Lorentz Theory Research Articles

Quantization of Lorentzian 3D gravity by partial gauge fixing

D = 2 + 1 gravity with a cosmological constant Λ has been shown by Bonzom and Livine to present a Barbero–Immirzi-like ambiguity depending on a parameter γ. We make use of this fact to show that, for Λ >0, the Lorentzian theory can be partially gauge fixed and reduced to an SU(2) Chern–Simons theory. We then review the already known quantization of the latter in the framework of loop quantization for the case of space being topologically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity.

Radiation reaction: general approach and applications, especially to electrodynamics

Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent c-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radiation heat bath, giving an exact result for the radiation reaction problem which has no unsatisfactory features such as the runaway solutions associated with the Abraham–Lorentz theory. In addition, we show how atomic energy and free energy shifts due to temperature may be calculated. Finally, we give a brief review of applications to Josephson junctions, quantum statistical mechanics, mesoscopic physics, quantum information, noise in gravitational wave detectors, Unruh radiation and the violation of the quantum regression theorem.

Spatially covariant theories of a transverse, traceless graviton: Formalism

General relativity is a generally covariant, locally Lorentz covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kucha\ifmmode \check{r}\else \v{r}\fi{}, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of local Lorentz covariance. In this paper, we explore modifications of general relativity that retain the same graviton degrees of freedom, and therefore explicitly break Lorentz covariance. Motivated by cosmology, the modifications of interest maintain explicit spatial covariance. In spatially covariant theories of the graviton, the physical Hamiltonian density obeys an analogue of the renormalization group equation which encodes invariance under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.

Density functional theory and multicomponent wave functions

AbstractSome consequences of using multicomponent wave functions are analyzed. In particular, paradoxical properties of a density functional derived from Dirac and Lévy‐Leblond equations are discussed. The application of a recently formulated N‐electron “relativistic Schrödinger theory,” based on a 4N‐component wave function, to the construction of a Lorentz and gauge covariant density functional theory is suggested. © 2012 Wiley Periodicals, Inc.

Optical and electrical properties of CuS nanoparticles in terahertz frequency

The spectral response of the mixture composed of CuS nanoparticles and polyethylene powder was measured by the terahertz time-domain spectroscopy (THz-TDS). The low-frequency optical properties of pure CuS nanoparticles, including absorption coefficient, complex dielectric constants as well as conductivity, were calculated by the effective medium theory. The Lorentz theory of dielectric response and the Drude-Smith model of conductivity provide good fits on the measured dielectric function as well as conductivity, respectively. In addition, some terahertz optical properties, such as the frequency of the lattice vibration and the time constant for the carrier scattering, are also obtained by the fitting. Our investigation could help to reveal the material properties in the terahertz range and to find out the promising physical effect for special application.

Effective Magnetic Permeability Measurement in Composite Resonator Structures

This paper studies the measurement of magnetism in the structured arrays of resonators. In a recent study, we showed how the unit-cell setup is a representative of the magnetic behavior of a whole structure composed of sufficiently long resonators. Here, we investigate the limits and the validity of such a setup for the characterization of metamaterials composed of finitely long resonators having a length that is smaller than the cell dimensions. According to Lorentz's theory, we show the spatial regions over which to average the effective field, and we derive the expression of the effective magnetic permeability for the unit-cell setup and for an extended structure. To test our conjecture, we compare experimental results that are performed on the unit-cell setup to solutions of an equivalent circuital model and to measurements that are directly obtained on a 3 × 3 structured array. Finally, we comment on the operative meaning of the measurement of the effective magnetic permeability in composite media.

On the application of the theory of Lorentzian plasma to calculation of transport properties of multicomponent arc plasmas

The application of the Lorentzian plasma theory for the calculation of the properties of multicomponent electric arc plasma is considered. It is shown that this model gives satisfactory results in the temperature range, which is corresponding to the weakly ionized arc plasma and arc plasma with dominant first ionization. The calculations are provided for the arc plasmas of noble gases and their mixtures between them and also that with metals. It is also pointed that the discrepancy between the electron temperature and gas temperature can be significant even at relatively weak electric fields, that fact must be taken into account under the simulation of arc discharges.

Resolution of the Abraham–Minkowski controversy

The momentum of light inside ponderable media has an electromagnetic part and a mechanical part. The local and instantaneous density of the electromagnetic part of the momentum is given by the Poynting vector divided by the square of the speed of light in vacuum, irrespective of the nature of the electromagnetic fields or the local or global properties of the material media. The mechanical part of the momentum is associated with the action of the electromagnetic field on the atomic constituents of the media, as specified by the Lorentz law of force. Proper interpretation and application of the Maxwell–Lorentz equations within the material bodies as well as at their surfaces and interfaces is all that is needed to obtain a complete picture of the momentum of light, including detailed numerical values at each and every point in space and time. That the Abraham–Minkowski controversy surrounding the momentum of light inside material media has persisted for nearly a century is due perhaps to an insufficient appreciation for the completeness and consistency of the macroscopic Maxwell–Lorentz theory, inadequate treatment of the electromagnetic force and torque at the material boundaries, and an undue emphasis on the necessity of coupling the equations of electrodynamics to those of the theory of elasticity for proper treatment of mechanical momentum. The present paper reports the resolution of the Abraham–Minkowski controversy within the framework of the classical theory of electrodynamics, without resort to such complicating and ultimately unnecessary factors as pseudo-momentum, special surface forces, alternative energy–momentum tensors, and hidden momenta, that have caused so much confusion for such a long period of time.

