Is Einstein Still Right?

by Clifford M. Will

  Nevertheless, Ciufolini had an idea to get around this problem. If there were a second LAGEOS satellite orbiting at the same altitude and in an equally circular orbit, but with its inclination relative to the equator chosen so that the two inclinations added up to 180 degrees, then the calculations showed that the Newtonian rotation of that orbit would be exactly the same as for the existing LAGEOS, but in the opposite sense. The relativistic rotation would be exactly the same size and in the same direction for both orbits; this effect does not depend on the tilt angle. Thus, one could measure the rate of rotation of the planes of each orbit and simply add them together. The Newtonian part would cancel exactly, leaving twice the relativistic part. Injecting a satellite into just the right orbit would be challenging, but doable. Ironically, Ciufolini’s proposal was a variation of a 1976 idea by none other than Francis Everitt and his colleague Richard van Patten; their proposal was for two satellites in polar orbits about 600 kilometers above the Earth, moving in opposite directions. In this configuration the Newtonian effect is much, much smaller, making it easier to cancel and reveal the frame dragging precession. It never attracted much attention, and Everitt and van Patten returned their attention to Gravity Probe-B. Even though their proposal was published just six weeks before the launch of LAGEOS I, they were apparently unaware of what the geophysicists were working on. Science is rife with missed opportunities caused by the compartmentalization of different fields. It would be ten years before Ciufolini would hit upon LAGEOS as a tool for measuring frame dragging.

  At the time of Ciufolini’s proposal, the geophysics community was planning to launch a second LAGEOS satellite in order to advance their studies of the Earth. Ciufolini and many relativists campaigned vigorously to have LAGEOS II launched with the special inclination angle of 70.16 degrees (LAGEOS I was at 109.84 degrees) needed to measure frame dragging, but other considerations prevailed in the end. LAGEOS II was launched in 1992 with an inclination of 52.64 degrees, mainly to optimize coverage by the world’s network of laser tracking stations, which was important for geophysics and geodynamics research.

  This was a major disappointment, but Ciufolini, now based in Italy, and his colleagues tried to make the best of it. Because the cancelation effect was not ideal, the errors in measuring the frame dragging rotation would be larger than they had hoped, but between 1997 and 2000 they reported having measured the 30 milliarcsecond effect to between 20 and 30 percent precision, although some critics argued that their error estimate was optimistic.

  The turning point came with a space project known as GRACE. This joint mission between NASA and the German Space Agency, whose official name was Gravity Recovery and Climate Experiment, was launched in 2002 and ended in late 2017. GRACE consisted of a pair of satellites (dubbed Tom and Jerry) flying in close formation (200 kilometers apart) on polar orbits 500 kilometers above the Earth. Each satellite carried a satellite-to-satellite radar link to measure the distance between them very precisely, and a GPS receiver to track the orbit of each satellite separately. As the pair pass over a region with excess mass, such as a mountain, the gravitational attraction of the mass pulls the satellites toward each other, while if they pass over a region with a deficit of mass, such as a valley or depression, the satellites are pulled apart (see Figure 4.7). As the satellites passed repeatedly over different parts of the Earth they were able to map out its gravitational field in fine detail and with unprecedented accuracy. Furthermore, over the fifteen years of the mission, GRACE was able to measure time variations in the gravity field of the Earth. For example, it could measure the gravity variation caused by seasonal changes in the amount of water in the Amazon and Ganges river basins, and the changes in gravity caused by mass loss in the ice sheets of Greenland and Antarctica. These measurements have obvious implications for water management and climate change. It could also monitor the rise of the North American and European land masses as they continue to “rebound” from the loss of the ice that had weighed them down during the last ice age.

  Figure 4.7 Measuring variations in Earth’s gravity using GRACE. Top: As the two satellites pass over a mountain, its gravitational attraction pulls them toward each other. Bottom: As they pass over a large depression, the absence of mass causes them to separate a bit.

