Is Einstein Still Right?

by Clifford M. Will

  What could possibly possess the United States to give away roughly 80 million dollars worth of valuable technology? The answer was science. We have already discussed the importance of multiple detectors for identifying gravitational wave signals using Weber’s principle of coincident detections. That was the reason for two LIGO observatories in the first place, and for building the Virgo detector in Europe and KAGRA in Japan.

  But more importantly, we have seen how multiple detectors can make use of the various arrival times of signals to triangulate the sky location of the source (page 170). The more detectors that see the event and the farther they are from each other, the more precisely they can localize the source. However, all the current detectors, LIGO, Virgo and KAGRA, are firmly in the northern hemisphere and lie within 15 degrees latitude of each other, with the southernmost, LIGO-Livingston, at 30 degrees latitude, and the northernmost, LIGO-Hanford, at 46 degrees latitude (Virgo and KAGRA are at 43 and 36 degrees respectively). So, to a very crude approximation, all four detectors lie on the same imaginary plane cutting through the Earth.

  This means that a gravitational wave approaching the Earth from an area near due north or due south would produce rather small time delays among the four detectors, and thus the errors in locating the source on the sky will be larger, despite having four detectors. But having a detector in the southern hemisphere, far from this “plane,” would add critical additional time delay information. Analyses showed that such a detector would enhance the ability to localize the source in the sky by a factor of five to ten.

  A factor of ten is a big deal. In Chapter 8, we explained how the coincident detection of a gravitational wave produced in the merger of two neutron stars in 2017 by three instruments (the two LIGO detectors and Virgo) allowed for the localization of the source in the sky to a moderate accuracy. This, in turn, allowed astronomers all over the world to point their telescopes to the right spot in the sky and find the light emitted following the collision. But we were lucky with that one. The neutron star merger occurred quite close to Earth (a mere 140 million light years away), so the number of galaxies within the region singled out by LIGO and Virgo was not too large. This allowed the first observers on the case to scan the galaxies one by one to identify the galaxy with unusual electromagnetic emission, and then alert others as to the precise location.

  If the source had been farther away, then it would have been much more difficult to home in on the right galaxy containing the merger event. A spot of a given size on the sky that one wishes to search for represents a larger physical area the farther away one wishes to look (see Figure 9.2), and if the area is larger, then more galaxies will exist within the chosen region. Thus, localizing the gravitational wave source more narrowly can be a big advantage, allowing telescopes to find the electromagnetic emissions much faster, catching the emitted light earlier in this rapidly varying process.

  Figure 9.2 The importance of good localization of gravitational wave sources on the sky. For a nearby source the region on the sky may contain only a handful of galaxies, making it possible for astronomers to scan them one by one in search of an electromagnetic counterpart. For a more distant source, the number of galaxies in the region increases, making scanning by telescopes more challenging. The narrower the cone, the smaller the number of galaxies to scan.

  As a result, LIGO and the NSF specifically sought out a partner in the southern hemisphere to house the H-2 interferometer. The plan would be to put the interferometer equipment into storage, and then when the partner had constructed the large vacuum tubes and all the related infrastructure, the US would hand it all over to be installed. They first tried Australia, which had a very active gravitational wave effort, with many scientists already members of the LIGO–Virgo collaboration. There was even the 80 meter prototype interferometer AIGO near the town of Gingin, about 100 kilometers north of Perth, developed by researchers at the University of Western Australia. It had been used to develop advanced instrumentation for LIGO. But despite approval of the plan by the NSF and intense lobbying by Australian scientists and gravitational physicists worldwide, in October 2011 the Australian government declined the opportunity, saying that it did not have the money in its science budget for such a new endeavor.

  A year later the US government approved an approach to India. Unlike the Australians, the Indian gravitational wave scientists did not have a home-grown interferometer prototype, but many of them were members of the LIGO–Virgo collaboration, and had spent time at the various sites. They quickly formed a consortium of enthusiastic researchers and began lobbying the relevant agencies of the Indian government to promote LIGO-India. The approvals slowly worked their way up the various government hierarchies. A temporary glitch in the process occurred when somebody in the Indian government realized that the detector would be measuring seismic signals continuously and that this data would be shared by the entire collaboration of researchers. Such data was viewed by the government as a matter of national security, because it was used to monitor whether the country’s neighbor Pakistan was conducting nuclear testing, and therefore it could not be viewed by anybody outside India. Reaching a workable compromise on this issue set negotiations back by about a year. Finally, on 17 February 2016, Prime Minister Narendra Modi announced the government’s approval of the project. Interestingly, and perhaps not entirely coincidentally, this was a week after LIGO’s announcement of the first gravitational wave detection. Construction is expected to begin in 2020, with the first science collection expected roughly five years later.

  Researchers in Japan and India are not alone in thinking of the future of gravitational wave physics. The LIGO–Virgo collaboration has been thinking hard about how to make the detectors in Hanford, Livingston and Cascina even more sensitive. The first suite of upgrades is planned for the beginning of the 2020s. One upgrade envisioned is to employ improved reflective coatings on the mirrors to reduce the amount of laser light absorbed by the mirrors themselves. This will help reduce the thermal undulations of their surfaces.

