• Issue 43 / July - September 2003

    The Search for Gravitational Waves

    Melvin A. Lewis

    Gravitational waves released from cataclysmic events in our galactic neighborhood are 40 orders of magnitude weaker than Coulomb forces and are nearly undetectable on Earth. One order of magnitude is a factor of ten. These waves originate in nature as we speak, having been sent on their way, perhaps thousands or millions of years ago, as a result of such distant events as exploding stars (supernovas), coalescing black holes, and less dramatic binary stars in their routine orbiting of each other. Gravitational wave astronomers have developed unique antennas and the associated signal processing hardware to capture these waves, which are described as "distortions in space-time," as opposed to the more customary field terminology of electromagnetics. Unlike radio waves, however, gravitational waves from astronomical sources have not been conclusively detected yet.

    Defining the target

    Gravitational waves are generated only by the equivalent of a rotating or oscillating system -- that is, two or more masses accelerating toward or away from each other and exhibiting a quadrupole moment of inertia.

    Only such quadrupole and higher multipole sources can generate gravitational waves because, whereas there are negative electric charges, there are no negative masses. A negative electric charge oscillating back and forth is the equivalent of a positive charge moving in the opposite direction, and this equivalence enhances the generation of electromagnetic waves. Since there is just one gravitational polarity, however, a mass can oscillate only with respect to a counterweight. This counterweight reacts to the oscillation and generates a gravitational disturbance that almost, but not quite, cancels the disturbance of the body.

    As explained by physicist Paul Davies of Australia's University of Adelaide, the gravitational disturbances would completely cancel out but for the time required for them to travel between the masses. It is this out-of-phase imbalance in the disturbance's cancellation that propagates a gravitational wave. For this reason, such waves are not generated by quiescent stars, those rotating on their axis symmetrically or even exploding symmetrically, because there is no quadrupole moment. However, that situation changes if they explode asymmetrically or change their shape.

    On the other hand, a typical binary star system has a quadrupole moment and should produce a slow periodic gravitational wave. A near-enough binary star system would cause a measurable distortion a little in excess of one part in 1021 on Earth.

    For the wave to lie in the gravitational-wave detector's frequency range (typically 1000 +/-1 Hz.), though, the two stars of the binary must be in the final stage of coalescing, a rare situation. For comparison, a supernova is expected to produce damped exponential impulse waveforms, each of which lasts for 1 millisecond. A collision or collapse of a binary system between two neutron stars, or between a neutron star and a black hole, would produce gravitational waves with a sliding frequency in the 1 to 1000 Hz range, as one star spirals in on its partner.

    Why are we searching?

    A long time ago, in the Large Magellanic Cloud-one of our Milky Way's two companion galaxies, a star exploded. In 1987, 160,000 years later, radiation from that event finally reached Earth. The first to see the brightening star were astronomers in the southern hemisphere.

    Scarcely 24 hours earlier, in other parts of the world, other types of detectors had "seen" something. At the University of Rome (Italy) and the University of Maryland at College Park (the U.S.), gravitational-wave detectors registered 12 fairly large and about 100 small pulses over a period of 2 hours. Around the same time, the Mont Blanc Neutrino Observatory (France) registered five pulses of neutrinos over a 7-second interval. Similar recordings were made by neutrino detectors in Kamioka, Japan, and Frejus, France.

    Astrophysicists are still debating the significance of those observations recorded on Feb. 23 and 24. But others claim the pulses registered in Rome and Maryland may have been due to actual gravitational radiation from an identifiable source -- the supernova of 1987.

    Physicists find this ambiguity unsatisfactory. They want to detect the gravitational waves themselves, directly and unequivocally. Indeed, the detection of waves has been called "the most important of all tests" of Einstein's general theory of relativity by theoretician Kip S. Thorne of the California Institute of Technology (CalTech) in Pasadena. The sensing or reception of gravitational waves also may deepen astronomers' understanding of the dynamics of such violent events as supernovas, exploding black holes, and the interactions between black holes and neutron stars. As a bonus, whatever is learned about detecting ultra-weak signals might help engineers measuring extraordinarily small displacements or strains.

    The understanding, according to Einstein's general theory of relativity, is that all objects exist in four-dimensional space-time (that is, in a continuum having three dimensions of space and one of time). The mass of every object curves space-time, a curvature that manifests itself as the gravitational field of the mass. The greater the mass, the greater the curvature of space-time, and the greater the gravitational field.

