Plucking the Strings of Relativity

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As scientific theories go, Albert Einstein’s general relativity has had an amazing run. James Clerk Maxwell’s theory of electricity, magnetism, and light gave way to a quantum
theory of light within 50 years. Quantum mechanics was superseded by quantum field theory in less than 20 years. But after 100 years, Einstein’s theory of gravity, space, and time is still state of the art.


The longevity of general relativity owes as much to its complexity as it does to the wide variety of strange new phenomena it predicted. In fact, my late colleague and Nobel laureate Subrahmanyan Chandrasekhar often said that Einstein’s understanding of general relativity was quite limited! Chandra was not trying to cut Einstein down to size; he was trying to indicate how deep and profound the theory is.


While the mathematical solution describing the simplest black hole was discovered in 1916, the solution describing the more interesting spinning black hole was not found until 1963. And it wasn’t until the late 1960s, when John Wheeler coined the term “black hole,” that the mathematics describing these mysterious entities were fully understood and their reality was no longer doubted.


Likewise, debate raged into the 1970s about whether general relativity really predicted gravity waves and, if so, whether the waves actually carried energy. Singularities, places where space and time literally end, remained a mystery until Stephen Hawking and Roger Penrose clarified the subtle mathematics involved. Their singularity theorems made black holes and the Big Bang more understandable and more beautiful.


By the end of the 20th century, advances in technology allowed most of general relativity’s predictions to be tested. It began in 1919 with Sir Arthur Eddington’s apparent confirmation that gravity bends starlight as it passes near the sun. Ten years later, astronomer Edwin Hubble verified the basic tenet of Einstein’s theory—that space is flexible—when he discovered that galaxies are racing away from each other, like raisins in a rising loaf of raisin bread. In 1960 a Harvard laboratory measured the warping of time in a gravitational field, and some 20 years later researchers found indirect evidence for the existence of gravity waves.


But even with all these successes, it is clear that Einstein won’t have the final word on gravity. Like Newton’s theory before it, which was incompatible with special relativity and was not powerful enough to describe the universe, general relativity has shortcomings that point to a grander theory. That by no means implies failure. The ultimate reward for a great theory lies in its ability to raise questions that lead to its demise and help to shape its successor.


Standing on Einstein’s shoulders, physicists can now ask a new set of simpler but more profound questions. Though they are phrased in the language of general relativity, the theory cannot answer them. These questions get at the very nature of space and time and set a high bar for relativity’s successor.



1. HOW IS GRAVITY RECONCILED WITH QUANTUM MECHANICS?


From problems come solutions. For example, the incompatibility of Newtonian gravity and special relativity led Einstein to general relativity. Now our challenge is to reconcile the two great achievements of 20th-century physics—Einstein’s general relativity and his nemesis, quantum mechanics, the theory he helped create but never accepted.


Superstring theory, now often called M-theory, looks like the most promising approach to marrying quantum mechanics and gravity while unifying all the forces of nature at the same time. Like general

relativity, M-theory is bold: It knits together the strands of physics by describing all

particles and forces as fantastically small strings of energy vibrating in 10 spatial dimensions and one dimension of time. Even if M-theory is not the answer, it provides a taste of the kind of radical thinking about space-time that is now required as well as the wonderful surprises that lie ahead.



2. WHAT ARE SPACE AND TIME AND WHERE DID THEY COME FROM?


If M-theory describes the marriage of gravity and quantum mechanics, it appears that the latter got the better prenuptial agreement. Quantum mechanics provides the framework for the theory, with the description of gravity conforming to it, not vice versa. This runs counter to Einstein’s hope that the geometry of space-time would provide the new paradigm for unifying the forces. There’s already plenty of evidence that space and time are secondary, so-called emergent phenomena. For example, there are mathematical solutions of M-theory in which the number of spatial dimensions can change. This suggests that space and time are not fundamental and that they emerge from something else. From Newton’s fixed space and time to Einstein’s flexible space-time, and now to space and time as emergent phenomena, we have come a long way. Maybe we will soon be ready to tackle the question of why time moves in one direction only.



