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After Einstein: The Dark Mysteries

A computer simulation of the collision of two black holes, which merged about 1.3 billion years ago to form a single black hole sixty-two times the mass of the sun. The gravitational waves were detected last September by the Laser Interferometer Gravitational-Wave Observatory (LIGO), which announced the discovery in February 2016.
SXS (Simulating eXtreme Spacetimes) Project
A computer simulation of the collision of two black holes, which merged about 1.3 billion years ago to form a single black hole sixty-two times the mass of the sun. The gravitational waves were detected last September by the Laser Interferometer Gravitational-Wave Observatory (LIGO), which announced the discovery in February 2016.

Nature and Nature’s laws lay hid
    in night:
    God said, Let Newton be!—and
      all was light.
It did not last: the devil, shouting
    “Ho.
    Let Einstein be,” restored the
      status quo.

—Alexander Pope, with a continuation by J.C. Squire

1.

On Thursday, November 25, 1915, Albert Einstein, no longer a patent clerk and by then a respected university professor, presented his fourth and final lecture in a series at the Prussian Academy of Sciences in Berlin. Titled “The Field Equations of Gravitation,” this lecture, or at least the ideas it contained, completely overhauled our conception of gravity. Einstein proposed a fundamental rethinking of the nature of space, time, and matter. He redrew our cosmic map in a radical transformation, the likes of which had never happened before—or since.

Of course an established scientific model is often called into question when scientists obtain more accurate or new observational or experimental data that do not fit the accepted theory. Most often these mismatches bring about relatively small refinements in the understanding of phenomena. Take, for example, the case of nineteenth-century measurements of deviations in the orbit of the planet Uranus from the trajectory expected from Newton and Kepler’s seventeenth-century laws. Using mathematical calculations, the French astronomer Urbain Le Verrier predicted the cause to be the existence of a hidden, perturbing gravitating body lurking nearby. Within months, the young astronomer Johann Gottfried Galle searched for and detected the planet Neptune in 1846. Newton’s laws remained intact.

Later, when more accurate measurements of the motion of the planet Mercury also revealed a tiny, almost imperceptible wobble, Le Verrier attempted to use the same solution to resolve the discrepancy. He predicted the existence of another new planet, Vulcan, orbiting uncomfortably between the sun and Mercury. This time, the search was futile. As it turns out, it would be Einstein who would end up explaining Mercury’s wobble.

2.

Very rarely in science, there are instances when the anomalous data lead not to small refinements but to an entirely new theory. To say that was the case with Mercury’s wobble would be misleading. Einstein certainly did not set out to explain Mercury’s orbital anomaly, but he did. Einstein developed the entire theory of general relativity from a profound intuition and pure abstract thought. Deep mathematical understanding and insights, not new data, were the basis for his breakthroughs.

Einstein’s approach originated when he was still a student and was dissatisfied with what he felt were incompatibilities between physical descriptions of the motions of objects—classical mechanics—and the theory of light—classical electromagnetism. He was convinced that a simpler and more elegant connection between the two theories could render them fully consistent. In 1905, he arrived at the solution with his special theory of relativity.

Einstein postulated that all phenomena follow the same laws of physics, no matter the situation in which measurements are made—whether by stationary observers or those moving at a constant speed. He showed that, as a consequence, observers moving at different speeds would measure the lengths of objects and the passage of time differently. The same object will appear shorter to a fast-moving observer than it will to a slow-moving or stationary observer. Likewise time will appear to move more slowly to a fast-moving observer than to a slower one.

Einstein’s equations, which enable the calculation of the contractions and shortening of time intervals for moving observers, depend on an additional daring assumption: the speed of light in a vacuum (186,282 miles per second) as measured by an observer at rest and by one in motion had to be the same. This in turn implies that nothing at all can move faster than light. These limits may seem innocuous enough in our slow, daily experiences, but can yield unexpected results for objects and observers moving close to the speed of light.