  With the dramatic improvements in accuracy for Earth’s gravity field provided by GRACE, Ciufolini and his colleagues could now remove the Newtonian effects and uncover the tiny frame dragging effect more precisely. In 2010 and 2011, as GP-B was in the final phase of data analysis, Ciufolini and colleagues reported a result from LAGEOS in agreement with general relativity to about 10 percent, about a factor of two better than the final GP-B result.

  Meanwhile, Ciufolini had succeeded in convincing the Italian Space Agency to go for a third laser-ranged satellite, called LARES (Laser Relativity Satellite), to be launched with an inclination of 69.5 degrees, very close to the required angle relative to LAGEOS I. However, the agency informed Ciufolini that, in order to reduce cost, it would not provide a launch vehicle powerful enough to achieve the same distance from the Earth as that of the two LAGEOS satellites, again preventing perfect cancelation of the Newtonian effect, which varies as the inverse cube of the radius of the orbit. Still, the advantage of having the proper inclination was enough to convince the LARES team to accept the launcher offered. LARES was launched on 13 February 2012, and in 2016, combining data from all three satellites with improved Earth data from GRACE, the LARES team reported a test of frame dragging at the 5 percent level.

  The main difficulty in all of these precession experiments is that near Earth, gravity is just too weak! It would be wonderful to measure how gyroscopes precess near a black hole or a neutron star. The magnitude of the relativistic precession effects might be so large that one could see the precession “by eye.” But this, of course, is completely impractical. The nearest black hole observed, V616 Monocerotis, is 3,000 light years away, and the nearest neutron star, Calvera, is between 250 and 1,000 light years away, so sending a gyroscope experiment there (maybe called “GP-X”) is hopeless. But rotating neutron stars themselves can act as gyroscopes as effectively as can spheres of fused silica. And many neutron stars also act as “pulsars,” emitting a beam of radio waves that we can detect, and some are in orbit around other stellar bodies. In fact, these celestial lighthouses have taken testing general relativity into a whole new realm, as we will see in the next chapter.

  1 Disclosure: Cliff was a member of the National Academy panel, and later was appointed by NASA as Chair of an external Science Advisory Committee for Gravity Probe-B from 1998 to 2011.

  CHAPTER 5

  Celestial Lighthouses for Testing Relativity

  It is unlikely that Joe Taylor and Russell Hulse will ever forget the summer of 1974. It started uneventfully enough. Taylor, a young professor at the University of Massachusetts at Amherst, had arranged for his graduate student Hulse to spend the summer at the Arecibo Radio Telescope in Puerto Rico looking for pulsars. They had put together a sophisticated observational technique that would allow them to scan a large portion of the sky using the radio telescope in such a way that it would be especially sensitive to signals from pulsars. At that time around a hundred pulsars were known, so their main goal was to add new ones to that list, in the hope that, by sheer weight of numbers, they could learn more about this class of astronomical objects. But apart from the possible payoff at the end of the observations, the bulk of the summer would be spent in rather routine, repetitive observing runs and compilation of data that, as in many such astronomical search programs, would border on tedium. But on 2 July, good fortune struck.

  On that day, almost by accident, Hulse discovered something that would catapult both Hulse and Taylor into the astronomical headlines, excite the astrophysics and relativity communities, and ultimately yield the first confirmation of one of the most important predictions of general relativity.

  At least as far as relativists are concerned, the discovery ranks up ther
e with the discovery of pulsars themselves. That discovery was equally serendipitous. In late 1967, radio astronomer Antony Hewish and his graduate student Jocelyn Bell at Cambridge University were attempting to study quasars by exploiting the phenomenon of scintillation, the rapid variation or “twinkling” of the radio signal that is caused by clouds of electrons in the solar wind out in interplanetary space. These variations are typically random in nature and are weaker at night when the telescope is directed away from the Sun, but in the middle of the night of 28 November 1967 Bell recorded a sequence of unusually strong, surprisingly regular pulses in the signal. After a month of further observation, she and Hewish established that the source of this signal was outside the solar system, and that the signal was a rapid set of pulses with a period of 1.3372795 seconds.

