Is Einstein Still Right?

by Clifford M. Will

  One class of models for what happens after two neutron stars merge came to be called “kilonova models.” This is a variant of the word “supernova,” but it has nothing to do with the explosion of a massive star. According to these models, when neutron stars merge, they will spew a few hundredths of a solar mass of material into space at about a few tenths the speed of light. Some of this material will fall back onto the remnant, maybe forming a disk of material that is slowly swallowed or “accreted” by the remnant. But some of the ejected material will have enough of an initial velocity after the collision that it will escape altogether, creating a cloud of very hot and very neutron-rich material. As the cloud expands and cools, the r-process produces elements like gold, platinum and silver, as well as heavier elements in the lanthanide part of the periodic table (elements that are crucial for computers, cell phones and batteries).

  And this is precisely what optical and infrared telescopes observed when following up the gravitational wave detection. In fact, the electromagnetic radiation detected from the radioactive decay of material in the hot cloud expanding from the merger site suggests that about fifty times the mass of the Earth was produced in silver, a hundred times the mass of the Earth in gold and five hundred times the mass of the Earth in platinum, a mere second after the merger.

  Astronomer and science TV host Carl Sagan once said that we are made of star dust. He was referring to the elements forged through nuclear fusion in stars and supernovae. But now we know that we are not just that. A little part of us also contains neutron star dust (not too much, as that would be toxic). What’s more, neutron star dust (in the form of gold, platinum and silver) is forged into jewelry that routinely adorns our bodies. We even sometimes bind ourselves to each other through rings of neutron star dust.

  We close this chapter with an extroardinary test of Einstein’s theory provided by GW170817 and GRB170817. We already learned from the black hole inspirals that the speed of gravitational waves is independent of wavelength, in accord with general relativity, but we learned nothing about the actual value of that speed. That is because only gravitational waves were received from those inspiral events, and since we do not know exactly when the signals were emitted, there is no way to calculate the speed of the waves. General relativity predicts that the speed of gravitational waves is exactly the same as the speed of light. The nearly simultaneous arrival of the gravitational waves and the gamma ray burst proved that they are the same to incredible precision. The argument goes like this.

  The LIGO–Virgo collaboration compared the time at which the peak of the gravitational waves arrived at the detectors to the time at which gamma rays arrived at the Fermi satellite. After correcting for the altitude and location of the satellite and for the radius of the Earth, the scientists concluded that the gamma rays arrived about 1.7 seconds after the peak of the gravitational wave train. This delay is presumably caused by the fact that the gamma ray emission did not start when the neutron stars first touched each other, which does coincide with the peak of the gravitational wave signal, but instead the gamma ray emission originated in whatever violent explosion followed the merger. The details of that explosion are still an area of active research, but different models suggest a delay between 1 and 10 seconds.

  Let us assume that the gamma rays were emitted at exactly the same time as the peak of the gravitational waves, that is, roughly at the time the neutron stars first touched. If so, then we would attribute the delay in the gamma ray arrival entirely to gravitational waves moving more quickly than the gamma rays. How much more quickly would they have traveled? The travel time of the gravitational waves is simply the distance traveled divided by their velocity, and similarly the travel time of the gamma rays is the same distance divided by the speed of light. Remember that the distance over which this little race occurred is 130 million light years. The difference in these travel times must equal the 1.7 second time delay measured, which then allows us to estimate that the gravitational waves were faster than the gamma rays by at most about three quarters of a millimeter per hour. Alternatively, let us assume that the gamma rays were emitted 10 seconds after the gravitational waves. In this case the faster gamma rays would have narrowed the gravitational waves’ head start to 1.7 seconds, requiring them to be faster by about 3 millimeters per hour. Comparing these two estimates to the speed of light, a million billion millimeters per hour, one sees that the permitted speed difference is truly minuscule: smaller than parts in 1015! As we discussed earlier, many of the latest attempts to account for the accelerated expansion of the universe and the effects attributed to dark energy by invoking an alternative gravitational theory require that the speed of gravitational waves be different from that of light. The single observation from GW170817 and GRB170817 that this is not the case forced theorists to throw a large heap of such theories immediately into the trash. Conversely, if we assume that general relativity is correct, and thus that the two speeds are identical, then the 1.7 second delay between the arrival of the two signals corresponds precisely to the delay between the emission of the two signals, a fact that is already proving very important in sorting through the many complex models for how the gamma rays were generated.

  In the end, most of us were wrong in our predictions that neutron star mergers would be the first events detected by LIGO–Virgo. But hey, ninth place isn’t so bad! Those unexpectedly massive black hole inspirals were loud, and the rate of such events is obviously higher than people expected. The third observing run of LIGO–Virgo began on 1 April 2019 at even better sensitivity, with the expectation of more detections of black hole mergers, neutron star mergers, and maybe even mixed mergers of a black hole and a neutron star. As we end this chapter we don’t want you to get the impression that this is it. The ground-based interferometers will also be searching for other sources of gravitational waves, and completely different kinds of detectors are in operation or under development, including one destined to go into space. The future is loud for gravitational wave detection, and we can look forward to hearing many more movements in the symphony of the universe.