In making the speed of light absolute, Einstein had made time relative. In 1907, Hermann Minkowski, an insightful mathematician, showed that what Einstein had really done was change time into a coordinate akin to the three dimensions we experience in space. Einstein quickly accepted this conception of a four-dimensional entity—space-time—as a necessary consequence and convenient mathematical representation of his theories.

Special relativity applies to objects moving at constant speeds, but Einstein knew that his theory would have to describe accelerating objects. While working toward this end, he realized in 1907 that a person in free fall, whose acceleration is caused by gravity, would not feel her own weight. Yet according to classical Newtonian physics, gravity is a force, and a person in free fall would feel pulled down by it. Einstein discovered that Newton’s description of gravity was insufficient.

With his general theory of relativity, Einstein provided an entirely new interpretation of reality that was based on the concept of space-time. According to general relativity, masses generate a gravitational field that deforms the shape of space-time. In this view gravity is not understood as a force exerted by objects with mass but as a distortion of the fabric of space-time. Masses create pockets in that fabric, and these pockets dictate how objects move on curved trajectories, such as a ball traveling in a parabolic trajectory or a planet in orbit. The entire universe is embedded in space-time (there is nothing above or below), altered by the pockets generated by all bodies that have mass, including planets, stars, black holes, and galaxies. The presence of these pockets not only affects motion but also alters the flow of time in their vicinity, such that time moves more slowly in a stronger gravitational field.

This radical new description of reality provided concrete, testable predictions and was therefore falsifiable. Einstein proposed several tests. One consequence predicted by Einstein is “gravitational lensing,” or deflections in the paths of light rays that encounter space-time distortions created by very massive bodies with strong gravitational effects. The existence of gravitational lensing was confirmed in 1979 by the appearance of a particular quasar—an extremely luminous stellar body produced by the release of tremendous amounts of energy as gas becomes compressed by the gravitational field of a massive, so far invisible, object we call a black hole. Because of the bending of the quasar’s light rays, owing to the presence of a galaxy between it and Earth, this quasar appears as two images. The position of each image is determined by the properties of the distortion in space-time caused by the intervening galaxy.

General relativity also predicts that dramatic changes in the structure of space-time would generate quakes that would propagate like waves on the surface of a pond. These so-called gravitational waves, which, as I will describe, were recently discovered, would echo through the history of the universe.

The validity of the general theory of relativity as the appropriate description for the universe had many far-reaching implications. The so-called field equations of general relativity permitted solutions that described the properties of space-time deriving from specific distributions of masses. In fact, descriptions of the detailed shape of space-time generated by all the matter in the entire universe can be computed.

In the 1920s, the Russian physicist Alexander Friedmann and the Belgian priest Georges Lemaître found solutions that describe a matter-filled expanding universe, in which space-time stretches over the history of the universe. Such a description had never been attempted before. Einstein’s equations revealed that the contents of the entire universe, its geometry, and its fate were intricately linked. Knowledge of any two would permit the determination of the other.

Starting with Edwin Hubble’s first measurements of the expanding universe in 1929, followed more recently by the measurement of an accelerating expansion, the equations predict the existence of other mysterious, hitherto unseen elements in the universe: dark matter and dark energy. Our current knowledge of the universe suggests that the bulk of the matter content is dark matter, which is composed of exotic particles unlike the ordinary atoms that lie on the familiar periodic table of elements. Dark matter does not emit any light and therefore, while it exerts gravity, it remains unseen. Its presence is inferred indirectly from its effect on the motions of visible stars and by the light-bending that it causes. Dark energy on the other hand is a mysterious force that seems to power the accelerating expansion of the universe. Its true nature also remains elusive, although its effects are observed. And of course, general relativity had something to say about the planet Mercury orbiting closest to the center of our solar system—the one most influenced by the gravity of our massive sun.

3.

Newton’s laws reigned supreme for more than two centuries before Einstein challenged them. In Newton’s remarkable treatise Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), also known as The Principia, the first edition of which was published in 1687, he formulated his Three Laws of Motion that coupled Johannes Kepler’s Laws of Planetary Motion with his own mathematical conception of the nature of gravity. Although the night sky had been documented and mapped assiduously since ancient times for purposes of forecasting, Kepler was one of the first to explain its motions. His quest was for a celestial physics, a set of underlying principles he believed governed the motions of the orbs. Newton provided just that, formulating laws he believed were divine in origin.

