Cracking the Einstein Code – Relativity and the Birth of Black Hole Physics - Hardcover

Melia, Fulvio; Kerr, Roy

Hardcover

ISBN 10: 0226519511 ISBN 13: 9780226519517

Publisher: University of Chicago Press, 2009

Synopsis

Albert Einstein's theory of general relativity describes the effect of gravitation on the shape of space and the flow of time. But for more than four decades after its publication, the theory remained largely a curiosity for scientists; however accurate it seemed, Einstein's mathematical code - represented by six interlocking equations - was one of the most difficult to crack in all of science. That is, until a twenty-nine-year-old Cambridge graduate solved the great riddle in 1963. Roy Kerr's solution emerged coincidentally with the discovery of black holes that same year and provided fertile testing ground - at long last - for general relativity. Today, scientists routinely cite the Kerr solution, but even among specialists, few know the story of how Kerr cracked Einstein's code. Fulvio Melia here offers an eyewitness account of the events leading up to Kerr's great discovery. "Cracking the Einstein Code" vividly describes how luminaries such as Karl Schwarzschild, David Hilbert, and Emmy Noether set the stage for the Kerr solution; how Kerr came to make his breakthrough; and, how scientists such as Roger Penrose, Kip Thorne, and Stephen Hawking used the accomplishment to refine and expand modern astronomy and physics. Today, more than 300 million supermassive black holes are suspected of anchoring their host galaxies across the cosmos, and the Kerr solution is what astronomers and astrophysicists use to describe much of their behavior. By unmasking the history behind the search for a real world solution to Einstein's field equations, Melia offers a firsthand account of an important but untold story. Sometimes dramatic, often exhilarating, but always attuned to the human element, "Cracking the Einstein Code" is ultimately a showcase of how important science gets done.

About this title

About the Author

Fulvio Melia is professor of physics and astronomy at the University of Arizona and the author of numerous books, including, most recently, The Galactic Supermassive Black Hole.

Excerpt. © Reprinted by permission. All rights reserved.

CRACKING THE EINSTEIN CODE

Relativity and the Birth of Black Hole PhysicsBy FULVIO MELIA

The University of Chicago Press

Copyright © 2009 The University of Chicago
All right reserved.
ISBN: 978-0-226-51951-7

Contents

PREFACE.........................................ix1 Einstein's Code...............................12 Space and Time................................53 Gravity.......................................154 Four Pillars and a Prayer.....................245 An Unbreakable Code...........................396 Roy Kerr......................................547 The Kerr Solution.............................698 Black Hole....................................829 The Tower.....................................10010 New Zealand..................................10511 Kerr in the Cosmos...........................11112 Future Breakthrough..........................121AFTERWORD.......................................125REFERENCES......................................129INDEX...........................................133

Chapter One

EINSTEIN'S CODE

The scene could have been straight out of Universal Studios, Hollywood. Two men are breathing rhythmically in a smoke-filled modest little room facing south toward the capital of Texas. They sit quietly no more than an arm's length apart, lost in thought. Roy Kerr, the younger of the two, is hunched over a secondhand desk with his back to the door, studying the equations he has just scribbled in a notebook. His older friend and mentor, Alfred Schild (1921-1977), puffs away at a pipe while occupying a worn-out armchair to his right. It is late morning, and rays of sunlight filter through the bushes outside the window, creating a mosaic of light and shadow across the paneled walls.

At stake in this drama is the breakthrough solution to Einstein's equations of general relativity that have defied the greatest scientific minds of the twentieth century. So impenetrable is this description of nature, that Einstein himself succeeded only partially in divining its impact on the meaning of space and time. But it is now 1963, and the freshly minted mathematician out of Cambridge University, settling in at Schild's newly established Center for Relativity at the University of Texas at Austin, is about to crack the great physicist's famous code.

Much has been written about Albert Einstein (1879–1955) and his profound influence on our view of the universe, but very little is known about the golden age of relativity, spanning the period 1960–75 following his death. This book is the story of the brilliant young scientists of that era who accepted the challenge of unraveling the mysteries hidden within the seemingly unfathomable language of general relativity, culminating with Kerr's uncloaking of one of the most important and famous equations in all of science.

