And energy is just another sort of mass.
Energy might be more diffuse than mass, perhaps, but as E=mc2 shows, they're both just different versions of the same thing. Once again, the two sides of the equation— the "E" and the "m"—don't actually have to slip across and "turn into" one another. Rather, what the equation's really saying is that a chunk of what we call mass actually is energy: it's just that we're not used to recognizing it in that guise. Similarly, a glowing or compressed amount of energy really is mass: it just happens to be in a more diffuse form than we easily recognize as mass.
Chandra was about to glimpse the process leading to black holes. He merely had to trace this logic forward as it spiraled in an escapable catch-22. A compressed star core is under a lot of new pressure, and that pressure can be considered a sort of energy, and wherever there's a concentration of energy, the surrounding space and time will act just as if there's a concentration of mass. Gravity in the remnant star gets more intense, due to all this "mass." But that stronger gravity continues squashing what's left, so the pressure gets greater once more. Since the pressure can yet again be treated as simply more energy, then—as Chandra now saw by the tremendous insight of E=mc2—it acts as yet more mass. The gravity ratchets up.
In a small enough star, the buildup of pressure is low enough for the stiff material near the star's center to resist it. But if the star is massive enough, the process keeps on going. It doesn't matter how tough the star's material is; indeed, if it's exceptionally resistant, that will soon just make it worse. For suppose a giant star could hold up under even greater pressure than expected: immense, unthinkable, trillions upon trillions of tons bearing down. Well, that extra pressure would "be" more energy, which would mean it acts just as if it had more mass, and so the gravity would get even stronger, compressing it ever more.
Regardless of how hard the substance is at the core, the inside of the star will be crushed until. . .
Until what?
Chandra had all the openness to fresh thoughts of youth, but even he had to pause now. Could he be predieting that the inside of the star would actually disappear? If he was right, then rips were opening up in the very substance of the universe! He took time off for prayers and meals; he even spent hours politely listening to a Christian evangelist, who explained to this devout Hindu why all religions from India were the work of the devil. "He was a missionary," Chandra remembered later, "but he was also . . . anxious to please. Why be rude to him?"
When Chandra resumed work in his deck chair, he realized that he couldn't actually say what would happen to the remaining substance of the star, as it poured into the hole created by this never-ending collapse. But it was known in accord with other work of Einstein that space and time near the star would be strongly distorted by its presence. No light would ever escape; nearby stars that were pulled into its gravitational presence would get torn apart by what seemed an "empty" location in space.
This, along with other insights, was central to the modern concept of black holes. But once Chandra reached England, his vision was resisted by almost everyone he presented it to; often with less politeness than he'd granted the missionary. Eddington himself, the man who'd been so inspiring for Cecilia Payne, was now too old for any more such fancies. It was "stellar buffoonery," he declared. It was "absurd." But by the 1960s there was the first evidence of a star (look in the direction of the constellation Cygnus the Swan, and it's a little to one side) that spins around an area that to our telescopes seems to be entirely empty space. The only thing that would be powerful enough to do this in so small a space would be a black hole. In the center of our own galaxy, there's strong evidence of another black hole, a truly monstrous one, which has accumulated to a great size over the aeons, swallowing, on average, the equivalent of one ordinary star each year. Space-time is actually being "torn" open—as the young Chandrasekhar had been the first to see.
Chandra tried to fight Eddington's hostility in the 1930s, but when he found that even British astrophysicists who believed he was right were scared to back him in public, he ended up leaving England. He received a kinder welcome in America, and in an association with the University of Chicago went on to decades of work-culminating in his Nobel Prize in 1983, over a half century after that Arabian Sea voyage—which proved central in understanding what's in store for us next.
Six billion years from now, if Earth is flung loose from the fuel-emptied sun, any survivors or sensing devices left on our planet's surface will see a horizon darker than today's night sky. For the stars themselves will have used up their fuel and be dying out: the most fiery ones first, then the rest.
Earth's flight won't be stable through this darker expanse. Our Milky Way is already on track to collide with the Andromeda galaxy, and in several billion years, about the time of Earth's escape or immolation in the solar system, the great collision should finally happen. The spaces between stars are so great that most of the dimmed suns will just slowly pass between each other, without direct impact, but the turbulence will be enough to shift an escaped Earth's trajectory once more.
If Earth slingshots inward, then in a few tens of millions of years we will be within range to be absorbed by the giant black hole at the galaxy's center. If we get slingshot outward, however, the end will simply be delayed. By 1018 years from now (1 followed by eighteen zeroes, or 1,000,000,000,000,000,000 years from now), all galaxies are liable to have emptied out because of such collisions. The black holes in the centers of the galaxies will slowly travel on their own, sucking mass and energy from the universe wherever they contact other objects. If it's another black hole that they randomly impact, then they simply merge, to become an even larger devourer. A few hours after coming within range of one of these, Earth and any distant descendants on it will be taken out of existence.