Newton’s Universal Law of Gravitation was spectacular. It united the terrestrial with the celestial, offering an explanation for the motions of the planets as well as apples falling from trees to earth. Although there were many unanswered questions about the nature of gravity that plagued Newton’s theory, it proved to be remarkably successful because of the reach of its explanatory power. But as the quality of available astronomical data improved, and the orbits of planets were more accurately tracked, the first crack in Newton’s theory appeared.

In his new book, The Hunt for Vulcan:…And How Albert Einstein Destroyed a Planet, Discovered Relativity, and Deciphered the Universe, Thomas Levenson traces the history of these cracks: first, the discrepancies in the orbit of Uranus and, second, the tiny hitch in Mercury’s orbit. The tale goes well beyond chronicling the rectification of a mistake to probe the deeper issue of how scientific ideas evolve to include new facts. Levenson reveals the personal and psychological side of science, in particular how scientists grappled with abandoning old ideas when no alternative to replace them was available.

Levenson has made a rich study of the French astronomer and mathematician Urbain Le Verrier. The very traits that made him an excellent and gifted scientist were also a source of his flaws. His ambition and drive pushed him to make calculations that exposed lacunae in Newton’s model, and the same qualities made him a ruthless and manipulative scientist.

What is fascinating about Levenson’s account is that there were numerous claimed and reported sightings on several continents of the fictional planet Vulcan. It was thought that Vulcan could be spotted most easily when it moved across the disk of the sun during a solar eclipse. There was unbridled eagerness in the American astronomical community to settle the matter of the existence of Vulcan during the total solar eclipse on July 29, 1878. Observers flocked to Rawlins, Wyoming, where the total eclipse would last for two minutes and fifty-six seconds. The transcontinental railroad curved exactly along the eclipse route, making it a particularly good viewing spot for the astronomers armed with their cumbersome equipment.

Yet no consensus was reached on that day. Some observers claimed to see Vulcan move past the sun and others failed to see it. A conclusion to the matter had to wait for the lecture delivered by Einstein thirty-seven years later. Mercury’s motion could now be explained as the result not of a hidden planet but of a perturbation resulting from the pocket in space-time created by the sun.

The stage was set for unfixing the universe, and black holes became real.

4.

Einstein did not believe that the field equations of general relativity would have any exact solutions; he thought there might be approximate solutions that could offer adequate, but not precise, descriptions for various distributions of masses in the universe. Soon after presenting the theory in his final lecture at the Prussian Academy in 1915, he heard from the German physicist Karl Schwarzschild, who had found an exact solution for the modification in space-time produced by a tiny, compact mass. Schwarzschild’s solution points to a location—a “singularity”—where all the known laws of physics inevitably break down. In addition, the solution also implies the existence of a boundary wall—called the event horizon or Schwarzschild radius—that demarcates the point of no return beyond which no object or even light can escape the gravitational pull of a black hole. This is precisely why black holes are dark and do not even reflect light that grazes the event horizon. The extreme gravity of black holes causes dramatic bending of light rays, as visualized so beautifully in Christopher Nolan’s recent movie Interstellar.

‘The Planets’; nineteenth-century engraving by J.J. Grandville
‘The Planets’; nineteenth-century engraving by J.J. Grandville

Marcia Bartusiak’s latest book, Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved, traces the history of the idea of black holes. By her own admission, she does not claim to provide a status report on our current scientific understanding of black holes. What she accomplishes deftly is to provide a fascinating account of how the scientific community came to embrace the idea of a black hole. As she tells it, the concept of a black hole was once considered controversial, an abstract and curious mathematical absurdity, a mere solution to an equation that need not bear any resemblance to reality. The implications of the equations are indeed improbable. Matter is very tightly packed in a black hole, resulting in its intense gravity. The gravity exerted by a black hole on space-time is so extreme that it no longer produces a pocket but rather a sharp puncture. For instance, to possess the enormous gravity of a black hole, the entire mass of the earth would have to be packed into an object the size of penny.

