Wheeler wanted his students to be bold, like him. Though conservative in his politics and always gentlemanlike in his demeanor, Wheeler was never afraid to dive into the deep end when it came to physics—to try out a range of ideas, no matter how speculative. So much so that he once considered writing a book titled Not Crazy Enough. One of his former students, Robert Fuller, notes that this open-mindedness set Wheeler apart as a physicist. He had the ability to dislike a singularity yet be fascinated at the same time by the fact that it appears in the equations. “He was so playful with ideas, so willing to consider the opposite of anything,” says Fuller. “He got that from his mentor Niels Bohr, who was always going around saying, ‘The opposite of any deep truth is also a deep truth.’ Wheeler quoted that every chance he got.” He gave any contrary hypothesis its due consideration. Just as Max Planck in 1900 invented the “quantum” to handle a brewing catastrophe in thermodynamics, Wheeler wondered whether the Schwarzschild singularity signaled where another breakthrough lay hidden in fundamental physics.
The Princeton team began their work on gravitational collapse by following up and extending the work of Oppenheimer and his cohort, an endeavor in which the Princetonians now had a decided advantage. One of the world’s first digital computers—MANIAC, which stood for Mathematical Analyzer, Numerical Integrator, and Computer—was available at the nearby Institute for Advanced Study, making the task of calculation easier. One of the group’s early results was presented at an international physics conference in Belgium in 1958. Wheeler and his students, B. Kent Harrison and Masami Wakano, figured that a collapsing star would spew out so much light and matter that it would save itself, ultimately settling down as a stable white dwarf or neutron star. Yes, Wheeler told the audience, like Oppenheimer they had seen that a star more massive than about two suns would implode, squeezing its mass to an extreme density. But did it end up disconnecting from the universe? No, answered Wheeler firmly. To save nature from such an absurdity, they had the elementary particles at the center of the star somehow transform into radiation—“electromagnetic, gravitational, or neutrinos, or some combination of the three. … A motion picture of a large mass of [nuclear matter] dissolving away under high pressure into free neutrinos presents a fantastic scene,” the team reported. This allowed enough mass to escape that the star safely settled down, perhaps as a mere neutron star—not a singularity. There was as yet no physics to fully explain this mechanism, but there was also no physics to prove it absolutely wrong. How gravity acted at the quantum level, in spaces no bigger than an elementary particle, was still a big unknown. It’s a condition, the Princeton group noted, “which lies at the untamed frontier between elementary particle physics and general relativity.”
Oppenheimer was in the audience and at the end of Wheeler’s talk took the floor and politely disagreed. Why count on new physics appearing down the line? “Would not the simplest assumption about the fate of a star of more than the critical mass be this,” he asserted, “that it undergoes continued gravitational contraction and ultimately cuts itself off more and more from the rest of the Universe?” Oppenheimer thought the entire matter had already been solved with his 1939 paper. But Wheeler, as yet, was not convinced. “It is very difficult to believe ‘gravitational cutoff’ is a satisfactory answer to the problem,” he replied. Like Eddington before him, Wheeler was hoping to theoretically wipe the singularity off the face of the cosmos.
But with further work on this problem, Wheeler and his students soon learned that a star of great mass would not be stopped from its collapse in the way they had described. Their radiative model simply didn’t work. Determined, Wheeler considered the next potential loophole on his list. Perhaps electromagnetic forces come into play. The repulsive forces between particles of similar electric charges might be powerful enough to halt the collapse. But again, their calculations proved that the gravity of all that collapsing matter overwhelmed such electromagnetic forces.
Kip Thorne arrived in 1962 to join Wheeler’s burgeoning quest. He went to Princeton specifically to work with Wheeler and clearly remembers, on entering Wheeler’s office, being greeted like an esteemed colleague rather than “a green graduate student” looking for a thesis topic. Top on Wheeler’s agenda were the many unresolved aspects of gravitational collapse, which they thoroughly discussed. “I emerged, an hour later, a convert,” said Thorne.
