A Black Hole Mystery Wrapped in a Firewall Paradox
August 19, 2013
This time, they say, Einstein might really be wrong.
A high-octane debate has broken out among the world’s physicists about what would happen if you jumped into a black hole, a fearsome gravitational monster that can swallow matter, energy and even light. You would die, of course, but how? Crushed smaller than a dust mote by monstrous gravity, as astronomers and science fiction writers have been telling us for decades? Or flash-fried by a firewall of energy, as an alarming new calculation seems to indicate?
Alicia DeSantis/The New York TimesAn unexpected paradox involving black holes pits two basic tenets of modern science against one another: the theory of quantum mechanics, which governs subatomic particles, and Einstein’s theory of general relativity, which explains how gravity works.
Jim Wilson/The New York TimesLeonard Susskind.
Jim Wilson/The New York TimesRaphael Bousso.
This dire-sounding debate has spawned a profusion of papers, blog posts and workshops over the last year. At stake is not Einstein’s reputation, which is after all secure, or even the efficacy of our iPhones, but perhaps the basis of his general theory of relativity, the theory of gravity, on which our understanding of the universe is based. Or some other fundamental long-established principle of nature might have to be abandoned, but physicists don’t agree on which one, and they have been flip-flopping and changing positions almost weekly, with no resolution in sight.
“I was a yo-yo on this,” said one of the more prolific authors in the field, Leonard Susskind of Stanford. He paused and added, “I haven’t changed my mind in a few months now.”
Raphael Bousso, a theorist at the University of California, Berkeley, said, “I’ve never been so surprised. I don’t know what to expect.”
You might wonder who cares, especially if encountering a black hole is not on your calendar. But some of the basic tenets of modern science and of Einstein’s theory are at stake in the “firewall paradox,” as it is known.
“It points to something missing in our understanding of gravity,” said Joseph Polchinski, of the Kavli Institute for Theoretical Physics in Santa Barbara, Calif., one of the theorists who set off this confusion.
Down this rabbit hole are many of the jazzy magical mysteries of modern physics: Black holes. The shortcuts through space and time called wormholes. Quantum entanglement, also known as spooky action at a distance, in which particles separated by light-years can still instantaneously appear to remain connected. The reward for going down this hole could be a new understanding of why we think we live in a universe with space and time at all, with suitably unpredictable consequences. After all, if Einstein hadn’t been troubled a century ago by logical inconsistencies in the Newtonian universe, we might not have GPS systems, which rely on his theory of general relativity to keep time, in our pockets today.
Black holes are the most extreme predictions of Einstein’s theory, which describes how matter and energy warp the geometry of space and time the way a heavy sleeper causes a mattress to sag. Too much matter and energy in one place could cause space to sag so far that the matter inside it would disappear as if behind a magician’s cloak, collapsing endlessly to a point of infinite density known as a singularity. Einstein thought that idea was ridiculous when it was pointed out to him at the time, in 1916, but today astronomers agree that the universe is speckled with such dark monsters, including beasts lurking in the hearts of most galaxies that are millions and billions of time more massive than the Sun. Many of them resulted from the collapse of dead stars.
General relativity is based on what Einstein later called his “happiest thought,” that a freely falling person would not feel his weight. It is known simply as the equivalence principle; it says that empty space looks the same everywhere and to everyone.
One consequence of this principle is that an astronaut would not feel anything special happening when he fell through the point of no return, known as the event horizon, into a black hole. Like a bungee jumper, he would feel weightless then and all the way until he hit the bottom, which could take seconds or years depending on how big the hole was, and he would be stretched like a noodle by tidal forces and then crushed into a speck. At the event horizon there would be “no drama,” in the lexicon — at least in the physical sense, as opposed to the intellectual trauma of knowing you were not ever going home. Things or people went in, they got crushed to infinite density and disappeared. That was the traditional view of black holes.
Things got more interesting, however, in 1974 when Stephen Hawking, the British cosmologist, stunned the world by showing that when the paradoxical quantum laws that describe subatomic behavior were taken into account, black holes would leak particles and radiation, and in fact eventually explode, although for a hole the mass of a star it would take longer than the age of the universe.
This was a breakthrough in combining general relativity, the gravity that curves the cosmos, with quantum theory, which describes the microscopic quirkiness inside it, but there was a big hitch. Dr. Hawking concluded that the radiation coming from a black hole would be completely random, conveying no information about what had fallen into it. When the black hole finally exploded, all that information would be erased from the universe forever. “God not only plays dice with the universe,” Dr. Hawking said in 1976 in a riposte to Einstein’s famous doubts about the randomness of quantum theory, “he sometimes throws them where they can’t be seen.”
Particle physicists cried foul, saying that this violated a basic tenet of modern science and of quantum theory, that information is always preserved. From the material in the smoke and flames of a burning book, for example, one could figure out whether it was the Bible or the Kama Sutra; the same should be true of the fizz and pop of black holes, these physicists argued. A 30-year controversy ensued.
It was front-page news in 2004 when Dr. Hawking finally said that he had been wrong, and paid off a bet.
The Firewall Paradox
Now, however, some physicists say that Dr. Hawking might have conceded too soon. “He had good reason,” said Dr. Polchinski, “but he gave up for the wrong reason.” Nobody, he explained, had yet figured out exactly how information does get out of a black hole.