It is not always possible to discern the reasons why a scientific investigation meanders raggedly or slowly toward its ultimate goal, but in the development of relativity, the complexity of its mathematical formalism is certainly one of them. The difficulty of designing suitable experiments to test Einstein's theory is another. But neither of these reasons emerged for want of interest. Einstein became an instant celebrity soon after founding general relativity in 1915–16, with the quick, auspicious confirmation of one of his predictions—that gravity should bend the path of light as well as that of any particle with mass. This result resounded across the front pages of newspapers around the world, and scientists took note of the new ideas almost right away.

Indeed, only a few months after Einstein's publications began circulating around Europe, Karl Schwarzschild (1873–1916), a soldier on the Russian front, amazingly already succeeded in finding a description of space and time consistent with Einstein's theory, but only for a highly idealized situation, that is, for the gravitational field surrounding a static, spherically symmetric mass. Einstein greeted Schwarzschild's news with enthusiasm, and his solution is used to this day to describe phenomena in regions of strong gravity.

How odd, then, that arguably the most elegant scientific theory ever devised should slowly wither into the decades that followed this remarkable beginning. Those who knew him best have written that already by the 1930s Einstein's interest in general relativity had almost completely lapsed. Having by then moved to Princeton, he could count the number of colleagues working in this field on just one hand. Relativity theory had become irrelevant to science—a situation that sadly persisted up until Einstein's death. He would never know about the breathtaking discovery that would be announced just a few years later—a splendid confirmation of another prediction made several decades earlier.

This experimental achievement—a compelling demonstration in 1960 by the Harvard physicists Robert Pound and Glen Rebka that time slows down in the presence of gravity—sparked the revolution that followed during relativity's golden age, leading to that special moment in Roy Kerr's sepia-tinted office shortly afterward.

In the intervening years, failure to uncover practical applications of Einstein's theory was compounded by the lack of progress in the experimental verification of general relativity as the correct description of nature. Ironically, part of the problem was the Schwarzschild solution itself, which in time would be used to predict that truly bizarre objects, variously called dark or frozen stars, must exist somewhere in the cosmos. Today we call them black holes, but back then no one—particularly Einstein—believed they could be real. Yet the Schwarzschild solution clearly demonstrated that the end result of a gravitational collapse must be the formation of a singularity—a point of infinite density—that creates a closed pocket of space and time forever disconnected from the outside world.

Many thought that nature could not possibly create something so unreasonable, believing that no object in the universe is truly static and that, at the very least, its rotation would inhibit any collapse toward a singularity. And so began the search for the "holy grail" of relativity—a description of space and time surrounding a spinning object. Everything we see in the universe rotates, the argument went, so in order to demonstrate that Einstein's theory is a true description of gravity, we must be able to show that his equations do in fact describe space and time surrounding a spinning mass.

But what a challenge this turned out to be! Some of the world's most renowned physicists spent their entire careers working on this problem, making some progress, but losing interest or hope in their waning years. Of course, by the middle of the twentieth century, quantum mechanics had forged well ahead of relativity in relevance and measurability, cementing its place as the overarching theory in the physics pantheon. It didn't help that relativity and quantum mechanics seemed to be incompatible with each other, since the former uses perfectly measurable locations and times, whereas the latter is essentially a theory of spatial imprecision.

The Pound-Rebka experiment changed all that, principally because even the quantum mechanicists could not easily discount its remarkable implications. In fact, among the staunchest supporters of relativity and its relevance to modern physics was Vitaly Ginzburg, co-recipient of the 2003 Nobel Prize in physics for his work in the 1950s on superconductivity, a phenomenon in which some materials carry currents freely, without any resistance, by virtue of a quantum effect that becomes important at very low temperatures.

