Nobel Lecture: LIGO and the discovery of gravitational waves I^*

Figure 1

An attempt at visualizing Einstein’s concept of gravity (the General Theory of Relativity) in which distortions in the geometry of space and time have replaced the gravitational force of Newton. Think of a jungle gym of rectangular bars in the three spatial dimensions. The intersection points of the bars are all evenly spaced and straight lines. Imagine also that a clock is placed at all the intersection points and that all the clocks read the same time at the same moment in time. The situation when there are no masses in the vicinity. Now, take a two-dimensional cut through the structure and place the Sun and Earth into the picture. The structure near the Sun and to a smaller extent that near the Earth is distorted. Also, although not shown, the clocks at the intersection points near the Sun and to a lesser extent those near the Earth run a little more slowly than those in the less distorted parts. The orbit of the Earth around the Sun is now dictated by the distortion of space and the time dilation—the path an object with no forces would follow in the new geometry.

Figure 2

A gravitational wave + polarization. Gravitational waves are emitted by accelerated masses. They propagate at the speed of light. Once they have become plane waves some number of wavelengths from their source they become transverse waves which cause a strain in space perpendicular to the direction in which they propagate. The strain stretches space in one dimension while simultaneously contracting space in a perpendicular dimension. The strain $h=\mathrm{\Delta }l/l$ is the change in distance between two places divided by their separation. The figure tries to show this by distributing a set of probe masses throughout space. The gravitational wave propagates perpendicular to the plane of the figure and the masses. Time evolves from the top left to the bottom right by going through one complete cycle of an oscillating strain. L in the figure symbolizes the LIGO detector. The thing to notice is the change in length of the arms of the L which becomes the measurable in the detector. The longer the arms the larger is the measurable displacement signal. The extension of one arm with the contraction of the other arm enables the use of a Michelson interferometer which is specifically sensitive to the difference in light travel time along the two arms.

Figure 3

Russell Hulse and Joseph Taylor were awarded the Nobel Prize in Physics in 1993 for the discovery of the binary pulsar system, which became a remarkable test laboratory for general relativity. They were able to measure relativistic periastron precession of $4\mathrm{deg}/\mathrm{yr}$ and many other relativistic dynamical effects which allowed them to solve for the individual masses of the neutron stars. As shown in Fig. 4 they solved for the dynamics of this system and minimized the residual between their data and the full relativistic model of the motion; to do this it was necessary to include the loss of energy by the system to gravitational radiation.

Figure 4

The change in orbital period of the binary pulsar as a function of epoch. The dots indicate the measured reduction of the orbital period as the neutron stars lose total energy by radiation of gravitational waves. The line is the expectation from the General Theory of Relativity. The system was the first to show the effects of gravitational radiation and also provided the first demonstrated source of gravitational waves for direct detection. As Barry will show, the coalescence of a pair of neutron stars has been detected by LIGO and VIRGO. From [15].

Figure 5

Joseph Weber was the first to attempt to detect gravitational waves from astrophysical sources directly. The concept for doing this was generated by John Wheeler and Weber at the 1957 Chapel Hill conference on gravitation. The idea was to measure the distortions induced by a gravitational wave in a cylinder. Instead of thinking of the gravitational wave as a strain in space, they thought of the wave as exerting tidal forces on the cylinder and calculated the motion of the bar as an oscillator in inertial space. The tidal force was just another Newtonian force on the bar. Weber imagined short pulses of gravitational waves with some Fourier components at the resonant frequency of the cylinder. The wave would pass through the cylinder and leave it ringing. In the picture on the right, Weber is attaching some strain gauges to the cylinder to measure the excitation. The cylinder is placed in the vacuum chamber (behind him) when searching for gravitational waves.