By 1032 years into the future, protons themselves might have begun to decay, and gradually very little of ordinary matter will be left. The universe will be composed of a greatly reduced category of things. There will be electrons of the sort we're used to, with a negative electric charge, and there will be curious antimatter versions of electrons, with a positive charge, and along with neutrinos and gravitons there will be the swollen black holes, and even a cooled remnant of photons left over from the first seconds of creation, still traveling at their eternal 670 million mph speed after all these ages.
It doesn't end there, for given enough time even black holes can evaporate. Everything they engulfed will be released back—not in any recognizable form, but as an equivalent amount of radiation.
The universe will have ended up in a state curiously transposed from what it was at the start. For in the very first moments of creation, long before the sun was formed, the universe was immensely dense, immensely "concentrated." That great density meant that large amounts of radiation were "pushed" along E=mc2, from the "E" side to the "m" side. The ordinary matter we're familiar with took shape out of pure energy, ultimately creating the stars and planets and life-forms we know. But now, near the end of time, over 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years into the future, it's different. Everything is far more dispersed, far more diffuse.
What will exist then will be spread over distances we cannot imagine. The rush of activity of early epochs will be over. That was just an interlude in the final history of the universe. Now, mass and energy only very rarely transform into each other. There is a great stillness.
The work of Einstein's equation is done.
Epilogue
What Else Einstein Did
It wasn't actually E=mc2 and his other work from 1905 that first made Einstein famous. If that were all he had done, his name would have become recognized within the specialized community of theoretical physicists, but probably not otherwise known to the public. In the 1930s he would have been just another distinguished refugee: living a quiet life perhaps, but in no special position to sign
a letter warning of atomic dangers, which could be delivered to FDR in 1939.
It didn't turn out like that of course. Something else happened that built on E=mc2 but went further—and ended up making him the most famous scientist in the world.
What Einstein published in 1905 only covered cases where objects are racing along smoothly, and gravity, with its accelerating pull, doesn't play much of a role. E=mc2 is "true" in those cases, but will it hold true even if you get rid of those restrictions? That limitation and others had always troubled Einstein, and in 1907 he got the first hint of a wider solution: "I was sitting on a chair in my patent office in Bern when all of a sudden a thought occurred to me . . . . I was startled."
He later called this "the happiest thought of my life," for a few years later, in 1910, it led to his reflecting on the very fabric of space, and how it was affected by the mass or energy of objects at any one location in it. The work took several years, partly because although Einstein was in a league of his own in physics, he was only fair in mathematics. It wasn't quite as bad as he once described to a junior high school student in America, when he wrote her, "Do not worry about your difficulties in mathematics. I can assure you that mine are still greater." But it was enough to justify Hermann Minkowski's lament, when he saw the early drafts of Einstein's efforts: "Einstein's presentation of his subtle theory is mathematically cumbersome—I am allowed to say so because he learned his mathematics from me in Zurich."
To help him with the math, though, Einstein had his old friend from university days, Marcel Grossman, the one who'd loaned him crib sheets when they were undergraduates. (Grossman was also the friend whose father had written the letter getting Einstein the patent office job.) Grossman sat with Einstein for long hours, to explain what tools from recent mathematics he might use.
What Einstein's "happiest thought" of 1907 led him to was the idea that the more mass or energy there was at any one spot, the more that space and time would be curved tight around it. It was a far more powerful theory than what he'd come up with before, for it encompasses so much more. The 1905 work had been labeled "special" relativity. This now was general relativity.
A small, rocky object, such as our planet, has only a little bit of mass and energy, and so only curves the fabric of space and time around it a bit. The more powerful sun would tug the underlying fabric around it far more taut.
Examples of warped space-time.
MODIFIED FROM A DIAGRAM IN THE SCIENCES
BY JAMES TREFIL AND ROBERT M. HAZEN
(NEW YORK: JOHN WILEY & SONS, 1998)
The equation that summarizes this has a great simplicity, curiously reminiscent of the simplicity of E=mc2. In E=mc2, there's an energy realm on one side, a mass realm on the other, and the bridge of the "=" sign linking them. E=mc2 is, at heart, the assertion that Energy = mass. In Einstein's new, wider theory, the points that are covered deal with the way that all of "energy-mass" in an area is associated with all of "space-time" nearby, or, symbolically, the way that Energy-mass = space-time. The "E" and the "m" of E=mc2 are now just items to go on one side of this deeper equation.
The entire mass-loaded Earth rolls forward, automatically following the shortest path amidst the space-time "curves" that spread rippling around us. Gravity is no longer something that happens stretching across an inert space: rather, gravity is simply what we notice when we happen to be traveling within a particular configuration of space and time.
The problem, though, is that it seems preposterous! How can seemingly empty space and time be warped? Clearly that would have to occur, if this extended theory, which now embedded E=mc2 in its wider context, were to be true. Einstein realized that there could be something of a test—some demonstration that would be so clear, so powerful, that no one could doubt that this wild result he'd come up with was right.
But what could that be? The proving test came from the heart of the theory, that diagram of a warp in the very fabric around us. If empty space really could be tugged and curved, then we'd be able to see distant starlight "mysteriously" swiveled around our sun. It would be like watching a bank shot in billiards suddenly take place, where a ball spins around a pocket and comes out with a changed direction. Only now it would occur in the sky overhead, where nobody had ever suspected a curved corner pocket to reside.