  Another upgrade is to introduce a technique that laser scientists have been perfecting in recent years called “squeezing” of light. A laser beam consists of light particles or photons. When a photon bounces off a mirror, the mirror recoils a small amount, just as a billiard ball recoils when struck by another ball. This is an example of the conservation of momentum. But because of the disparity between the momentum of a tiny photon and that of the mirror, the recoil of the mirror is ridiculously small. (By now you may be used to the fact that “ridiculously small” can still be a problem for gravitational wave detection.) And since photons are fundamentally governed by quantum mechanics, Heisenberg’s uncertainty principle introduces randomness in their behavior that leads to noise in the motion of the mirrors, especially at high frequencies. While Heisenberg’s principle asserts, for example, that you cannot know both the position and velocity of a particle to arbitrary precision, it fully permits you to reduce the uncertainty in one variable, as long as you can live with a larger uncertainty in the other. With squeezed light, you can decrease the uncertainty in the aspects of the photon beam that make the mirrors recoil, while letting it increase in aspects that don’t affect the mirrors. The result is to reduce this “photon noise” in the high-frequency regime. This was first demonstrated using the GEO-600 detector in Hanover, Germany in 2011, and is being implemented in the larger interferometers.

  The next round of upgrades is planned for around 2025–2030, and will involve importing the KAGRA technology to cool the test masses down to a temperature of about 120 kelvin. Other improvements include new mirrors made of silicon and new suspensions for the mirrors that will better isolate them from seismic vibrations. When all is said and done, these new detectors should be twice as sensitive as advanced LIGO. A factor of two improvement in sensitivity doubles the distance to which sources can be detected, increases the accessible volume by a factor of eight (since volume increases as radius cubed), and thus increases the n
umber of galaxies accessible to detectors by a factor of roughly eight!

  The upgrades of the current LIGO and Virgo detectors, together with the new detectors in Japan and India, are being called second-generation detectors. They involve basically improving on the original “L”-shaped concept envisioned in the 1970s by Gerstenshtein and Pustovoit, Weber and Forward, and Rai Weiss. There is an ambitious plan being hatched for a “third”-generation detector of a quite different design, called the Einstein Telescope, or ET.

  The Einstein Telescope is currently planned as an underground triangular interferometer, in which the angle between the arms is 60 degrees instead of 90. It turns out that there is no law that says that an interferometer must have arms at right angles to each other. The current interferometers have right-angled arms largely for historical reasons. The original table-top interferometers built by Michelson in the late nineteenth century to measure the speed of light and to try (unsuccessfully) to detect the motion of the Earth through a hypothetical “aether” had right-angled arms. But history is not the only driver for 90 degree arms; it turns out that at 90 degrees, the response of an interferometer to a given incoming gravitational wave is the largest it can be. However, if you make the angle smaller or larger than 90 degrees the response does not decrease by all that much. At 60 degrees between the arms, the response is still about 86 percent of the maximum possible (the actual factor is the sine of the angle between the arms).

  But then, a very nice thing happens. Suppose you are planning to excavate two tunnels for the arms of your 60 degree interferometer. By increasing the excavation budget by only 50 percent, you can dig a third tunnel to complete the triangle. Then, by installing an interferometer at each vertex of the triangle, as shown in Figure 9.3, you can triple the number of interferometers you can install. The loss in sensitivity in going from 90 to 60 degrees is easily compensated by having three interferometers running simultaneously in the same place. In the current design for ET, each side of the triangle is to be 10 kilometers long, as compared to 3 or 4 kilometers for the existing interferometers. The increase in arm lengths exploits the fact that the change in separation between two objects that a gravitational wave induces is proportional to the distance between them. Moreover, the tunnels will be 100 to 200 meters below the Earth’s surface to reduce seismic and gravity noise, and the mirrors will be cooled to temperatures near absolute zero to reduce thermal noise. Three detectors allow us to measure gravitational waves with increased sensitivity arriving from all directions, and they make it possible to separate the different polarizations of the waves at a single site. To be brutally realistic, today’s vision of ET is so expensive that it is likely that only a single version will be built. So ET is designed to extract the most science possible if one is limited to a single high-sensitivity instrument.

  Figure 9.3 Three-interferometer concept for the Einstein telescope. In an equilateral triangular tunnel, three separate interferometers can be installed. The proposal calls for arms 10 kilometers long.

  Third-generation gravitational wave detectors such as ET will inaugurate the era of precision experimental relativity in extreme gravity. The Einstein Telescope’s increased sensitivity will allow it to hear signals from even farther away than any other ground-based detector. For example, ET is expected to detect essentially all mergers of stellar-mass and intermediate-mass black holes, as well as neutron stars, anywhere in the observable universe. Moreover, the events that advanced LIGO and Virgo have already detected would have been a hundred times louder, had they been detected by ET. Such increased sensitivity will allow us to dig deep into even the smallest features of the waves, enabling us to extract tiny details of the source that generated them. In addition, we will be able to carry out tests of general relativity that are at least a factor of a hundred more stringent than current tests.

