## Saturday, March 22, 2014

### Gravitational Waves 1

Gravitational waves, in brief, are the propagations of gravitational fields through space. Before dealing with gravitational waves directly, we attempt to provide historical context and a way to visualize how the waves work.

In 1865, James Clerk Maxwell (1831-1879) published a paper outlining his theory of electromagnetism, compiling and uniting earlier work into a single theory explaining the properties of both electricity and magnetism. For example, it deals with the properties objects possessing positive and negative charges, and the forces they exert on their environments (electric and magnetic fields). This theory also describes electromagnetic waves, or propagating changes in the electromagnetic field. Such waves are characterized by their wavelength and amplitude.

The above simplified diagram of a wave shows its wavelength and amplitude. We also define the frequency of a wave as the number of oscillations per second. In the diagram above, the wave has a frequency of 2 Hz. For electromagnetic waves, amplitude corresponds to intensity of the wave, and wavelength to type (or in the case of visual light, color). The continuous interval of electromagnetic wavelengths is known as the electromagnetic spectrum and includes many familiar types of radiation, including radio waves, microwaves, infrared rays, visible light, ultraviolet rays, X-rays, and gamma rays (all of these types are discussed in the link above).

Such waves are produced when charged objects move through space, causing a change in electric field. When a charge has moved, it will not exert the same forces on its surroundings as it had previously. The change in field is "carried" by waves, which move at the speed of light, a finite (though very fast) speed. The diagram below shows an example of electromagnetic wave production by a dipole, or a pair of equal and opposite charges.

As the charges oscillate up and down, an electromagnetic wave is produced, and propagates away from the dipole (the blue and red parts of the oscillation are the electric and magnetic field components, respectively). Since the oscillation is periodic, the wave signal it produces is also periodic. The magnitude of the charges forming the dipole determines the amplitude of the generated wave. Also, the frequency of the oscillation determines the frequency of the electromagnetic waves.

At the beginning 20th century, though Maxwell's theory had supplanted earlier understandings of electromagnetism, Newton's was still the dominant paradigm for gravitation. The theories did have similarities, among them the fact that both electromagnetic and gravitational forces shrank with distance in inverse proportion with the square of this distance (F ~ 1/r2). However, while there were both attractive and repulsive electromagnetic forces, gravity was always an attractive force. Another crucial difference was that, as shown above, electromagnetic fields move at the speed of light. Newton's theory, though, simply assumed that all bodies pulled instantaneously on one another. Albert Einstein (1879-1955) developed the theory of general relativity in 1916 and resolved this difference. His theory predicted that differences in gravitational fields would move analogously to electromagnetic fields: using gravitational waves. Further, these postulated gravitational waves would travel at the speed of light.

Gravitational waves, in Einstein's theory, would also be produced in an analogous manner to electromagnetic waves. Instead of oscillating charges, oscillating masses would produce the waves. For example, two massive bodies (such as black holes) orbiting one another at close range would produce gravitational radiation, as in the diagram below.

The conception above illustrates how gravitational waves move away from the orbiting system in all directions. Unlike their electromagnetic counterparts, gravitational waves travel undisturbed through matter, and as a consequence are much more difficult to detect. Nevertheless, they do have a subtle effect on the matter which they pass through. The medium through which gravitational waves travel is the fabric of space itself. The diagram above illustrates distortions of a two-dimensional space fabric; in reality, gravitational waves would cause small "ripples" in our three-dimensional space.

Beginning in the 1960's scientists on Earth have constructed increasingly sophisticated gravitational wave detectors. The first variety were known as Weber bars, or large bars of metal which, if sufficiently isolated from the surrounding environment, could oscllate as gravitational waves passed through them. However, the waves had to be very strong to be detected, and the original models were not up to the task. More modern Weber bars have been supercooled to temperatures very near absolute zero to reduce outside vibrations and increase their sensitivity.

Another method for identifying incoming gravitational waves is known as laser interferometry.

Laser interferometry works by using light beams to measure distances. In the usual design (diagram above), a laser creates a beam of light which is split by a beam-splitting mirror into two beams which travel down the two perpendicular arms of the interferometer. On the return trip, if the arms are exactly the same length, the beams interfere with one another in such a way that all the light travels back to the laser. If, however, the arms have slightly different lengths, some light will be reflected by the beam-splitter into a detector.

The Laser Interferometer Gravitational-Wave Observatory (LIGO) wass one project making use of a laser interferometer to detect gravitational waves. In each of LIGO's facilities (there is one in Louisiana and one in Washington) there was a laser inteferometer with arms four kilometers (2.5 miles) long. Theory held that when a gravitational wave passes through the detector, it distorts space and actually alters the lengths of the arms slightly. Since the arms are perpendicular, the distortions are different, and sufficiently strong waves should then cause the laser beams to be enough out of sync to send light to the detector. There were two LIGO stations to weed out false data and to determine which way gravitational waves moved through the Earth. Despite the precision of LIGO, it did not make any unambiguous detections during its operation (2002-2010).

Despite these setbacks, concepts for more precise instruments and new detectors have since been developed, and the road to gravitational wave detection has also proceeded through more indirect means (see the next post).

Sources: http://www.britannica.com/EBchecked/topic/242499/gravity-wave, http://rsta.royalsocietypublishing.org/content/366/1871/1849.full, http://www.tapir.caltech.edu/~teviet/Waves/differences.html, http://www.geo.mtu.edu/~scarn/teaching/GE4250/EM_wave_lecture.pdf, http://ned.ipac.caltech.edu/level5/ESSAYS/Boughn/figure1.gif, http://upload.wikimedia.org/wikipedia/commons/3/35/Onde_electromagnetique.svg, http://www.vias.org/wirelessnetw/img/wndw-print_img_3.png, spaceplace.nasa.gov, http://en.wikipedia.org/wiki/Gravitational-wave_detector, http://www.learner.org/courses/physics/visual/visual.html?shortname=ligo_interfermometer, http://www.ligo-la.caltech.edu/LLO/overviewsci.htm