    According to the same theory, massive objects that rotate or explode asymmetrically, or oscillate, give off gravitational waves or ripples that propagate through space-time, like ripples or waves on the surface of the ocean.

    Gravitational waves conform to an inverse square law relationship, just like electromagnetic waves. The force of both types of energy declines in proportion to the square of their distance from their source. But gravitational waves are so much weaker than the Coulomb electric force, which renders the detection of such weak waves a monumental challenge to instrumentation.

    The evidence that gravitational waves exist is compelling, albeit indirect. The firmest evidence relies on observations made over 7 years by astronomers Joseph Taylor, of Princeton University in New Jersey, and Russell Hulse, then at the University of Massachusetts at Amherst but now also at Princeton. Their measurements of radio waves from a binary pulsar designated PSR1913+16 show that the pulsar's 8-hour orbit around the neutron star is gradually contracting; the faster the pulsar revolves around the neutron star, the smaller its orbit gets. As the rate of decrease agrees to within 0.5 percent with predictions derived from the general theory of relativity, the finding is excellent circumstantial evidence for orbital decay being a result of energy lost by gravitational radiation. Even though the gravitational radiation itself was not detected, Taylor and Hulse shared the 1993 Nobel Prize in Physics for this work.

    But what would it take to observe the weak gravitational radiation directly? Gravitational waves are generally believed to travel at the speed of light and to deform or distort an object geometrically as they pass through it. For plane-polarized gravitational waves, the two directions are at 45 degrees to each other, not perpendicular as they are for light. In other words, a passing gravitational wave distorts an object first in one direction, then (in the next half-cycle) in another, rotated at a 45-degree angle to the initial direction. It takes another half gravitational wave cycle for the wave to distort at the 90-degree angle characteristic of electro-magnetic waves in the first half-cycle.

    Resonant bar detector

    In principle, it should be possible to sense this distortion and its after-effects with the aid of strain detectors attached to a suitable "antenna" -- a space-time seismometer, if you will. But such an antenna resembles nothing familiar to electrical engineers. In its simplest manifestation, the antenna is a large solid cylindrical bar.

    The pioneering resonant-bar detector was designed in the late 1950s and built in the early 1960s by Joseph Weber, professor of physics at the University of Maryland. Weber's design called for a mechanically isolated cylinder of solid aluminum weighing several metric tons. Piezoelectric strain transducers attached at intervals around its circumference converted the vibrations induced by any passing gravitational wave into an electric signal. Weber's bar resonated mechanically around 1 kHz, so that it would "ring" after being distorted by an incoming damped-exponential wave, the shape expected of a gravitational wave from a supernova. Subsequently, other bar detectors were built at many institutions around the world.

    The main problem with resonant-bar antennas is their insensitivity. Even the latest of them yield dimensionless strain sensitivities of about one part in 1018 (that is, only 10-18 meter distortion per meter of length), too little to detect gravitational waves from any but the nearest and most violent events.

    The laser alternative

    The laser interferometer owes its sensitivity in detecting gravitational waves to an arrangement of mirrors suspended on vibration-isolated pendulums. Two pairs of mirrors create two light paths perpendicular to one another. A laser beam is split and the halves sent down each path, rebounding back and forth along the leg between the mirrors hundreds of times before being recombined. The multiple passes create the very long light path required to amplify the gravitational-wave input to detectable amplitude.

    In brief, if a gravitational wave passes by, the pendulums holding the mirrors are expected to move a little apart in one leg and a little together in the other leg, in each case by the same tiny fraction of the laser light wavelength. Their movement would shift the relative phase of the two halves of the laser beam, momentarily upsetting the interference patterns that would otherwise be cancelled out. At that instant, the interference pattern would brighten by an amount proportional to the strength of the gravitational wave. The job of monitoring the interference pattern for brightening is handled by electro-optic detectors, which indicate when a passing gravitational wave is detected and which recover its variation over time.

    Not only are laser-interferometer detectors potentially more sensitive than resonant-bar antennas, they are also better at detecting a variety of sources because they are inherently broadband. They respond to gravitational waves having a frequency from 10 Hz to 10 kHz, versus the resonant-bar antennas' 1-Hz bandwidth at 1 kHz.

