetric magnetic lenses are considered. An extension of the theory to the cases of electrostatic and other electromagnetic lens systems is outlined. This work is complementary to an already known similar approach to the spinor electron optics based on the Dirac equation and provides the corresponding framework when the optics of charged particles, with or without spin, is described with scalar wave functions in the nonrelativistic and relativistic situations.

A new finite element method for spherically symmetric relativistic collapse

In a previous paper a mixed finite element-finite difference numerical method was used to model relativistic spherical collapse. The method was unsatisfactory in some cases, and a new method is described in this paper. Einstein's equations are written in a standard form, and a weighted residual, moving finite element method is applied to derive a discretization. Tests are made on static and pressureless collapse, in both Newtonian and. relativistic situations. Shocks are smoothed using an artificial viscosity, and the results are compared to finite difference codes for the Riemann shock tube problem. Some collapse and bounce models are made, and the resulting shock is investigated. The code seems to be fast and accurate, with reasonable shock descriptions.

Bound states of a charged particle and a dyon

Bound states of a charged particle in the field of a dyon are studied in the non-relativistic as well as the relativistic situations. In the relativistic case all angular momentum channels except the lowest are considered. Bound state energies and wavefunctions are calculated explicitly.