  As a standard of time measurement, these pulses were as good as any atomic clock that existed at the time. It was so unexpected to have a naturally occurring astrophysical source with such a regular period that, for a while, they entertained the thought that the signals were a beacon from an extraterrestrial civilization. They even denoted their source LGM, for little green men. The Cambridge astronomers soon discovered three more of these sources, with periods ranging from a quarter to one and a quarter seconds, and other observatories followed with their own discoveries. The little green men theory was quickly dropped, because if the signal was truly from an alien civilization then it should have shown a Doppler shift as the alien planet orbited around its alien star. The only Doppler shift they saw was due to the Earth’s motion around our Sun. The sources of these signals were renamed “pulsars” because of the pulsed radio emission.

  This discovery had an enormous impact on the world of astronomy. The discovery paper for the first pulsar was published on 24 February 1968 in the British science journal Nature, and in the remaining ten months of that year over one hundred scientific papers were published reporting either observations of pulsars or theories of the pulsar phenomenon. In 1974, Hewish was rewarded for the discovery with the Nobel Prize in Physics, along with Martin Ryle, one of the pioneers of the British radio astronomy program. In some circles controversy still lingers over the decision of the Swedish Academy not to include Bell in the award. Now a renowned astronomer, academic leader and proponent of women in science, Dame Bell-Burnell (“Dame” being the female title that accompanies knighthood) has consistently expressed agreement with the Nobel decision.

  Within a few years of the discovery, there was a general consensus about the overall nature of pulsars. Pulsars are simply cosmic lighthouses: rotating beacons of radio waves (and in some cases of optical light, X-rays and gamma rays) whose signals intersect our line of sight once every rotation period. The underlying object that is doing the rotating is a neutron star, a highly condensed body, typically a bit more massive than the Sun, but compressed into a sphere of around 20 kilometers in diameter, 500 times smaller than a white dwarf of a comparable mass, or 100,000 times smaller than a normal star of that mass. Its density is therefore about 500 million metric tons per cubic centimeter, comparable to the density inside the atomic nucleus. Neutron stars are so dense that a single teaspoon of neutron star matter on Earth would weigh the same as about 1,000 Great Pyramids of Giza in Egypt. As their name would indicate, neutron stars are made mostly of neutrons, with a contamination of protons and an equal number of electrons. Because a neutron star is so dense, it behaves as the ultimate flywheel, its rotation rate kept constant by the inability of frictional forces to overcome its enormous rotational inertia. Actually, there are some residual braking forces that do tend to slow it down, but an example of how small this effect can be is given by the original Bell–Hewish pulsar: its period of 1.3373 seconds is observed to increase by only 43 nanoseconds per year. Of the one hundred or so pulsars known by 1974, every one obeyed the general rule that it emits radio pulses of short period (between fractions of a second and a few seconds), and with a period that is extremely stable, except for a very, very slow increase. We will see that this rule almost proved to be the downfall of Hulse and Taylor.

  Why a neutron star? Was this just a figment of the theorist’s imagination, or was there some natural reason to believe in such a thing? In fact, neutron stars did begin as a figment of the imagination of the astronomers Walter Baade and Fritz Zwicky in the mid 1930s, as a possible state of matter one step in compression more extreme than the white dwarf state. This remarkable suggestion was made only a few years after the discovery of the neutron! Such highly compressed stars, they suggested, could be formed in the course of a supernova, a cataclysmic explosion of a star in its death throes, that occurs in galaxies throughout the universe, including our own. While the outer shell of such a star explodes, producing a flash of light that can momentarily exceed the light output of the entire galaxy and ejecting a fireball of hot gas, the interior of the star implodes until it has been squeezed to nuclear densities, whereupon the implosion is halted, leaving a neutron star as the cinder of the supernova. The neutron star should also be spinning very rapidly, for the following reason. All stars for which decent data exist are known to rotate, the Sun being the nearest example. Therefore, just as the figure skater spins more quickly when she pulls in her arms, exploiting the conservation of angular momentum, so too the collapsing, rotating core of the supernova should speed up.