Figure 6

Schematic of a Michelson interferometer used as a gravitational wave detector. The gravitational wave at a low frequency $f_g$ is incident from above the plane of the interferometer. Start by following the light from the laser to the symmetric port of the beam splitter ($+$ no phase inversion of the light on reflection). The laser generates carrier light (red amplitude). The violet vectors indicate the propagation direction of the light. The laser light that gets reflected by the beam splitter heads to the mirror on test mass 1 reduced by the reflectivity of the beam splitter. On reflection from test mass 1, which is moving due to the gravitational wave, the carrier generates two sidebands one at a frequency $f_g$ above the carrier (blue) and another $f_g$ below (green). The beam heads back to the beam splitter. The beam from the laser that gets transmitted by the beam splitter heads toward test mass 2; the carrier is reduced by the transmission of the beam splitter. That beam on reflection from test mass 2 also gets two sidebands from the motion of the test mass 2, but they have the opposite sign because the gravitational wave is compressing space on the test mass 1 side while expanding space on the test mass 2 side. The beam from test mass 2 gets reflected toward the detector from the antisymmetric port of the beam splitter (the phases of the carrier and the sidebands are inverted). The beam from test mass 1 is transmitted by the beam splitter toward the detector. The beams from the two sides of the interferometer are added. If the paths on the two sides take equal time from the first encounter with the beam splitter to the second one (or take a difference in time that is an integral number of periods of the light wave), the carrier cancels while the sidebands double at the detector. The sidebands carry the information about the gravitational wave to both the wave amplitude and the phase. To make the sidebands detectable as a current in the photodetector requires a small amount of carrier to beat against the sidebands.

Figure 7

Bottom left: F. A. E. Pirani, who showed that it is possible to measure the relative motion of two free masses traveling through a gravitational wave (so-called geodesic deviation) in a coordinate-independent manner, a critical idea that was not fully accepted until the 1957 Chapel Hill Conference. Bottom middle: A schematic diagram of an interferometric gravitational wave detector with suspended masses, multiple passes along the interferometer arms and a technique to reduce the amplitude noise of the laser light. Bottom right: The 1.5-meter prototype at MIT and the three graduate students who constructed and operated it. Top line: The gravity research group at the Max Planck Institute of Astrophysics in Garching, Germany, who built a 3-meter interferometer prototype and then a 30-meter one to show that the idea scaled properly. The group invented many of the solutions for the noise in these systems including the idea of suspending all the optics in the phase sensitive part of the interferometer and the need to frequency stabilize the laser to deal with scattering by stray light. Schnupp came up with the idea to make a slight imbalance in the interferometer arms to use external phase modulation. Schilling invented the idea of power recycling to increase the modulated light in the interferometer. Middle line: The gravity research group in Glasgow, Scotland, Drever developed Fabry-Perot cavities as multipass elements in the interferometer arms and also invented the idea of power recycling ([2]). Brian Meers ([10]) was the first to suggest putting another partially reflecting mirror between the photodetector and the beam splitter to tailor the interferometer spectral response by reflecting the sidebands back into the main interferometer arms. Ward developed a method to align the interferometer.

Figure 8

The abstract of the paper on the 30-meter interferometer operated by the Max Planck Group in Garching showing that an interferometer had attained better sensitivity than the best cryogenic Weber bar detectors. The 30-meter results were important in helping to make the case for long baseline instruments such as LIGO. The top two photos are of the 40-meter instrument constructed at Caltech by Whitcomb and Drever. The 40-meter at Caltech and the 5-meter at MIT (Fig. 13) were the final test beds for the first LIGO detector.

Figure 9

Kip Thorne around 1980 with his measurement challenge to the experimenters based on his and others’ estimates of possible astronomical gravitational wave source dynamics and populations.

Figure 10

In 1979 the NSF supported a study ([9]) with industry to look at the feasibility of building a multikilometer baseline interferometric gravitational wave detector. The study summarized the current state of prototype research and estimates for gravitational wave sources. It looked at the ability of industry combined with academic research to develop adequate optics, lasers, vibration isolation and control systems to meet the scientific requirements. The designs and costs of the vacuum system and the buildings as well as cost scaling relations were developed. Possible sites for up to 10 km baseline systems both above and below ground were investigated. One of the intents of the study was to be the factual basis for a proposal to the NSF by a consortium of scientists and institutions to build a pair of detectors in the United States.

