Minkowski Form Research Articles

On graviton–photon conversions in magnetic environments

Graviton–photon conversions in a given external electric or magnetic field, known as the Gertsenshtein mechanism, are usually treated using the four-potential for photons. In terms of the electric and magnetic (EM) fields, however, proper identification of the fields in curved spacetime is important. By misidentifying the fields in Minkowski form, as is often practiced in the literature, we show that the final equation for photon conversion is correct in transverse-tracefree gauge only for planar gravitational waves in a uniform and constant external field. Even in the former method, to recover the EM fields from the four-potential in curved spacetime, one should properly take into account the metric involved in the relation. By including the metric perturbation in the graviton conversion equation, we show that a magnetic environment can cause tachyonic instability term in gravitational wave equation.

Isotropic Durgapal IV fluid sphere in bigravity

We analyze an isotropic uncharged fluid sphere model within bigravity considering the Durgapal IV metric (M.C. Durgapal, J. Phys. A: Math. Gen. 15, 2637 (1982)). In this work, we investigate the effects of the scale parameter k on the local matter distribution. Here, we have chosen the compact star candidate SMC X-1 with observed values of mass = (1.29 ± 0.05) M⊙ and radius [Formula: see text] km, respectively, to analyze our results analytically as well as graphically. For smaller values of k, we get the stiff (or hard) equation of state (EoS). Here, we solve the modified Einstein field equations in the presence of the background metric γμν. Due to this constant curvature background, the density and pressure terms are modified by adding an extra term, which affects the EoS. For r ≪ k, the background de Sitter space–time reduces into Minkowski form, and the coupling vanishes. We discuss certain physical quantities of our obtained solution, such as density, isotropic pressure, sound speed, pressure-density gradients, compactness, and surface redshift, to claim the physical viability of our model. It is found that our model clearly satisfies all the energy conditions, the causality condition, and the dynamical equilibrium via a modified Tolman–Oppenheimer–Volkov equation. Finally, we can conclude that our proposed model is physically realistic and well behaved.

On the origin of photon mass, momentum, and energy in a dielectric medium [Invited

The debate and controversy concerning the momentum of light in a dielectric medium (Abraham vs Minkowski) is well-known and still not fully resolved. In this paper, we investigate the origin of both momenta in the frame of special relativity by considering photons in media as relativistic quasiparticles. We demonstrate for the first time to the best of our knowledge that the Minkowski form of the photon mass, momentum, and energy follows directly from the relativistic energy conservation law. We introduce a new expression for the momentum of light in a dispersive medium, consistent with the experimentally observed propagation of photons at the group velocity. Finally, the effect of light-induced optical stretching is discussed, which can be used for experimental verification of the existing expressions for the photon momentum.

Example of a simple thought experiment that goes in favor of the Minkowski form of the photon momentum in medium

A novel approach to the Abraham-Minkowski dilemma based on a simple thought experiment is presented. The mathematical analysis of the simple thought experiment, which is based on a plane, monochromatic, uniform electromagnetic wave that propagates through the infinite, homogeneous, linear and isotropic dielectric medium without losses and impinges the surface of a perfect mirror, shows that the presented thought experiment goes in favor of the Minkowski form of the photon momentum in medium.

New Theory of Light and Resolution of the Abraham-Minkowski Controversy

The Abraham-Minkowski controversy about the momentum of light in media has been debated for over a century and has been informed by many distinguished distributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of momentum are need to be modified according to the new theory of light. We prove that the total momentum of a photon in matter is the same as compared with that in free space by using the new relations between energy and mass of light with refractive index.

A level-set method for magnetic substance simulation

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.