Theorists in the Soviet Union, most notably Yakov Zel’dovich, were already ahead in this game. In the West, physicists had largely ignored the papers on gravitational collapse until Wheeler came along. “In Western circles,” noted Werner Israel, “the work of Oppenheimer and Snyder was a forgotten skeleton in the cupboard … dismissed as the wildest speculation.” But the Soviets had embraced their papers far earlier. Having those articles on Landau’s “golden list” gave the Russians the incentive to pay attention. Landau had also included the Oppenheimer-Snyder results in a well-used textbook he coauthored. If a star was massive enough, the textbook stated in 1951, “a body must tend to contract indefinitely.” Soviet physicists didn’t doubt Landau’s wisdom at all; he was so revered that they took continued gravitational collapse for granted.
Like Wheeler, Zel’dovich had a background in nuclear physics. Working as a lab assistant right out of high school, carrying out impressive research, he learned so much chemistry and physics on his own that he was awarded a doctorate in his early twenties without having attended classes at a university. He went on to become a key member of the teams that built the first Soviet atomic and hydrogen bombs. In fact, his knowledge of astrophysics aided his work on the bomb. Dipping deeply into a book by Landau on gas dynamics, he and his teammates, including Andrei Sakharov, came to recognize that “the physics of stars and the physics of a nuclear explosion have much in common.”
Each pioneer, in the West and in the East, placed his own stamp on their “intellectual progeny,” as Thorne put it. “Wheeler was a charismatic, inspirational visionary,” said Thorne. He’d sometimes provide some general ideas but largely encouraged his students to become independent researchers, offering advice when needed. If their research took time, that was fine with him.
Yakov Zel’dovich (American Institute of Physics Emilio Segrè Visual Archives, Physics Today Collection)
On the other hand, “Zel’dovich was the hard-driving player/coach of a tightly knit team,” continued Thorne. Everyone on the team vigorously explored an idea together, trying to keep up with Zel’dovich’s blazing intellectual pace. In his camp, one and all got credit. Both Wheeler and Zel’dovich handed down those separate styles and approaches to the next generation of general relativists, who carried black-hole research into its golden age.
A turning point for both sides arrived in the mid-1960s when physicists were at last able to successfully simulate the implosion of a stellar core on its death, using the same advanced computers and same mathematical techniques that allowed physicists to design nuclear weapons. Thorne recalled Wheeler rushing into a relativity class one day with the news of the latest results from these simulations, carried out at the Livermore National Laboratory in California by the endeavor’s chief gurus Sterling Colgate and Richard White. Wheeler often traveled to Livermore to keep tabs on their work. “When the mass of the star was much larger than the 2-Suns maximum for a neutron star, the implosion—despite its pressure, nuclear reactions, shock waves, heat, and radiation—produced a black hole. And the black hole’s birth was remarkably similar to the highly idealized one computed nearly twenty-five years earlier by Oppenheimer and Snyder,” said Thorne. If the stellar core was weighty enough, it turned out that nothing—no other force in the entire universe—could stop gravity from creating a black hole.
In the Soviet Union Zel’dovich, too, saw that his know-how in bomb design could apply to simulating a star collapsing. Both Cold War adversaries knew this, but neither dared discuss their bomb work with each other. “I had many discussions with [Zel’dovich] and shared a sleeping car compartment with h
im one time from Warsaw to Moscow, and we never talk[ed] about that subject,” recalled Wheeler. “But Zel’dovich one day was writing on the board a formula for the explosion of a star. He gave me a wink, and I winked back. He and I knew it came from another context.” And those bomb-related calculations, carried out independently in the Soviet Union, arrived at the very same answer as in the West. Black holes were inevitable.
With such evidence in hand, Wheeler utterly reversed his earlier, negative opinion concerning the singularities of completely collapsed stars. Formerly determined to get rid of black holes somehow, he now became their greatest champion. But it was more than his own theoretical deliberations and the computer simulations that finally convinced him. Also crucial was a new way to look at a black hole. If you were viewing a star collapsing from very far away, you would never see the star fully shrivel down to nothingness. Due to time dilation effects, you would only get to see the star’s surface “freeze” into place just as it reached the critical circumference—its event horizon. Why is that so? It’s because, as Einstein pointed out very early in his work on general relativity, time slows down in a gravitational field, and as the star gets denser and denser in its collapse, it takes longer and longer for the star’s photons to escape—and it’s those photons that allow us to see what’s happening. By the time the star reduces to the size of its event horizon, then it takes an infinite amount of time for us to see any further progression. Time stops in its tracks. It’s like a movie projector going slower and slower, until it halts and lingers on just one image. That’s why Soviet scientists gave such a collapsing object the name “frozen star.”