Figure 11

The 1989 proposal ([16]) to build and operate LIGO. Rochus (Robbie) Vogt, who had become Director of the LIGO project in 1987, organized a joint Caltech/MIT collaboration to write the proposal. The proposal specified specific parameters for the project: two sites run in coincidence—one in Hanford, Washington and the other in Livingston, Louisiana—a 4 km baseline, an initial detector design and strain sensitivity spectrum, an environmental monitoring system, the vacuum system for the instrumentation and the vacuum system for the beam tubes, the buildings and permanent infrastructure. The proposal also provided a plan for a developmental approach for the detector with an initial detector using then available technology, having the possibility for detection; and a later advanced detector with not yet fully available technology, in the development stages at the various LIGO research laboratories, having a good chance for detection. The facilities were designed to accommodate both the initial and the advanced detector. I worked with engineers Boude Moore and later Larry Jones on the design, construction and qualification of the 4 km beam tubes.

Figure 12

By 1994 the NSF as well as both the Caltech and MIT administrations felt the management of the LIGO project needed strengthening. In 1994 Professor Barry Barish of Caltech became Director of LIGO. He substantially increased the management and technical staff of the project. He brought in Dr. Gary Sanders as the Project Manager and engaged Dr. Albert Lazzarini and Dennis Coyne as system scientist and engineer. He asked Dr. Stan Whitcomb to manage the design and construction of the first interferometer. Barish also realized that a larger group than only the Caltech and MIT groups would be needed to analyze the data and to publish results. He was the architect for the LIGO Scientific Collaboration. Barry asked me to be the first spokesperson for the Collaboration.

Figure 13

The MIT group in the 1990s and some of the research that was done. Front row, left to right: Michael Zucker, Nergis Mavalvala, Peter Csatorday, Peter Fritschel, Joseph Kovalik, and R. Weiss. Next row back: Yaron Hefetz, David Shoemaker, and Brett Bochner. Back: Brian Lantz.

Figure 14

A schematic diagram of the advanced detector that made the 2015 measurement of the gravitational waves from a binary black hole collision. The interferometer has all the ingredients needed to make the factor of ${10}^{-12}$ sensitivity improvement in measuring the small displacements of the test masses. To the main elements of the interferometer presented in Fig. 7 are added input test masses with partially transmitting coatings between the beam splitter and the end test masses. The combination of the input and end test mass comprises an optical resonator (Fabry-Perot cavities) which can be thought of as bouncing the light between them many times (typically several hundred times) to increase the gravitational wave induced sidebands by the number of bounces before returning the light to the beam splitter. One attempts to make the number of bounces the same in both arms. As in Fig. 7 the sidebands from the two arms add going toward the photodetector and the carrier cancels. No sidebands return to the laser, but all the carrier does. Between the beam splitter and the laser a new partially reflecting mirror is inserted, the power recycling mirror. The position of this mirror and its transmission is arranged to make another interferometer that cancels the carrier from the laser reflected by the power recycling mirror with the carrier transmitted back by the recycling mirror from the beam splitter. This eliminates the carrier being reflected by the interferometer to the laser and builds up the carrier power between the beam splitter and the input test masses by several hundred. This is the equivalent of using a more powerful laser. The optical configuration described was used in the initial LIGO interferometer. Finally, the advanced detector includes another partially reflecting mirror between the beam splitter and the photodetector, the signal recycling mirror. This mirror reflects the sidebands back into the interferometer and modifies the spectral response of the entire interferometer to the sidebands, thereby tuning the spectral response of the detector to the gravitational waves being sought.