  CHAPTER 9

  A Loud Future for Gravitational Wave Science

  After reading Chapter 8, you may think that there is nothing else to learn from gravitational waves. But the detections of 2015–2017 are only the beginning. After a two-year hiatus to make additional improvements at the LIGO and Virgo observatories, a third observing run, called O3, began on 1 April 2019. Right away, new detections were made on 8 April, 12 April and 21 April. By the middle of August 2019 there were around eighteen binary black hole mergers, two binary neutron star mergers, and, on 14 August, a possible black hole–neutron star merger. There were even a few events that were later retracted when additional analysis revealed them to be either instrumental or terrestrial in origin. In contrast to the extreme secrecy that surrounded the early detections, the LIGO–Virgo collaboration has gone fully public, now announcing detections as they come in. In fact, you can download a “gravitational wave” app to your smartphone that will send you an alert every time a sufficiently credible signal is detected. You can select a generic alert tone, or you can choose a tone that sounds like a gravitational wave “chirp.” The reason for this openness is to allow astronomers to react more quickly, in the hope of finding electromagnetic counterparts to the gravitational wave events. By the time you read this paragraph, it will almost certainly be hopelessly out of date, with a regular stream of recorded signals from binary black holes, binary neutron stars, mixed mergers, or possibly something entirely new and unexpected.

  But that is not all. There is an ambitious effort to take gravitational wave physics to the next level, and it begins in Japan. Mount Ikeno is near the city of Hida, in the center of Japan. About 1,000 meters below the mountain’s surface is the Mozumi mine, owned by the Kamioka Mining and Smelting Company, which operated for over a century. Today, the mine is no longer operational, at least not for the extraction of minerals. Instead, it houses some of
the most sophisticated physics experiments in the world. Super-Kamiokande, for example, is a detector built to observe and characterize high-energy neutrinos, those tiny subatomic particles that travel very close to the speed of light. They can be created in the Sun as a byproduct of nuclear fusion, or in the atmosphere when other high-energy particles, emitted in supernovae and other events, collide with atoms such as nitrogen and oxygen. Super-Kamiokande also looked for possible decays of the proton, one of the elementary building blocks of atoms. It found none, and provided a lower limit on the proton’s lifetime of around 10 billion trillion trillion years (that’s a 1 followed by 34 zeros).

  The Mozumi mine is also home to a new gravitational wave detector that is beginning operations: the Kamioka Gravitational Wave Detector, or KAGRA. This detector is similar to LIGO and Virgo, with two perpendicular arms that are 3 kilometers long. Unlike LIGO and Virgo, however, the KAGRA detector is deep underground. And unlike the LIGO/Virgo mirrors, which are at room temperature, KAGRA’s mirrors will be cooled to around 20 kelvin (− 253 degrees Celsius or − 423 degrees Fahrenheit). But why?

  Going underground helps to diminish two important sources of noise: seismic noise and “gravity noise.” The Earth is continuously shaking, even if we can’t always feel it move under our feet. These seismic vibrations originate in erupting volcanoes, the grinding of tectonic plates against each other, or even man-made explosions. They travel in all directions on the surface of the planet and through the interior. Many of the interior waves are quenched because of the high densities and the molten core inside the Earth. The strongest vibrations travel along the Earth’s surface. Isolating the mirrors of LIGO and Virgo from these external vibrations was a major undertaking, but despite those sophisticated efforts some of these vibrations still get through, forcing the mirrors to shake a tiny bit. These vibrations are especially troublesome at the lower frequencies, say 10 hertz and below, getting in the way of our ability to detect the low-frequency vibrations due to gravitational waves. So, placing a gravitational wave detector deep inside a mountain is a way to protect the instrument from surface seismic vibrations.

  Similarly, gravity above and around the instrument is not constant. Imagine a clump of cold, dense air passing over an interferometer on the surface (left panel of Figure 9.1). Because the mirrors are several kilometers apart, the mass in the clump can gravitationally attract the mirrors differently, inducing small motions that act as a background noise. You might say that such effects must be ridiculously small, and they are. But they can still be larger than the ridiculously small motions induced by the gravitational wave we want to detect. There is no way to shield gravity, but if you put the interferometer deep underground (right panel of Figure 9.1), you add distance between it and the clump. Since the force of gravity falls off inversely with the square of the distance to the source of the perturbation, this helps to mitigate the effect. Because everything with mass produces gravity, including people driving cars and even the compressions associated with seismic waves, gravity noise is a problem, and isolating the detectors underground can help reduce these effects.

  Figure 9.1 Left: The gravitational attraction of a dense cloud can move the mirrors in an interferometer on the ground. Right: For an interferometer such as KAGRA deep under a mountain, the cloud is farther away, reducing its gravitational effects.