Many scientists found the existence of black holes difficult to accept. Slowly, however, the idea has not only become accepted but has also become a subject of active research. Black holes are now an important part of our understanding of how galaxies form and evolve in the universe. Our own galaxy, the Milky Way, contains one black hole that is four million times the mass of our sun. From a nearly complete census of neighboring galaxies, we find that these gravitational oddities lurk in the centers of galaxies, revealing their presence only through their gravitational pull on the stars that orbit closest to them. The immense gravity of these dormant black holes, which are no longer increasing in mass, is even apt to rip apart any star that strays into their regions of influence. Farther afield, in distant galaxies that harbor a central black hole, gas is sucked into them by their strong gravitational pull. As the gas flows in, it gets heated and begins to glow, rendering the black holes visible as quasars—growing black holes that are actively feeding on gas. The light emitted from the glowing gas is so intense that quasars are some of the brightest objects in the universe. Quasars are visible from when the universe was barely 1 percent of its current age.

Astronomers now believe that black holes, despite their odd behaviors, are an inevitable consequence of the standard physics that describes the evolution of stars, which predicts that stars born fifteen to twenty times more massive than our sun, after exhausting their fuel supply of hydrogen, will become compact and end their lives as black holes. Although black holes may have exotic properties, they are important constituents of the universe. Theories of black holes entered the scientific mainstream once astronomers began discovering compact objects with strong gravity—the first were pulsars, or rapidly twirling neutron stars, which were discovered by Jocelyn Bell and Antony Hewish in 1967.

The path of a radical scientific idea from curiosity to acceptance can be arduous, and charting its course illuminates the scientific process. Scientists themselves, even the very proposers of these new ideas, often resist acceptance. Einstein was notorious for this. Despite making some of the most astonishing breakthroughs in modern physics in the twentieth century, he famously denied the implications of his own theories. Einstein found both Schwarzschild’s and Friedmann’s exact solutions to the field equations hard to accept in view of their implications. Because he believed that the universe had to be static, he dismissed as “abominable” the theoretical calculation by Friedmann that the universe was expanding despite mounting observational evidence from the astronomers Hubble and Vesto Slipher that galaxies were speeding away from us.

Long after the astronomical community accepted that these findings were evidence for an expanding universe, Einstein held out. Fixity was so fundamental to his sense of how the universe works that eventually, when he publicly acknowledged expansion at a seminar held in the library at Mount Wilson Observatory in 1931, there was a collective gasp from the audience. The hypothesis of the existence of black holes was counterintuitive and bizarre not only to Einstein but to most physicists.

Bartusiak’s book excels in describing the open questions concerning black holes and the controversies surrounding future directions in black hole research. These include the as-yet unsuccessful quest to further synthesize Einstein’s theory of general relativity with quantum mechanics. Einstein himself spent the latter part of his life working on such a synthesis—a quantum theory of gravity—that would ultimately unify all physical theories, coupling the macroscopic, microscopic, and cosmic realms. Such a theory remains elusive.

5.

Although the idea of black holes is now firmly established and accepted, and the predictions of the theory of general relativity have been confirmed, further high-precision tests of the theory are continuing. Opportunities to test the theory are rare; so are opportunities to find any potential limits that might be revealed close to the extreme gravity of a black hole. Astronomers are now pursuing a new tack to obtain more indirect information from black holes.

The goal of one new project is to map the shadow of the nearest black hole to us—the one at the center of our galaxy—using new instruments collectively called the Event Horizon Telescope (EHT). The extreme deformation of the fabric of space-time around a black hole causes light that skirts past nearby to cast a kind of shadow around the event horizon. The EHT is using radio telescopes in Mexico, Chile, and Germany to discern this shadow around the black hole at the center of the Milky Way. These telescopes scattered around the globe are combined to behave akin to a single collecting dish with an area almost the size of the Earth’s surface. This innovative technique will make the shadow discernible. By combining several telescopes to attain the sensitivity required, scientists hope to verify the properties of the black hole at the center of our galaxy.