Figure 15

The noise budget of the initial LIGO interferometer as described in the 1989 proposal. Note the vertical axis is the spectral amplitude $\text{strain}/\sqrt{\mathrm{H}\mathrm{z}}$. To convert to the rms strain, which has been used in other parts of this paper, multiply the plotted value by the square root of the detection bandwidth. At approximately 100 Hz with a 100 Hz detection bandwidth, the rms detector sensitivity is about ${10}^{-22}$ strain. The plot shows the principal noise terms that limit the performance of the detector. At frequencies above 200 Hz, the quantum noise (shot noise) limits the performance. The line labeled radiation pressure, which does not limit this detector, is the other part of the quantum noise due to the fluctuations in radiation pressure on the mirror. The two terms together constitute the quantum limit and are the equivalent of the noise in a Heisenberg microscope but here with a macroscopic object such as a 10 kg mirror rather than an electron. In this naive rendering one can reduce the shot noise by increasing the optical power but at the expense of increasing the radiation pressure noise. The noise near 100 Hz, the sweet spot for this detector, is limited by the thermal noise in the pendulum suspension, in this case phonon excitations at the end points of the pendulum. At frequencies below 70 Hz the detector is limited by incomplete removal of the ground vibrations (seismic noise) at the mirror. Seismic noise and pendulum thermal noise were greatly reduced for the advanced detector (Fig. 16). The broad noise spectra called residual gas are the phase fluctuations induced by forward scattering of residual gas molecules traveling through the optical beams in the long arms. This term is the primary reason for ultrahigh vacuum in the beam path. The sharply rising curve at low frequencies labeled gravity gradients is due to the fluctuating Newtonian gravitational forces on the end test masses caused by time dependent density fluctuations in both the atmosphere and the ground. Even though there is some hope in being able to measure these fluctuations or reduce them by burying the instrument, these constitute a severe limit to measure low frequency, less than a few Hz, gravitational waves on the ground.

Figure 16

Some properties of the advanced detector. Right: A quadruple pendulum system developed at Glasgow University which provides four stages of high frequency ground noise isolation as well as low pendulum thermal noise by using fused silica fiber supports (pioneered by Braginsky’s Moscow group) in the final pendulum stage. Top left: A dual active seismic isolation system, initially developed at Stanford University, which becomes a platform for the quadruple suspension. The active system measures the motion of a platform with a three-dimensional seismometer and then feeds this back to a set of controllers to null the seismometer. Two such active systems are placed in series. Bottom left: The noise budget for the advanced detector. The dominant noise has become the quantum noise at both high and low frequencies (discussed in Kip’s lecture). The noise limiting the performance at the sweet spot near 100 Hz has become the thermal noise generated in the mirror coatings. At this writing in February 2018, the noise in the advanced detector, as Barry will show, is about a factor 2.5 worse at the sweet spot than this projected noise curve.

Figure 17

A key individual at the National Science Foundation (NSF) was Dr. Richard Isaacson, who became discipline chief for Gravity in the Division of Physics in the mid-1970s. He had received his Ph.D. from the University of Maryland in Charles Misner’s group and had written a paper that rigorously showed gravitational waves carried energy and momentum away from their sources—an issue that was still controversial in the 1960s. Isaacson sensed the scientific promise in a vital program of research in experimental and theoretical gravitation and became a powerful advocate for the field at the NSF. He convinced the Director of the Physics Division, Dr. Marcel Bardon, that gravitational wave detection, although risky since the technology needed development and the sources were not certain, was the type of science which could produce transformative results and was well suited to the NSF. In addition to his advocacy within the Foundation, Isaacson guided the scientists in the field with strategic advice and wisdom about what was possible. After he retired from the NSF, he made a profession of a significant hobby in a study of textiles and the cultures that produce them in Asia. He curated an exhibit of the tent bands of yurts for the Washington Textile Museum.

Figure 18

Three Directors of the National Science Foundation who played critical roles in the evolution of the LIGO project: Eric Block was the first Director to consider going forward with the large baseline LIGO project. Walter Massey defended the program during the time when astronomers considered LIGO premature and a possible waste of funds. Neal Lane was a strong advocate for a line item in the congressional NSF budget to support Major Research Equipment Funds for Construction (MREFC). LIGO was one of the first projects to take advantage of these funds, and since then the funds have been used to begin many other large NSF projects.