Though his interests were mainly in quantum mechanics, Ginzburg would nonetheless become an inspirational figure to many young physicists drawn to Einstein's theory in the early 1960s. Listening to him, the twenty-eight-year-old Roy Kerr understood that "cracking Einstein's code" was indeed the challenge he should ply with his mathematical talents—a task that would soon bring him to that fateful day sitting next to Alfred Schild in his smoke-filled office.

But the story begins well before Kerr's arrival in Texas, even before Einstein himself, in fact. Musings concerning the nature of space and the meaning of time began to appear thousands of years earlier, in places such as the Greek colony of Elea in southern Italy. Before we explore the evolution in Einstein's thinking that led to his theory of general relativity, and the inspired work that followed during its golden age, we will therefore begin by tracing some of the incipient thinking that led to the problem in the first place. Our journey commences in the fifth century BC with the Greek philosopher Zeno, a man clearly far ahead of his time. Zeno realized even back then that the notion of an absolute space independent of time was paradoxical—anticipating by several thousand years the eventual unification of the two into the structure we now refer to as simply spacetime.

Chapter Two

SPACE AND TIME

Physical reality emerges from the sequential defoliation of spatial phenomena. At least that is how we perceive the external world. Never mind that the nature of space and the meaning of time—scrutinized by thinkers from the dawn of civilization in India, China, and Greece, through to the modern era—have defied complete demystification.

Across the ages, many have plumbed the depths of the unknown to uncover nature's secrets. Without question, however, the greatest contribution to our view of the universe was Albert Einstein's general theory of relativity (fig. 2.1), which takes space and time and folds them, twists them, and pulls them into a single interwoven unit, at once alluring and uncomfortably disquieting.

But his code of nature proved to be one of the most difficult to crack in all of science, and it was left to his colleagues and successors to continue the search, occupying them for the better part of the twentieth century. Their story is emotive and at times exhilarating, leaving us with little doubt concerning the remarkable impact this work has had on our cosmic perspective.

This is not say, however, that we finally understand completely what space and time are. Nature works in certain ways, and we can describe its methods, though at the most fundamental level, why things behave the way they do is still unknown. Every civilization, from antiquity to the present, has formulated its own notions of space (the "heavens") and time (the "beginning" and the "end"). Some luminaries, such as the Buddha, Siddhartha Gautama, the spiritual master from ancient India who founded Buddhism in the fifth century BC, and Lao-tzu, the Chinese philosopher credited with writing the central Taoist work (the Tao Te Ching) around the same time, commented (or wrote) extensively on this subject. In the Western world, the Greek philosophers Aristotle, Socrates, Plato, and Zeno had the greatest influence, extending their intellectual reach into the Renaissance, when Galileo Galilei (1564–1642) and Sir Isaac Newton (1642–1727) would supplant their erstwhile inscrutable view of the world with scientifically more consistent theories.

The essence of their teachings, crystallized in our consciousness, forms mental images we still use today. We view space as a three-dimensional continuum that envelops us, while time seemingly flows alone, serenely, unaffected by influences in the physical universe. In combination, they provide the canvas upon which the colors of interaction are splashed, the basis upon which matter, radiation, people, and planets are tangibly manifested.

Firmly rooted to Earth—the origin of all known life—the ancients understandably viewed space as an absolutely position-dependent concept. The Chinese, for example, considered the structure and rhythms of the universe to have perfect unity and continuity, though with an evident center: China in the middle of the world, its capital at the hub of the kingdom, and the royal palace at the nucleus of the capital.

People in the West had similar notions. According to Greek mythology, Zeus charged two eagles with finding the center of Earth, and released one to the east, the other to the west. They met at Delphi, on the slopes of Mount Parnassus in Greece. Over time this would become the site of the most important oracle of the classical world. Here stood the omphalos stone, which, translated into English, simply means (Earth's) "navel," revered by the Greeks as the center of Earth and the whole universe.