Normally we couldn't notice this light being bent by the sun, because it would apply only to starlight that skimmed very close to the outer edge of our sun. Under ordinary circumstances the sun's glare would block out those adjacent daytime stars.
But during an eclipse?
Every hero needs an assistant. Moses had Aaron. Jesus had his disciples.
Einstein, alas, got Freundlich.
Erwin Freundlich was a junior assistant at the Royal Prussian Observatory in Berlin. I wouldn't say he had the worst luck of any individual I've read about. Possibly there was someone who survived the Titanic, and then decided to try a ride on the Hindenburg. But it's probably pretty close. Freundlich was going to make his career, he decided, by shepherding the great general relativity equations forward, and performing the observations that would prove Professor Einstein's predictions were right. He was very generous about this—in the way that Lavoisier had been generous in letting his wife help him watch metal heat and rust. As a special honeymoon treat, Freundlich brought his new bride to Zurich in 1913 just so she could be there as he discussed stellar observations with the renowned professor.
An eclipse was predicted for the very next year, in the Crimea, and Freundlich prepared everything in detail. He even carefully arrived in the Crimea two months early, in July 1914. It was probably the worst possible place for a German national to be. War was declared one month later. Freundlich was arrested, put in prison in Odessa, and had all his equipment taken away. He finally got out in a prisoner exchange for a group of Russian officers who'd been arrested in Germany, but by then the eclipse had come and gone.
He didn't give up. In 1915, back in Berlin, Freundlich decided he could help Professor Einstein by measuring the way light got bent near distant binary stars. In February he had results that backed up the new theory, and Einstein began to spread the good news in letters to his friends. Four months later, though, Freundlich's colleagues at the observatory found he'd estimated the mass of the stars all wrong, and Einstein had to take it all back. For most people (as Freundlich's young wife perhaps tried to explain) that would have been enough, but Freundlich resolved to try yet again. Why didn't they try measuring how much distant starlight got deflected near the massive planet Jupiter; the one that the great Roemer himself had so persuasively used to resolve a scientific problem in an earlier era? Freundlich proposed it to Einstein. Einstein liked his earnest young helper, and in December he wrote to Freundlich's director at the Prussian Observatory, suggesting that he be allowed to try this.
It would have been less painful just to have sent him back to the Crimean prison. Freundlich's superior was furious that anyone would dare to interfere. He threatened to fire Freundlich, insulted him in front of his colleagues, and made sure that he never, ever was allowed to get his hands on the equipment that could be used to test the prediction near the orbit of Jupiter.
But that didn't matter. Freundlich was hopeful again. A great new eclipse expedition was being planned, for 1919. If conditions allowed international travel, he'd finally be able to prove what he could do.
In November 1918 World War I ended. There were no obstacles to a German national traveling now! It's not recorded what Freundlich felt as the great expedition set out, but we know exactly where he was when the results came through. He read it in the newspaper, back in Berlin.
He hadn't been invited along.
In fact, it was a cool Englishman we've already met who led the team. Arthur Eddington wore small metal-rimmed glasses, was medium height and barely medium weight, and spoke in sentences that tapered off whenever he had to pause for thought, which was fairly often. This of course meant in the good English manner that un
der his meek exterior there beat a soul of wild determination. By the time Chandra encountered him in the 1930s his personality had hardened, but at this time, in the period of World War I, he had the energy of a young man.
On May 29 of each year the sun is positioned in front of an exceptionally dense group of bright stars—the Hyades cluster. That wouldn't usually help anyone, for without a solar eclipse occurring on that particular date, there would be no chance to see how that rich field of stars gets their light bent around the sun. The glare from the daytime sun would overwhelm that small effect. But in 1919 there was going to be an eclipse, precisely on May 29. As Eddington innocently noted: "Attention was called to this remarkable opportunity by the Astronomer Royal [Frank Dyson] in March 1917; and preparations were begun. . . ."
What Eddington neglected to mention was that he would have been thrown into prison if he didn't go. For as a Quaker, Eddington was a pacifist, and as a pacifist, in the middle of World War I England, one of the rough prison camps in the Midlands was in store. The soldiers guarding the pacifist camps were often recently back from the front—or embarrassed that they themselves hadn't seen service there, which could be worse. Conditions were rough. There was steady abuse and beatings; a number of deaths.
Eddington's colleagues at Cambridge didn't want him to go through this, and tried to arrange for the War Department to defer him, as being important for the nation's scientific future. A letter confirming this was sent to him, from the Home Office, which he only had to sign and send back.
Eddington knew what was in store in the prison camps, but being a pacifist isn't the same as being a coward, as the actions of many Quakers years later in the American civil rights movement showed. Eddington signed the letter, since that was only fair to his friends, but then he also added a postscript, explaining to the Home Office that if he wasn't deferred on grounds of scientific usefulness, he'd still ask to be deferred as a conscientious objector. The Home Office was not impressed, and began proceedings to send him to one of the prisons.
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