Our current understanding of how the universe assembles predicts that galaxies grow by violently smashing into one another. This implies that the black holes that reside in the center of most, if not all, galaxies also collide and eventually merge, resulting in a more massive black hole with a larger event horizon. According to the theory of general relativity, as black holes collide they generate gravitational waves—tremors in the fabric of space-time. One ongoing experiment, the Laser Interferometer Gravitational-Wave Observatory (LIGO), announced in February the first direct detection of these gravitational waves.

To make this momentous discovery, experimenters simultaneously emitted light rays down two 2.5-mile-long tunnels arranged in an L shape. As a gravitational wave passes through the tunnels, their lengths alter slightly, and the light rays in each tunnel arrive at the crook of the L at different times. On September 14, 2015, the two LIGO sites, in Louisiana and Washington State, independently detected a gravitational wave by measuring a discrepancy in the time the light rays took to reach a sensor at the ends of the tunnels. The precision of the measurement is simply astonishing. The difference in length that each light wave traveled corresponds to 1/1000th of the radius of a proton, a subatomic particle that is itself minuscule, with a size of about 10-12 meters.

The signal captured precise details about the two black holes that, within a fraction of a second, collided, coalesced, and produced the gravitational wave. Scientists determined that they were thirty-six and twenty-nine times the mass of our sun, with event horizons approximately ninety-three miles wide. They produced a single black hole sixty-two times the mass of the sun. The difference in mass of the black holes before and after the collision was converted into energy in the form of gravitational waves. This is an enormous amount of energy, more than that in the visible light of all the stars in the universe combined. Scientists were also able to conclude that the black holes merged about 1.3 billion years ago, and that these ripples that stretched and compressed space traveled unimpeded to earth. The gravitational waves fall in the audible range and can be heard by us in the form of a chirping sound. We believe the universe to be full of black holes, and we are finally tuning in to hear them.

The verification of this event against Einstein’s equation was made possible by recent breakthroughs in computational techniques and hardware capacities that allowed a numerical calculation predicting the signal that ought to be observed. The predictions from simulation and the detected signal are in excellent agreement. Einstein, though, struggled with the idea of gravitational waves. In his first calculation, presented in 1916, he claimed erroneously that these waves would not transport any energy, a mistake in calculation that he rectified in 1918. He had second thoughts on the subject and in 1936 wrote a paper to retract his claim, and yet again made a mistake that was found by the reviewer. That paper was rejected and his prediction of gravitational waves remained intact.

The recent detection of gravitational waves marks the opening of an entirely new window of discovery. A detailed analysis of these waves will provide many more discoveries in astronomy and cosmology, as well as in fundamental physics. This is just the beginning of a new era. Advanced LIGO, with higher detection sensitivity, has also been collecting data and may soon report the detection of many more events from merging black holes.

Gravitational wave detectors in space are the next frontier. The European Space Agency has just launched a pilot, precursor mission, the LISA Pathfinder (eLISA), which will help us develop the technical specifications needed to make measurements for the future LISA mission that consists of interferometers much like LIGO but in space. This test probe was launched successfully on December 3, 2015. The recent LIGO detection will add scientific momentum to the LISA project. We are still actively probing and testing the limits of the theory of general relativity to see if it can explain more precise data.

In accordance with Einstein’s theory, our universe appears to be replete with invisible entities—dark matter, dark energy, and black holes. Two unseen components, dark matter and dark energy, remain elusive, and have not yet been directly detected, since they do not reflect or absorb light, our cosmic messenger. Vulcan has vanished, black holes are real, and it is good to have new mysteries. And yet as the wise fox tells the prince in Antoine de Saint-Exupéry’s fable The Little Prince, “L’essentiel est invisible pour les yeux”—the essential remains invisible to the eyes.

Letters

Einstein’s Observers September 29, 2016