  Still, despite the most visionary design concepts, all of these detectors have the same limitation. At low frequencies, an interferometer’s output is dominated by seismic and gravity noise, even when it is buried deep underground. The second and third generations of detectors may allow us to detect waves with frequencies as low as a few hertz, but to go to even lower frequencies is impossible for a detector on Earth. We need to go to space.

  The idea of going to space to detect gravitational waves is not new. In 1976, a NASA sub-panel on relativity and gravitation chaired by Rai Weiss published a report that discussed both ground-based laser inteferometers and the possibility of putting such a system in space. While that report envisaged a Michelson-type interferometer in orbit, some researchers, such as Peter Bender and James Faller of the University of Colorado, Ron Drever in Glasgow, and others, began to ruminate informally about an array of free-flying spacecraft. In papers published in 1984 and 1985, Faller, Bender and other Colorado colleagues outlined a possible space antenna for gravitational waves.

  They imagined putting three satellites into orbit around the Sun, separated by about a million kilometers. The three would be in an L-shape arrangement, just like the ground-based interferometers that were being studied at the time. Laser beams would be used to monitor the separation between the main satellite at the corner and the satellite at the end of each “arm.” There would be no beam tubes, of course, since the vacuum of space is far better than any human-made vacuum. The satellites would orbit freely, unencumbered by support wires and unaffected by Earth-bound seismic noise.

  However, you cannot send a laser beam a million kilometers, bounce it off a mirror and look for the reflected signal. The reason is that, no matter how well you focus the laser beam, it spreads out, and by the time it reaches the end satellite, the beam is so large that the mirror would reflect only the tiniest fraction. That reflected beam also spreads out, and so by the time it returns to the main satellite, there is effectively no light intensity left to detect. At the 4 kilometer distances of the ground-based interferometers this is not a major problem, but at a million kilometers, forget it. But there was a solution. Instead of reflecting the beam at the end satellites, equip each satellite with its own laser. Then capture the arriving laser beam using sophisticated optical devices, measure the value of the “time stamp” (also called “phase”) that was encoded in the beam when it was sent out, and imprint that value in a new and powerful signal emitted by the onboard laser back toward the main satellite. In fact, this kind of scheme is a laser version of the “radar transponder” used to track interplanetary spacecraft very precisely (see Chapter 3).

  But even though the vacuum of outer space is good enough for the laser beams to travel freely, it is not good enough for the satellites themselves. Satellites are being continuously buffeted by the solar wind and by the photons of light emitted by the Sun. To some degree, these effects are fairly constant in time, and can be modeled and accounted for. But they also fluctuate significantly, leading to a random jiggling of the spacecraft that is every bit as worrisome as seismic noise on Earth. To get around this, Faller and colleagues proposed to use the idea of “drag-free” control, a concept that had been tested using US Navy navigation satellites called TRIAD during the 1970s, and at the time was under active development for Gravity Probe-B (see page 71). The idea would be to have a small mass inside each spacecraft (a cube with reflective surfaces, for example) serve as the “end” of each arm (top left panel of Figure 9.4). The laser beam enters the spacecraft, bounces off a surface of the cube, and then enters a sequence of lenses and mirrors that measure the required information and send that to the onboard laser to generate the return beam.

  Figure 9.4 Drag-free control in LISA. If external forces push the spacecraft so that the central cube gets too close to a wall of the chamber, signals are sent to micronewton thrusters to nudge the spacecraft to keep the cube centered.

  The crucial thing is to protect that small cube from the buffeting action of the solar wind and the stream of solar photons. The surrounding spacecraft does the required shielding, of course, but those external forces could push the spacecr
aft so that the cube is no longer centered inside its protective chamber but gets too close to one wall (top right panel of Figure 9.4). Sensors inside the chamber detect this proximity and send signals to thrusters on the opposite side of the spacecraft. These thrusters nudge the spacecraft so that the cube is re-centered. The spacecraft has thrusters pointing in all six directions so that external forces from anywhere can be compensated. In this way, each cube moves on a path provided purely by curved spacetime, and by any ripples in spacetime that pass by in the form of gravitational waves. The typical force needed to do the job is measured in units of a “micronewton.” One micronewton is roughly the downward force exerted on your dog’s tail when a flea lands on it.

  These ideas would ultimately become LISA, the Laser Interferometer Space Antenna, a mission being developed by the European Space Agency, with participation by NASA, and planned for a launch in 2034. We have seen several examples in this book of the often long and tortuous path between inception and fruition of major undertakings in gravitational physics: 43 years between the proposal by Fairbank, Schiff and Cannon and the launch of Gravity Probe-B (Chapter 4); 30 years between Rai Weiss’ MIT report and LIGO’s first science run in 2002, and 44 years to the first detection. But at 54 years, LISA will set a record. To some, this may seem like an intolerably long time. Some of the originators of the idea may not live to see it finally come to fruition. Some may spend their entire careers working on this one project. But this is part of the landscape of science. When it comes to answering the deepest questions about the universe, scientists often have to play the long game; whether it involves constructing the most energetic particle accelerators, perfecting nuclear fusion, or building space telescopes.