    Input from space

    A third and truly exotic method of detecting gravitational waves has been proposed: monitoring the Doppler shift of the carrier frequency (or rather, the retransmission of the tracking station's frequency) from two or more interplanetary spacecraft simultaneously. This project is known as LISA (The Laser Interferometry Space Antenna).

    The technique is analogous to laser interferometry. The idea is to detect the Doppler shift in a spacecraft's microwave frequency as the craft is jostled by a passing gravitational wave -- that is, as space-time is warped in its vicinity.

    Inevitably, there are obstacles to overcome. Since the effects of a passing gravitational wave are so small, the reference oscillator must be extremely stable to detect any Doppler shift. Observers must also consider variations in the pressure of the solar wind (which differs from time to time and with the changing distance of the spacecraft from Earth), in forces from the attitude control thrusters (used to occasionally correct the space-craft's orientation), and in the refraction of Earth's atmosphere (through which the signal must travel). Subtracting all of these variations, the interplanetary detector is expected to have a theoretical sensitivity of about one part in 1016 -- corresponding to a displacement of about 0.065 mm over the shortest distance from Earth to Jupiter, and one-eighth of that over the shortest distance from Earth to Mars.

    The noise problem

    Noise degrades the sensitivity of any gravitational-wave receiver. The interference is mostly due to seismic activity in the earth, acoustic interference (also known as microphonics) from inhabited surroundings, and heat (thermal noise). Especially troublesome are the non-Gaussian tails of noise distribution, which produce a significant number of false detections.

    When a gravitational wave passes through the cylinder and distorts its shape, the moving input coil produces minute changes in the magnetic flux. That magnetic flux change then creates a relatively large variation in the voltage across the SQUID** junctions. In turn, these variations are passed along as voltage signals to succeeding stages of amplification -- generally room-temperature FET amplifiers with optimal filtering for the anticipated signals. If tuned mechanical transformers or resonators are installed between the antenna and the transducer, transfer of the gravitational wave's pulse is maximized and amplifier noise coupling is minimized.


    Much is being done to achieve a breakthrough in the detection of gravitational waves. A recent High Frequency Gravitational Wave conference held at MITRE Corporation featured proposals and experiment descriptions that could lead to an apparatus that uses gravitational waves for communications. Several large laser interferometer gravitational wave observatories are online and taking data while making sensitivity improvements. The reader is urged to delve further (see references below) to see why there is so much excitement about this new window on the universe.

    - Gibbs, W. W. "Ripples in Spacetime." Scientific American, April 2002.
    - Lewis, M. "Gravitational Waves versus Electromagnetic Wave Antennas." IEEE Antennas and Propagation Magazine 37, no. 3, June 1995. Also see
    - Blair, D. The Detection of Gravitational Waves. Cambridge Univ.: 1991.
    - Boughn, Stephen. "Detecting Gravitational Waves," American Scientist, no. 68. March-April 1980, 174-83. (An overview of the early work in the search for gravitational waves.)
    - Will, Clifford M. Was Einstein Right? New York: Basic Books, 1986. (A readable account of the binary pulsar PSR1913+16 and its role in providing evidence for gravitational waves.)
    - Blair, David G., ed. The Detection of Gravitational Radiation. England and New York: Cambridge Univ. Press, 1991. (Sums up the state of the art in gravitational-wave receivers.)
    - Misner, Charles, Kip S. Thorne, and John Wheeler. Gravitation. W. H. Freeman: 1973. (Still the most used book by students and practitioners in gravitational-wave research.)
    - Thorne, Kip S. Black Holes and Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton, 1994. See chapter 10: "The Ripples of Curvature," which summarizes plans for the Laser Interferometry Gravitational-Wave Observatory (LIGO).
    - E. Amaldi et al. "Coincidences among the Maryland and Rome Gravitational Wave Detector Data and the Mont Blanc and Kamioka Neutrino Detector in the Period of SN1987A." Annals of the New York Academy of Sciences, vol. 571, 1990, 561-76. (Proceedings of the l4th Texas Symposium of Relativistic Astrophysics). (Discusses whether or not gravitational waves were detected along with the first sightings of the 1987 supernova).
    - Grishchuk, Leonid. "Update on Gravitational Wave Research. Online at Los Alamos' website on preprints gr-qc/0305051, 13 May 2003. (Provides a more technical treatment.)

    ** A superconducting quantum interference device (SQUID) is a mechanism used to measure extremely weak signals, such as subtle changes in the human body's electromagnetic energy field.


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