But that doesn’t mean the star is actually freezing into place. In its frame of reference (not ours from afar), total oblivion is swift. If you were magically shifted onto the star itself, falling inward with the collapse, you’d pass right through the horizon without hesitation. The two different reference frames depict different outcomes simply because they do not share the same space and time. “You cannot appreciate how difficult it was for the human mind to understand how both viewpoints can be true simultaneously,” Russian physicist Evgeny Lifshitz told Kip Thorne.
But in 1958 David Finkelstein, then a young, little-known physicist at Stevens Institute of Technology in New Jersey, developed a new reference frame to handle these different viewpoints concurrently. A new perspective, if you will. It allowed physicists to picture how a collapsing star appears like a frozen star to us from afar yet still fully implodes from the standpoint of the hole. Plasma physicist Martin Kruskal had actually arrived at a similar result earlier. In the mid-1950s he had joined a small group of Princeton colleagues who wanted to learn general relativity on their own, and during that time Kruskal developed an even more extensive framework than Finkelstein later demonstrated. When Wheeler showed no interest in the new derivation, Kruskal just put it aside. A couple years later, though, Wheeler finally realized that his indifference had been an egregious oversight and soon wrote a paper on the coordinates under Kruskal’s name (to Kruskal’s surprise). It was published in 1960.
In the end, both Finkelstein and Kruskal made it easier for theorists to visualize—all at once—every strange, relativistic effect going on both from our vantage point here on Earth and right at a black hole’s event horizon far away in space. That made the physics far more comprehensible for Wheeler’s team. And it also broke the logjam in tackling relativistic problems once thought impossible to solve. “The field of gravitation was then almost completely dominated by Newton’s theory,” notes historian Jean Eisenstaedt, “and Kruskal’s interpretation came as a bombshell in the small sleepy relativist village.”
By 1962 Charles Misner, then at Princeton and working with Wheeler, recruited undergraduate David Beckedorff to take these new mathematical tools and essentially redo Oppenheimer and Snyder’s work for his senior thesis. According to Misner, Beckedorff’s treatise was the first description of the space outside an imploding star, showing how the matter falling inward crossed the event horizon. “Even if you sent a suicidal spacecraft at the speed of light, to try to catch up to that collapsing star, you’d never make it,” explains Misner. You’d have to go faster than the speed of light. This image wasn’t available in the Oppenheimer-Snyder paper. Beckedorff’s solution, worked out under Misner’s guidance, introduced an entirely new way to look at a black hole.
Before this physicists and relativists working on gravitational collapse were concerned only with the stellar matter: What was happening to the stellar material, what was its final state? “But it’s gone,” says Misner. “What’s left is the black hole. Previously people focused on the fate of the star, but now we were seeing that something had formed. It’s still there, and it can do things. It’s not just the graveyard of the star.” That, too, was a turning point for Wheeler. This new perspective allowed him and others to recognize the black hole as a real object, even though its mass is now hidden behind the event horizon.
And about that term event horizon—it was physicist Wolfgang Rindler, then at Cornell University, who first used the phrase in 1956. Only in his case, he was applying it to cosmological models of the universe. On one side of an event horizon, events can be seen by us; on the other side, said Rindler, they are “forever outside [our] possible powers of observation.” In the cosmological case, the celestial objects in our expanding universe have flown past the borders of the visible universe. At that far point, their light waves can never catch up to us as the universe continues to expand. It turns out this was also the perfect definition to describe Schwarzschild’s point of no return. Once an object is inside the event horizon, it can never again be seen from the outside. So, by the early 1960s, astrophysicists began using the term as well when talking about the outer boundary of a gravitationally collapsed star.