Gauge-invariant summation of All QCD virtual gluon exchanges

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying a physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. Similar but more complicated integrals will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al.

Polarized microwave forward model simulations for tropical storm Fanoos

In the present study, forward radiative transfer simulations are carried out for the tropical cyclone Fanoos that hit the coast off south India in December 2005. The in-house radiative transfer package used for this study employs the doubling and adding method to calculate radiances leaving the top of the one dimensional precipitating atmosphere. The particle drop size distribution is assumed to follow a modified gamma distribution in respect of the cloud liquid water and cloud ice water content. For precipitation, the Marshall-Palmer particle size distribution is used. All the hydrometeor particles are assumed to be spherical and Lorentz Mie theory is used to evaluate the interaction parameters like absorption, scattering coefficients and polarized scattering matrix. In order to validate the drop size distributions and interaction parameter calculations, the simulated brightness temperatures are compared with the TMI measured brightness temperatures for all the channels. For carrying out this exercise, vertical hydrometeors retrieved by TMI are used as input. The differences between simulated and measured brightness temperatures are found to be within ±10%. The maximum difference in the brightness temperatures between the present work and the Eddington model which the TRMM algorithm employs is about 4.5K. This may become significant when retrieval of precipitation is attempted by combining the forward model with a suitable retrieval strategy, under tropical conditions.

Hendrik Antoon Lorentz: his role in physics and society

Hendrik Antoon Lorentz (1853–1928) was appointed in 1878 to a chair of theoreticalphysics at the University of Leiden, one of the first of such chairs in the world. A few yearslater Heike Kamerlingh Onnes became his experimental colleague, after vehementdiscussions in the faculty. Lorentz strongly supported Kamerlingh Onnes then, andproved subsequently to be an ideal colleague. With Lorentz’s electron theory theclassical theory of electromagnetism obtained its final form, at the time oftencalled the Maxwell–Lorentz theory. In this theory the Zeeman effect could beexplained: the first glimpse of the electron. The Nobel Prize followed in 1902.The Lorentz transformation, established in 1904, preceded the special theory ofrelativity. Later on, Lorentz played a much admired role in the debate on the newdevelopments in physics, in particular as chairman of a series of Solvay conferences.Gradually his stature outside of physics grew, both nationally as chairman ofthe Zuiderzee committee and internationally as president of the InternationalCommission on Intellectual Cooperation of the League of Nations. At his funeral theoverwhelming tribute was the recognition of his unique greatness. Einstein said abouthim ‘He meant more to me personally than anyone else I have met on my life’sjourney’.

Philosophical Issues in Electromagnetism

AbstractThis paper provides a survey of several philosophical issues arising in classical electrodynamics arguing that there is a philosophically rich set of problems in theories of classical physics that have not yet received the attention by philosophers that they deserve. One issue, which is connected to the philosophy of causation, concerns the temporal asymmetry exhibited by radiation fields in the presence of wave sources. Physicists and philosophers disagree on whether this asymmetry reflects a fundamental causal asymmetry or is due to statistical or thermodynamic considerations. I suggest that an explanation appealing to the asymmetry of causation is more promising. Another issue concerns the conceptual structure of the theory. Despite its empirical success, classical electrodynamics faces serious foundational problems. Models of charged particles involve what by the theory's own lights are idealizations, I maintain, and this is a feature that is not readily captured by traditional philosophical accounts of scientific theories. Other issues I discuss concern (i) the relation between Lorentz's theory of the electron and Einstein's Theory of Special Relativity; (ii) the notion of the domain of a theory, the question of theory reduction, and the relation between classical and more fundamental quantum theories; and (iii) the role of locality constraints, their relation to the concept of causation; and the status of locality conditions in the semi‐classical theory of the Aharanov‐Bohm effect.

Higher-derivative 3-algebras

Starting with the N=8 supersymmetric Yang-Mills theory on D2-branes and incorporating higher-derivative corrections to lowest nontrivial order, we perform a duality to derive the Lorentzian 3-algebra theory along with a set of derivative corrections. We find that these corrections can be expressed entirely in terms of intrinsic 3-algebra quantities: the 3-bracket and covariant derivatives. Our analysis is performed for both bosonic and fermionic terms. We conjecture that the derivative corrections we obtain are relevant for Euclidean 3-algebra theories as well.