For a thousand years, up to the time of Galileo and Newton, thinkers who worried about such things also had to contend with Aristotle's concept of an absolute space fixed to the firmament and an absolute time. In his "cosmogonic" system, he argued that change (or movement) were associated with Earth and the Moon because of their imperfections. Perfection was seen as a state with no need for change, a characterization that seemed to apply to other planets, the Sun, and the stars, which were thought to be immutable and eternal. Such an exalted state of being requires an independent, self-defined space and an equally unrestrained and perfect time. This was the worldview Newton inherited as a student at Cambridge, one that over the course of his life he would transform with deep, insightful analysis.

In retrospect, we might wonder why it took so long to address the apparent inconsistencies in the interpretation of space and time head-on. To be honest, however, even today we do not have a compelling answer to some of the difficulties uncovered by the early thinkers, at least not in terms of pre-relativistic ideas.

Take Zeno's argument known as "the Arrow Paradox," for example. Zeno was born around 495 BC in the Greek colony of Elea in southern Italy, but very little is known about him. Though he developed some forty paradoxes, only eight have survived, thanks to the efforts of subsequent writers, such as Aristotle. Zeno's goal was to demonstrate that motion, change, time, and plurality are mere illusions—that in reality the universe is singular and immutable.

Like the other arguments known to us, the Arrow Paradox seems illogical, perhaps even confusing, but it cannot be discarded quite so easily. Aristotle himself abandoned Zeno's paradoxes without really proving their (assumed) fallacy, but they were revived many centuries later by mathematicians such as Bertrand Russell (1872–1970) and Lewis Carroll (1832–1898).

Let us suppose, as Zeno did, that absolute space and absolute time exist without any direct connection between the two, and let us imagine an arrow launched (for the sake of argument) along a straight-line trajectory. Then, simply stated, if the arrow exists distinctly at a sequence of discrete instants in time, and if no motion is discernible in any given instant, there cannot be any motion from one instant to the next.

Bertrand Russell described this as "a plain statement of an elementary fact." If we were to make an image of the arrow in flight, it would be very difficult for us to tell from the photograph whether the arrow was moving or not. With only a modest shutter speed, the arrow might appear blurred, since it would have changed location slightly during the exposure. But as the shutter speed increases, and the corresponding interval shrinks to zero, this blurring effect disappears, and in the limit when the interval goes to zero, there would be no difference at all in the appearance of a moving arrow and its stationary counterpart. But if there is no discernible difference between a moving and a nonmoving arrow in any given discrete instant, how does the arrow "know" from one instant to the next whether it is moving? How can the causality be transmitted forward in time through a sequence of such instants, in each of which motion does not exist?

Attempts to rationalize this inconsistency have met with only limited success, and the essential physical question remains—that is, what is different between the moving and nonmoving arrows during any given instant of time? No one now believes Zeno's denial of any real physical motion, but an answer to this question, partial as it is, could only emerge from the physical principles developed during the twentieth century. Modern physics has concluded, along with Zeno, that the classical image of space and time was simply wrong to begin with, and in fact motion could not be possible in a universe constructed according to the old ideas, as we shall soon see.

The evolution away from the ancient concept of space and time actually began with Galileo and Newton, two icons of the classical physics pantheon. In 1687 Newton published one of the most influential books ever written—the Philosophiae Naturalis Principia Mathematica, or Principia for short. In it he provided a new paradigm, though still describing time as a one-dimensional continuum existing on its own, and space as an absolute three-dimensional substrate, which might or might not contain material things. But Newton introduced a novel idea, subtle at first, but profound in its influence: space, he declared, does not have a center. Nor is it always necessary to describe motion relative to a special, fixed frame. The Principia shattered Aristotelian orthodoxy by abolishing the clear demarcation between heaven and Earth. No longer were the stars and the planets immutable embodiments of perfection, establishing the ultimate standard by which all (imperfect) motion ought to be measured.

(Continues...)

Excerpted from CRACKING THE EINSTEIN CODEby FULVIO MELIA Copyright © 2009 by The University of Chicago. Excerpted by permission of The University of Chicago Press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Edition details

• Publisher: University of Chicago Press
• Publication date: 2009
• Language: English
• ISBN 10: 0226519511
• ISBN 13: 9780226519517
• Binding: Hardcover
• Number of pages: 150