Dozen arguments in favor of the Minkowski form of the momentum of light in matter

We present arguments based on various physical phenomena that the light pulse in the optical medium corresponds to the Minkowski approach and is n times larger than that in free space, where n is the reflective index of the optical medium. Then we refute a single opposite argument in the form of the Balazs thought experiment, according to which the Abraham approach is correct and the momentum of light in the optical medium decreases by n times. Thus, after a dozen arguments presented in favor of the Minkowski approach, we conclude that the age-old debate about a magnitude of the momentum of light in an optical medium should be completed in favor of Minkowski.

Possible solution of Abraham–Minkowski controversy by generalizing the principle of invariance of light speed

Abraham–Minkowski controversy has been discussed from both classical and quantum levels. Here, we shall show that, assuming to generalize the principle of invariance of light speed from vacuum to lossless linear isotropic homogeneous media (LLIHM), a new type of covariant formulations of classical electrodynamics for LLIHM may be derived, which are similar to that for vacuum, and thus, Minkowski form of electromagnetic wave momentum density is obtained from a diagonally symmetric energy–momentum tensor. On the other hand, the momentum–energy relation is modified due to generalization of principle of invariance of light speed, and then, only the Minkowski momentum is obtained by applying wave–particle duality of a photon. Our work reveals close relationship between the principle of invariance of light speed and the Abraham–Minkowski controversy, which may be helpful to deeply understand Abraham–Minkowski controversy.

Another argument in favor of the Minkowski form of the momentum of light in matter

Magnitudes of the momentum of light are compared in a two situations where identical ideal reflectors are moving at identical speeds towards the light waves of identical energy density fluxes propagating in free space and in an optical medium. First, increases of frequencies the reflected waves are compared. Based on the Doppler law, it is shown that an increase of the frequency of the reflected wave in the second case is greater by n times as compared with that in the first case where n is the reflective index of the optical medium. Second, it is shown that an increase of the energies of the reflected wave in the second case is also by n times greater than that in the first one. As a result, the pressure on the reflector is greater by n times in second case than that in the first one. Third, it is shown that the pressure on the reflector is produced due to a change of the momentum density flux of the wave reflected from the reflector. Since the pressure on the reflector in the second case is greater by n times than that in the first case, a conclusion is made that the momentum flux density of the wave propagating in an optical medium is greater by n times than that of the wave propagating in free space provided that the energy density fluxes of these waves are identical.

Quaternionic representation of electromagnetism for material media

In this study, the electromagnetic fields are developed in the presence of both the electric and magnetic induction fields by quaternion algebra. In this sense, the polarization and magnetization effects, which are valid in the material media, gain much importance. Quaternions are one of the most convenient tools for representing electromagnetism with regard to having non-commutative but associative algebraic division ring. By defining the quaternion induction field, the quaternion source term has been obtained in basic and elegant notation for the first time. In addition, one type of Poynting theorem, named as the Minkowski form, has been presented including the permittivity and permeability constants by quaternions.

Additional arguments in favor of the Minkowski form of the momentum of light in matter

Two situations are considered. First, the equation of photon motion in an inhomogeneous optical medium, obtained from the laws of mechanics, is compared with the eikonal equation in optics. The equations are identical provided that the photon momentum in the optical medium changes in such a way that the momentum in the medium where the photon is located at given time exceeds the momentum in free space by a factor n. Second, a plane optical resonator partially filled with an optical medium is considered. It is shown that the momentum in the optical medium increases in direct proportion to the energy density of the light wave, which is proportional to n.

Momentum of a wave of any physical nature in a context of the Abraham-Minkowski dilemma

We consider the known Abraham- Minkowski dilemma about the momentum of light wave in matter from point of view a general approach to the momentum of any wave of any type, the energy of which is different from zero. We show that the wave has a momentum. The momentum density flow is in inverse proportion with the wave velocity and is equal to the energy density. As a particular case, the momentum of light wave in matter is proportional to its reflective index and, therefore, the momentum of light in matter corresponds to the Minkowski form.