A massive study of M2-brane proposals

We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the mass-deformed theory on N M2-branes: that there should be a set of discrete vacua in one-to-one correspondence with partitions on N. For the mass-deformed Lorentzian three-algebra theory, we find only a single classical vacuum, casting doubt on its M2-brane interpretation. For the mass-deformed ABJM theory, we do find a discrete set of solutions, but these are more numerous than predicted. We discuss possible resolutions of this puzzling discrepancy. We argue that the classical vacuum solutions of the mass-deformed ABJM theory display properties of fuzzy three-spheres, as expected from their gravitational dual interpretation.

Drawing the line between kinematics and dynamics in special relativity

Special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it shows that various phenomena that were given a dynamical explanation in Lorentz's theory are actually kinematical. In his book, Physical Relativity, Harvey Brown challenges this orthodox view. I defend it. The phenomena usually discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena in the same class, each of which played a role in the early reception of special relativity in the physics literature: the Fresnel drag effect, the velocity dependence of electron mass, and the torques on a moving capacitor in the Trouton–Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. In the process, I draw attention to the broader importance of the kinematics–dynamics distinction.

Extraction of Constitutive Relation Tensor Parameters of SRR Structures using Transmission Line Theory

In this paper, the transmission line theory is utilized to characterize the metamaterials comprising of microscopic elements of a periodic array, specifically, the traditional split-ring resonators (SRRs), as an example. The bianisotropic property of the metamaterials is characterized in a new way different from the existing wave methods. As evident from both simulations and experiments, the SRR array structure is found to be quite lossy even though it is made of very good conductor or even perfect conductor as in simulation. With the present characterization, we are able to explain physically very well on how or why the energy gets lost in this structure. Finally, the theoretical result is compared with numerical simulation data obtained based on quasi-static Lorentz theory to further verify our analysis.

Broad-bandwidth and low-loss metamaterials: Theory, design and realization

In this paper, we summarize some recent activities in the field of metamaterial research at the National University of Singapore (NUS). Integral equations are applied for electromagnetic modelling of supernatural materials. Some special characteristics of the metamaterials are shown. Moreover, quasi-static Lorentz theory and numerical method (i.e., the method of moments for solving the electric field integral equation) and the transmission line theory are both presented to obtain the effective constitutive relations of metamaterials, respectively. Finally, feasibility of fabricating metamaterials based on analysis of equivalent transmission line model in the microwave spectrum and even higher is also shown and correspondingly some broad-bandwidth and low-loss metamaterial structures are designed and synthesized.

Structural Distinctions: Entities, Structures, and Changes in Science

I argue that the pessimistic meta-induction (PMI) seems to point an ontological priority of the relations over the objects of the scientific theories of the kind suggested by French and Ladyman (2003). My strategy will involve a critical examination of epistemic structural realism (ESR) and an historical case-study: the prediction of Zeeman's effect in Lorentz's theory of the electron.

Precipitation of asphaltenes from solvent-diluted heavy oil and thermodynamic properties of solvent-diluted heavy oil solutions

Ratios of n-heptane (hep) to toluene (tol) affect the solubility of the asphaltenes in heavy oil extraction processes. Consequently phase changes and time after mixing n-heptane and heavy oil in toluene are important for understanding produced emulsions. The kinetics of phase change when n-heptane is added to toluene-diluted heavy oils, and the thermodynamic properties of partially deasphalted heavy oils were studied. The methods used were monitoring precipitation in time using light microscopy, quantitative asphaltenes analysis by near infrared spectroscopy, refractive index and densities measurements, and calculated solubility parameters of mixtures. At critical mass ratios of hep/tol from 1.37 to 2.0 in diluted heavy oil the precipitated asphaltene particles were observed under the microscope after lag times from 2 h to instantly. Lag times were longer at low initial oil concentration. The floc growth time decreased as heavy oil concentration in toluene increased. The growth patterns in time appeared as dots to beads (strings) to clusters (fractal-like flocs). Final wt% precipitated asphaltenes vs. mass fraction (hep+tol)/heavy oil followed sigmoidal relationships. Curves showing wt% soluble asphaltenes vs. mass fraction hep/tol after 24 h initially followed the same shape as time zero curves and diverged at the onset ratios of hep/tol. Slope for precipitated asphaltenes vs. solubility parameters curve showed a break at 16.4 MPa 1/2. Linear correlations were established for concentrations of soluble asphaltenes in residual oils and density, for refractive index and density and for refractive index and solubility parameter. The latter correlation was in accordance with Lorenz–Lorentz theory. These equations provided a means by which oil density, refractive index and solubility parameter can be predicted when these measurements are difficult to measure practically.

QUASI-STATIC ANALYSIS OF MATERIALS WITH SMALL TUNABLE STACKED SPLIT RING RESONATORS

This paper presents a quasi-static analysis of a metama- terial consisting of a three-dimensional array of small tunable stacked split ring resonators (SSRRs). The resonance frequency of the pro- posed resonator structure can be controlled by adjusting the auxiliary lumped elements which are inserted between the split of each ring. In addition, the size of the ring resonator can be reduced to an order of 0.01λ that is one tenth that of the split ring resonator (SRR) by choosing the proper lumped elements. The analysis is based on the quasi-static Lorentz theory, and the generalized matrix representation of the macroscopic constitutive relations of the composite medium is calculated.