3. WHAT LIES AT THE HEART OF A BLACK HOLE?

According to general relativity calculations, as one passes the event horizon (the point of no return) of a black hole, space and time switch roles. The inevitability of moving forward in time becomes instead the unavoidable plunge to the singularity at the center of a black hole. And that singularity prevents our knowing what lies beyond. It could be a wormhole, or shortcut, to another place in our universe or even to another universe entirely.


The singularities—the mathematical infinities that crop up in general relativity—are a clear sign that Einstein did not have the final word on gravity. At singularities the laws of physics appear to break down. More likely, our understanding is breaking down. M-theory has tamed some of the simpler singularities of general relativity, with the fuzziness of quantum mechanics taking the sharpness off these very pointy regions of space and eliminating the mathematical infinities. While M-theory has yet to determine precisely what lies at the heart of a black hole, it has shed light on some of their fundamental mysteries.


4. WHAT HAPPENED BEFORE THE BIG BANG?


More than 50 years ago Fred Hoyle coined the term “Big Bang” to draw attention to what he thought was a ludicrous feature of general relativity—a colossal creation of matter and energy from nothing. After the work of Hawking and Penrose, the beginning was clarified: The Big Bang was a space-time singularity out of which space, time, matter, and energy came to be. Thus, if general relativity is correct, there is no “before the Big Bang,” as time did not exist, nor did space, matter, and energy.


When he pondered what God was doing before he created heaven and earth, St. Augustine concluded that there was no before, “as time itself was [God’s] creation.” Relativity theory suggests that the universe began in a similarly tidy way, but is that the final answer? While Hawking and Penrose demonstrated the mathematical beauty of the Big Bang singularity, it nonetheless represents a breakdown in the laws of physics, one that blinds us from seeing anything before the Big Bang. Beyond the singularity could be an earlier, collapsing phase, or “big crunch,” of our universe or even the quantum creation of a universe from nothing. There may have been countless big bangs, as Alan Guth’s cosmic inflation theory implies, each creating its own universe within a larger multiverse.

5. WHY IS THE EXPANSION OF THE UNIVERSE

SPEEDING UP AND NOT SLOWING DOWN?



Answering this one is my personal quest. After Hubble found evidence that the universe is expanding, astronomers expected that the attractive force of gravity would continuously slow down the expansion and that by measuring that rate of slowing they could determine the shape and fate of the universe. According to Einstein, if the universe has a high density of matter, space curves back on itself like a ball, and the slowing would someday halt the expansion and lead to a recollapse. But if the density of matter is low, space would curve away from itself like the surface of a saddle, and the expansion would continue forever. If the density is poised precisely between those extremes, at what is called the critical density, space would be uncurved—flat—and the slowing would continue forever.



It all seems simple, but there is a twist. In 1998 two teams of astrophysicists—one led by Saul Perlmutter and the other led by Brian Schmidt—measured the change in the universe’s expansion rate by using distant supernova explosions as mileposts. They found, and others have since confirmed, that the expansion of the universe has been speeding up, not slowing down, over the past 6 billion years or so.

 

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Cosmic acceleration seems to fly in the face of everything we know about gravity, but Einstein’s theory actually predicts that gravity can be repulsive. And while the discovery of the cosmic speedup was a surprise to most, some theorists and I anticipated it. In trying to save the theory of inflation, which predicts that the universe is flat, we suggested that the gap between the critical density and the actual amount of matter is filled with something whose gravity is repulsive—something similar to what Einstein dubbed the cosmological constant, though in a new guise.