  So why were LIGO and Virgo not built underground? The reason is cost. As every Bostonian who has lived through the “Big Dig” project knows, digging tunnels is an extraordinarily expensive and complex undertaking even for something as worthy as managing traffic. Every major science project has to balance the scientific return and the risk of failure against the cost and timetable for construction. Compromises in scientific capability are often necessary to reach a budget that has a chance of being accepted by the governments who will be spending the taxpayers’ money. So going underground was never in the cards for LIGO or Virgo. But KAGRA had the advantage of the pre-existing tunnels and infrastructure (power, air handling, access) of the Kamioka complex, and while some excavation was necessary, it wasn’t a deal-breaker.

  The advantage of cooling the mirrors to low temperatures is related to an effect called Brownian motion. Robert Brown was a Scottish botanist, who in 1827 observed that tiny particles ejected by grains of pollen and suspended in water seemed to be in constant motion when observed under a microscope. While this phenomenon was initially thought to be caused by some mysterious “life-force,” it remained largely unexplained until Einstein developed a statistical theory of heat in one of his celebrated 1905 papers. Einstein realized that the jittery motion had to be a consequence of collisions between the grains and the fast and randomly moving water molecules. Heat, in fact, is nothing but a manifestation of the kinetic energy of the motion of molecules. As a result, the surfaces of all the mirrors in an interferometer are in a constant state of undulation, and this introduces an uncertainty in defining the precise distance between the mirrors’ surfaces as determined by the bouncing laser beams. In addition, no mirror reflects perfectly, and some of the laser light is absorbed by the mirrors, heating them up and adding to the thermal undulations. Both effects can be reduced significantly by cooling the mirrors to temperatures near absolute zero.

  KAGRA’s sensitivity to gravitational waves is expected to be comparable to LIGO’s and Virgo’s, perhaps even exceeding them at low frequencies where seismic and gravity noise dominate those detectors. But the Japanese project suffered from a number of delays. For example, in 2014–2015 some of the tunnels of the Mozumi mine partially flooded because of an excess of snow melting in the spring. This water was a problem not just because experimentalists would get their feet wet, but because it could contribute to gravity noise. The development of a plan to deal with this excess water delayed the construction of the detector. But in 2018 KAGRA’s construction was finally completed and a first run (with mirrors at room temperature) was successful. In early 2019, the KAGRA team reported a successful test with the mirrors at 16 kelvin, and readied themselves for joint observing runs with LIGO and Virgo toward the end of O3, in 2019.

  Meanwhile, a fifth gravitational wave instrument is under development, called LIGO-India. It will be built near the town of Aundh, a suburb of Pune in the Hingoli district of Maharashtra, southeast of Mumbai. The town is dedicated to the Hindu Goddess Shiva, the destroyer and transformer, and it hosts one of her twelve most important representations, or Jyotirlingas, in India. LIGO-India will consist of a replica of one of the LIGO interferometers, but located in India instead of in the United States. In fact, this replica was initially part of a smaller interferometer at the Hanford site of LIGO.

  When we have been describing LIGO and Virgo we have been a bit sloppy in using the term “interferometer.” The actual interferometer consists of the lasers, the beam splitter, the mirrors, the seismic isolation equipment, along with all the detailed instrumentation needed to make it all work. There is an equally important ingredient of the observatories, namely the enormous kilometers-long vacuum tubes created to house the interferometers. We tend to lump them together in the single word.

  When LIGO was first being designed, it was decided to fabricate and install two interferometers at the Hanford site. The second interferometer was identical to the first in every way—identical lasers, beam splitter and mirrors—except that the end mirrors were installed at the two-kilometer mark, instead of at the end of each vacuum tube, at four kilometers. This system was denoted H-2, while the longer system was denoted H-1 (the Livingston system was called L-1). In fact, the evacuated tubes were sized to be able to accommodate multiple interferometers and multiple laser beams.

  The reasoning behind this was redundancy and confidence. A gravitational wave arriving at the detector would induce a response in H-2 that would be exactly one half the size of the response of H-1, but would be otherwise identical. The seismic noise background in both instruments would be almost identical. In contrast, the Livingston detector, while conta
ining identical instrumentation, lived in a different seismic environment, with its own vacuum system for the beam tubes, and the concern was making a confident detection of a wave in the face of the disparate sources of noise. The initial LIGO runs from 2002 to 2010 involved all three interferometers at the two LIGO sites. When the improved instrumentation for the advanced LIGO detectors was being built during the period 2008 to 2010, an advanced interferometer system was fabricated for H-1, H-2 and L-1.

  But it turned out that the runs of the initial LIGO system were extremely successful. True, they did not detect gravitational waves, but they didn’t really expect to, because initial LIGO was not quite sensitive enough. But they learned so much about the various noise sources and how they affected the detectors that the LIGO team began to ask, do we really need H-2? If not, what could one do with the instrumentation that was being built? In 2009, Jay Marx, an experimental high-energy physicist who had taken over the directorship of LIGO from Barry Barish three years earlier, raised the idea of offering it, more or less free of charge, to somebody else willing to construct the vacuum tubes and to provide all the needed infrastructure for a working gravitational wave detector. Although the National Science Foundation was initially skeptical, it eventually signed off on the proposal.