Exhilarated by their successes, physicists in the Soviet Union, the United States, Great Britain, and continental Europe began to examine the characteristics of a black hole in more detail. They looked at each and every property a black hole could possibly have. What happens to the collapsing star’s magnetic fields, for example, as the event horizon emerges? They get severed from the dying star and snap off like rubber bands. From the outside, the lone black hole ends up having no magnetic field at all.
What if the collapsing star is deformed? Nothing in nature is perfect; maybe even a minor bump or bulge on a star would halt its collapse. Simulations up to this point usually had a perfectly spherical star, which perhaps falsely caused the virtual star to collapse uniformly within the computer calculations to an exact point. And, for a while, it appeared that would be physics’ savior in preventing the formation of singularities. In 1961 two Russians, Evgeny Lifshitz and Isaak Khalatnikov, seemed to have proven that irregularities did make a difference. In their simulations, they started with a lumpy star and found that some parts of this star would collapse faster than others and so experience a rebound at the center, preventing a singularity from ever forming. They went so far as concluding that singularities would never be created in a real universe. But that turned out not to be the case. Within several years they found a mistake in their calculations and, once corrected, arrived at the exact opposite conclusion. No matter what the stellar matter looked like at the start, the collapse is not halted and the end product—the black hole’s horizon—is blandly uniform.
Case by case led the relativists to one, undeniable conclusion. No matter what a star looks like before its gravitational collapse, all its distinguishing features vanish—leaving behind only three pieces of information. The only properties that remain are the former star’s mass, its spin, and its electric charge (though that charge would likely be neutralized after attracting equal and opposite charges from its environment). As John Wheeler liked to say, “A black hole has no hair,” no defining characteristic that makes it look different from any other black hole. “There is no way to tell from outside whether a black hole was created using neutrinos, or electrons and protons, or old gr
and pianos.” Or if it had been yellow, wrinkled, or polka-dotted. A black hole is a black hole is a black hole. Every distinctive feature of a star disappears behind its inscrutable event horizon. The gravitationally collapsed object should not be thought of as a frozen star at all. Instead it should be thought of as a soap bubble–like pure gravitational field—its only properties being mass, angular momentum, and electrical charge. The singularity itself would never be seen, forever cloaked behind the event horizon.
That an object so cosmic could appear so basic—described by a mere three numbers—was simply flabbergasting to everyone. It meant that each black hole is as elementary an entity as an electron or a quark. Here was the beauty and simplicity that Chandrasekhar referred to in his Nobel Prize lecture.
Armies of students worked on all the nuances of these problems for years, in order to nail down each and every feature of a black hole. There was always the chance that something might turn up to prevent a black hole from forming after all. But nothing turned up. “The matter of the core pours torrentially inward from all directions like a thousand Niagara Falls on its way down from the original [stellar] dimensions to ever smaller sizes,” wrote Wheeler in 1968. “In less than a tenth of a second … the collapse goes to completion, and little if anything is seen.”
Roger Penrose had already provided powerful ammunition to back up Wheeler’s statement. Penrose was a member of a highly influential group of British theorists who were devising a number of brilliant topological and geometrical tools to answer key questions about the physics of black holes. Trained in mathematics, not physics, Penrose first became interested in relativistic singularities after hearing Finkelstein lecture in the late 1950s in London. “When I got back to Cambridge, knowing very little about general relativity,” said Penrose, “I started to try and prove that singularities were inevitable. It seemed to me that maybe this was a general feature.” Yet, at the same time, they also seemed to him a bit “ridiculous and mysterious,” he noted. After intermittently working on the problem over the ensuing years, he at last published a theorem in Physical Review Letters in 1965 that has been called by some as “the most influential development in general relativity in the 50 years since Einstein founded the theory.” Four years before Lifshitz and Khalatnikov discovered the mistake in their calculations, Penrose proved, in less than three pages, that full gravitational collapse and singularities go hand in hand. It took a while to convince everyone because he used a mathematical approach not familiar to most physicists. But the bottom line was unmistakable: you couldn’t have total gravitational collapse without a singularity turning up at the end. “Deviations from spherical symmetry,” reported Penrose, “cannot prevent space-time singularities from arising.” (That is, as long as quantum mechanics is not taken into account, which black-hole theorists were not yet doing; more on that in chapter 12.)
Black Hole Page 10