[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Physical Review B

Tables of integrals

Wave propagation and group velocity

The various experimental sectors of physics in which superluminal motions seem to appear are briefly mentioned. In particular, a bird's-eye view is presented of the experiments with evanescent waves (and/or tunneling photons) and with the "localized superluminal solutions" (SLS) to the wave equation, like the so-called X-shaped beams. The authors also present a series of new SLSs to the Maxwell equations, suitable for arbitrary frequencies and arbitrary bandwidths, some of them endowed with finite total energy. Among the others, the authors set forth an infinite family of generalizations of the classical X-shaped wave and show how to deal with the case of a dispersive medium. Results of this kind may find application in other fields in which an essential role is played by a wave equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.).

On the localized superluminal solutions to the Maxwell equations

General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams

It is now well known that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group velocities $(0l{v}_{\mathrm{g}}l\ensuremath{\infty}).$ Some of them, which are rigidly moving and have been called localized solutions, attracted large attention. In particular, much work has been done with regard to the superluminal localized solutions (SLSs), the most interesting of which are the ``X-shaped'' ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinary-speed waves. In this paper we show, by contrast, that even a superluminal charge creates an electromagnetic X-shaped wave: namely, on the basis of Maxwell equations, we are able to evaluate the field associated with a superluminal charge (under the approximation of pointlikeness): It results in constituting a very simple example of a true X wave.

Localized X-shaped field generated by a superluminal electric charge.

In the context of the paraxial regime, usually valid for optical frequencies and also in the microwave spectrum of guided waves, the propagation of electromagnetic fields can be analyzed through a paraxial wave equation, which is analogous to the nonrelativistic Schroedinger equation of quantum mechanics but replacing time t with spatial coordinate z. Considering that, here it is shown that for lossless media in optical frequencies it is possible to construct a Lagrangian operator with an one-to-one correspondence with nonrelativistic quantum mechanics, which allows someone to use the same mathematical methods and techniques for solving problems. To demonstrate that, we explore a few applications in optics with increasing levels of complexity. In the spirit of a Hamiltonian formulation, the ray-tracing trajectories of geometric optics in paraxial regime are obtained in a clear manner. Following that, the gauge symmetries of the optical-field Lagrangian density is discussed in a detailed way, leading to the general form of the interaction Hamiltonian. Through the use of perturbation theory, we discuss a classical analog for a quantum not gate, making use of mode coupling in an isotropic chiral medium. At last, we explore the optical spin Hall effect and its possible applications using an effectivemore » geometric optics equation derived from an interaction Hamiltonian for the optical fields. We also predict within the framework of paraxial optics a spin Hall effect of light induced by gravitational fields.« less

Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect

An X-shaped localized pulse based on a zero-order Mathieu function is obtained by a proper superposition of Mathieu beams, and some properties are analyzed.

Cesar Augusto Dartora

Papers

On the localized superluminal solutions to the Maxwell equations

General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams

Localized X-shaped field generated by a superluminal electric charge.

Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect

Properties of a localized Mathieu pulse.