Strangely enough, the simplest example of energy with repulsive gravity involves Einstein’s nemesis, quantum mechanics, which holds that even a perfect vacuum is not empty. It is instead filled with so-called virtual particles, popping in and out of existence and living on borrowed time and borrowed energy in accordance with Heisenberg’s famous uncertainty principle. This is more than theory: In the late 1940s, physicist Willis Lamb detected the effect of virtual particles on hydrogen atoms in his Columbia University laboratory.



According to relativity theory, the energy associated with quantum nothingness—seemingly empty space—has re- pulsive rather than attractive gravity. Just as the strength of gravity around an object depends upon the object’s mass, the repulsive power of nothing depends upon how much “nothing” weighs. It has weight because empty space is actually teeming with virtual particles.



Therein lies the rub and the reason our prediction of cosmic speedup wasn’t a slam dunk. All attempts to compute how much nothing weighs have arrived at absurdly large numbers, more than 50 orders of magnitude larger than what is needed to account for the acceleration of the expansion. If space contained that much energy, the universe would be accelerating a great deal faster than it is. This mystery is tantalizing because it seems to involve a connection between quantum mechanics and gravity and could provide a clue to uniting general relativity with quantum mechanics. String theory may have something to say about how much quantum nothingness weighs because it actually permits the calculation of vacuum energy without pesky infinities cropping up. But it has yet to produce a definitive answer.



When it does, we might find that even quantum nothingness weighs nothing. If so, what is causing the expansion of the universe to speed up? It must be an energy form even more exotic than quantum vacuum energy. I coined the term “dark energy” for the whatever-it-is that is causing the universe to speed up. The possibilities being discussed for dark energy range from quantum vacuum energy to the influence of the unseen extra dimensions predicted by string theory.



Perhaps the most radical idea, and the one I am pursuing now, is that there’s no dark energy at all. (Remember, a foolish consistency is the hobgoblin of little minds.) Instead, our incomplete understanding of gravity is at fault, and when we understand it better, we’ll no longer need to invoke dark energy. Maybe a new principle is involved; for example, perhaps empty space naturally expands at an accelerating rate (while certainly not empty today, the density of the universe has diminished by more than 100 orders of magnitude since it began).







6. WHAT IS THE ULTIMATE FATE OF THE UNIVERSE?



Before we discovered that the universe’s expansion was accelerating, predicting our cosmic fate seemed straightforward: Measure the slowing of the expansion, the average density of matter and energy, or the shape of the universe. Any one or all three should give the answer. We now know the shape of the universe (flat) and the average density of matter and energy (critical density), and yet we don’t know what will happen. That’s because the connection between the three is severed when we allow for dark energy. Until we understand why the universe’s expansion is speeding up, we cannot know our cosmic destiny.



So the possibilities remain wide open. Continued acceleration would lead to a lonely universe in 100 billion years, when all but a few hundred galaxies become too red to see. On the other hand, cosmic speedup could be a passing fad, with dark energy dissipating and a cosmic slowdown returning. Or there could be a rapid slowdown and recollapse, or even a hyperacceleration that leads to the ripping apart of galaxies, stars, and eventually atoms.








In 1919 Arthur Eddington was told, “You must be one of three persons in the world who understand general relativity.” He responded by saying, “I am trying to think who the third person is!” After nearly a century, the depths of the theory are now well plumbed. While there are still parts to be tested with greater precision and aspects to be fully exploited (such as using gravity waves to detect the formation of black holes and events that occurred during the earliest moments of creation), physicists are ready and eager to go beyond Einstein in their understanding of gravity.



This is part of the natural progression in our quest to understand nature. Each successive theory deepens our knowledge of the physical world and at the same time raises new questions that it can phrase but not answer. Einstein’s theory of gravity transformed our concept of space, time, matter, and energy. It also provided us with the strong foundation needed to ask the next set of profound questions whose answers will further our knowledge of the universe, the laws that govern it, and probably even our place within it. Guided by Einstein’s wisdom for nearly 100 years, we are ready to move beyond him and answer the next questions on our own.