  Of the five supernovae in our galaxy of which we have historical records during the past thousand years, one occurred in the constellation Taurus in 1054. It was recorded by Chinese astronomers as a “guest star” that was so bright that it could be seen during the day. The remnant of that supernova is an expanding shell of hot gas known as the Crab Nebula. The observed velocity of expansion of the gas is such that, if traced backward in time for about 950 years, it would have originated in a single point in space. Several months after the discovery of the first pulsars, radio astronomers at the National Radio Astronomy Observatory trained the telescope on the central region of the Crab Nebula and detected radio pulses. The discovery was confirmed at the Arecibo observatory, and the pulse period was measured to be 0.033 seconds, the shortest period for a pulsar known at the time. Moreover, compared to other pulsars, the Crab pulsar was slowing down at an appreciable rate, around 10 microseconds in period per year. Put another way, the time required for the period to change by an amount comparable to the period itself is around 1,000 years, which is just the approximate age of the pulsar if it was formed in the 1054 supernova. Finally, if the pulsar is a rotating neutron star, the loss of rotational energy implied by its slowing spin turned out to be enough to keep the nebula of gas sufficiently hot to glow with the observed intensity.

  The fact that all these observations were so consistent with one another provided a beautiful confirmation of the rotating neutron star model for pulsars. The most recent nearby supernova occurred in 1987 in the Large Magellanic Cloud, a small satellite galaxy to the Milky Way.

  Other aspects of pulsars are not so clean cut or so simple, however, and one of these is the actual mechanism for the “lighthouse beacon,” if indeed that is how the radio pulses are produced. In the conventional model, a pulsar is thought to have one important feature in common with Earth: its magnetic northern and southern poles do not point in the same direction as its rotation axis. On Earth, for instance, the geomagnetic northern pole is near Ellesmere Island, in the far north of Canada, not in the middle of the Arctic Ocean, as is the north pole of the rotation axis. There is one key difference, however. The magnetic field of a generic pulsar is a trillion times stronger than that of Earth. Such enormous magnetic fields produce forces that can strip electrons and ions from the surface of the neutron star and accelerate them to nearly the speed of light. This causes the particles to radiate copiously in radio waves and other parts of the electromagnetic spectrum, and because the magnetic field is strongest at the poles, the resulting radiation is beamed outward along the northern and southern magnetic poles. Because these poles are not aligned with the rotation axis, the two
beams sweep the sky, and if one of them hits us, we record a pulse and call the source a pulsar. The precise details of this mechanism are still not fully worked out, partly because we have absolutely no laboratory experience with magnetic fields of such strength and with bulk matter at such monstrous densities. However, using massive computer simulations, researchers have recently been making progress in comprehending how the beams originate.

  Nevertheless, by the summer of 1974 there was agreement on the broad features of pulsars. They were rapidly rotating neutron stars whose periods were very stable except for a very slow increase with time. It was also clear that the more pulsars we knew about and the more detailed observations we had, the better the chances of unraveling the details.

  This is what motivated and guided Hulse and Taylor in their pulsar search. The receiver of the 1,000 foot radio telescope at the Arecibo observatory was driven so that as the Earth rotated, in one hour the instrument could observe a strip of sky a sixth of a degree wide by three degrees long. At the end of each day’s observations the recorded data were fed into a computer, which looked for pulsed signals with a well-defined period. If a candidate set of pulses was found, it had to be distinguished from terrestrial sources of spurious pulsed radio signals, such as radar transmitters and automobile ignition systems. The way to do this was to return later to the portion of the sky to which the telescope was pointing when the candidate signals were received and see if pulses of almost exactly the same period were present. If so, they had a good pulsar candidate that they could then study further, such as by measuring its pulse period to the microsecond accuracy characteristic of other pulsars. If not, forget it and move on to another strip of the sky.