Abraham-Minkowski dilemma in the light of the first principle

A novel approach to the Abraham-Minkowski dilemma based on the first principle is presented. Typically the Abraham form of the photon momentum has been considered to be inherent to the particle nature of photon. However, it was shown that by taking into consideration only the photon characteristics as a particle and implementing energy conservation law in the presented simple thought experiment the Minkowski form of the photon momentum also appears.

The momentum of an electromagnetic wave inside a dielectric derived from the Snell refraction law

Author of the paper [M. Testa, Ann. Physics 336 (2013) 1] has derived a conclusion that there is a connection between the Snell refraction law and the Abraham form of the momentum of light in matter. In other words, author derived the Snell law on assumption that the momentum of light in matter decreases by n times as compared with that in free space. The conclusion is derived under assumption that the forces exerted on an optical medium by an electromagnetic field do not distinguish between polarization and free charges. We show that, on the contrary, the Minkowski form of the momentum of light in matter directly follows from the Snell law. No previous assumption is required for this purpose.

Frozen time in hyperbolic spacetime motion

According to the Lorentz transformation and as clearly seen from the Minkowski diagram, hyperbolic spacetime motion of a test object relative to a stationary reference frame can be performed in a specific way such that time becomes frozen in the moving frame of the test object. In that case, time can be arranged to become frozen even at moderate relativistic velocities, in contrast to the minute traditional relativistic time dilation at such velocities. In the appendix, we give a simple illustration, in Minkowski form, of how time in a frame in hyperbolic motion can become frozen to a complete standstill relative to a stationary frame.

Noether derivation of exact conservation laws for dissipationless reduced-fluid models

The energy-momentum conservation laws for general reduced-fluid (e.g., gyrofluid) models are derived by Noether method from a general reduced variational principle. The reduced canonical energy-momentum tensor (which is explicitly asymmetric and has the Minkowski form) exhibits polarization and magnetization effects associated with dynamical reduction. In particular, the asymmetry in the reduced canonical momentum-stress tensor produces a nonvanishing reduced intrinsic torque that can drive spontaneous toroidal rotation in axisymmetric tokamak plasmas.

Penrose diagram for a transient black hole

A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, and then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of the Minkowski form. Coordinate curves on the diagram are computationally derived. Causal relationships between spacetime regions are briefly discussed. The life cycle of the black hole demonstrably leaves asymptotic observers in an unaltered Minkowski spacetime of uniform conformal scale.

On energy and momentum conservation laws for an electromagnetic field in a medium or at diffraction on a conducting plate

For a field-matter system, general nonstationary balance equations for energy and momentum densities and their transport velocities are obtained based on a rigorous nonstationary definition of these densities depending on the creation history of the field. We analyze the simplest dispersion law determined by conductivity dissipation; we find the electromagnetic energy density, phase velocity, group velocity, and energy and momentum transport velocities of a plane monochromatic wave. The low-frequency energy density is shown to be given by the electrostatic density in which the dielectric constant is replaced with its real part and the energy transport velocity is equal to the phase velocity. The group velocity can exceed the speed of light. We prove that the Minkowski form of momentum density must be used in the medium, and find the corresponding transport velocity, which in the case under consideration also coincides with the phase velocity. Energy and momentum conservation laws are shown to hold for a plane electromagnetic wave propagating in a medium or diffracted by a conducting plate.

The enigma of optical momentum in a medium

It is 100 years since Minkowski and Abraham first gave rival expressions for the momentum of light in a material medium. At the single-photon level, these correspond, respectively, either to multiplying or dividing the free-space value () by the refractive index (n). The debate that this work started has continued till the present day, punctuated by the occasional publication of ‘decisive’ experimental demonstrations supporting one or other of these values. We review the compelling arguments made in support of the Minkowski and Abraham forms and are led to the conclusion that both momenta are correct. We explain why two distinct momenta are needed to describe light in a medium and why each appears as the natural, and experimentally observed, momentum in appropriate situations.

Resolution of the Abraham-Minkowski Dilemma

The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.