That was the task that four researchers based in Santa Barbara — Ahmed Almheiri, Donald Marolf, and James Sully, all from the University of California, Santa Barbara, and Dr. Polchinski of the Kavli Institute set themselves a year ago. The team (called AMPS, after their initials) found, to their surprise, that following the known laws of physics would lead to a contradiction, the firewall paradox.
Their calculations showed that having information flowing out of a black hole was incompatible with having an otherwise smooth Einsteinian space-time at its boundary, the event horizon. In its place would be a discontinuity in the vacuum that would manifest itself as energetic particles — a “firewall” — lurking just inside the black hole.
Being incinerated as you entered a black hole would certainly contradict Einstein’s dictum of no drama. If this were true, you would in fact die long before the bungee-jumping ride ever got anywhere close to the bottom. The existence of a firewall would mean that the horizon, which according to general relativity is just empty space, is a special place, pulling the rug out from under Einstein’s principle, his theory of gravity, and modern cosmology, which is based on general relativity. This presented the scientists with what Dr. Bousso calls the “menu from hell.” If the firewall argument was right, one of three ideas that lie at the heart and soul of modern physics, had to be wrong. Either information can be lost after all; Einstein’s principle of equivalence is wrong; or quantum field theory, which describes how elementary particles and forces interact, is wrong and needs fixing. Abandoning any one of these would be revolutionary or appalling or both.
The firewall argument hinges on one of the weirder aspects of quantum physics, the action called entanglement. As Einstein, Boris Podolsky and Nathan Rosen pointed out in 1935, quantum theory predicts that a pair of particles can be connected in such a way that measuring a property of one — its direction of spin, say — will immediately affect the results of measuring the other one, even if it is light-years away.
Einstein used this “spooky action at a distance” to suggest the absurdity of quantum mechanics, but such experiments are now done in labs every day. You can’t use it to send a message faster than light, because the correlation shows up only when the two experimenters get together and compare their respective results. But it plays a crucial role in quantum computing and cryptography — and, it turns out, in explaining how information encoded in the Hawking radiation gets out of a black hole.
Consider two particles (let’s call them Bob and Alice) that have been radiated by a black hole. Bob left it eons ago, as it began leaking radiation; quantum entanglement theory dictates that in order for the black hole to keep track of what information it has been transmitting, Bob out there has to be entangled with Alice, who just left.
But that scenario competes with another kind of entanglement, between particles on either side of the event horizon, the black hole’s boundary. If space is indeed smooth, as Einstein postulated, and if quantum field theory is correct, Alice must be entangled with another particle, Ted, who is just inside the black hole.
But quantum theory forbids promiscuous entanglements. In the language of quantum information, Alice can marry either Bob or Ted, but not both, even if the second marriage happens inside the black hole where most of us can’t see it.
Alice should have a consistent explanation of the universe, Dr. Polchinski explained, “just as we ourselves must, even though we are inside the cosmic horizon.”
Meanwhile, physicists have more reason than ever to think that information cannot be lost. A celebrated 1997 paper by Juan M. Maldacena of the Institute for Advanced Study describes nature as a kind of hologram, in which the information about what happens inside a volume of three-dimensional space, for example, is encoded in quantum equations on its two-dimensional boundary, the way a 3-D image is encoded on the face of your bank card.
Mark Van Raamsdonk, a young theorist at the University of British Columbia, likes to use a spookier analogy to describe this, namely the chip that controls a Matrix-like video game. (Feel free to insert your own woo-woo music here.)
The discovery that the information needed to describe what happens in some volume is proportional to the area enclosing that volume is the strangest and most far-reaching consequence of Dr. Hawking’s discovery that black holes explode, and is still wreathed in mystery.
Dr. Maldacena’s universe is often portrayed like a can of soup, in which galaxies, black holes, gravity, stars and so forth, including us, are the soup inside, while the information to describe them resides, like a label, on the outside. Think of it as gravity in a can. The equations that represent the label are deterministic and there is no room in them for information to be lost, implying that information in the universe inside is also preserved.
Which leaves the firewall as the only way to stop the illegal marriage of Alice and Ted, Dr. Polchinski said — an odious solution because it contravenes the basic principle of general relativity.
Recently a new way of solving the firewall conundrum and of answering that haunting question has attracted a lot of attention, although no consensus. Dr. Maldacena and Dr. Susskind have proposed that Einstein could come to his own rescue via one more far-out notion in modern physics: wormholes.
In 1935 Einstein and Rosen found that, mathematically anyway, black holes could come in pairs connected by shortcuts through space — then known as Einstein-Rosen bridges, now known as wormholes. A wormhole would not be traversable by any means we now know about, ruling out time travel and other violations of relativity, despite the dreams of science fiction writers and interstellar pioneers.
In 2010, Dr. Van Raamsdonk of British Columbia suggested that such wormholes were the geometric manifestations of quantum entanglement. After all, neither of these phenomena, which seemed to transcend local space, could be used for sending direct messages. Brian Swingle at M.I.T. had made a similar suggestion a year earlier.
In effect, what these theorists were saying was that without the phenomenon of entanglement, space-time would have no structure at all. Or as Dr. Maldacena put it, “Spooky action at a distance creates space-time.” If true, this insight would be a step toward a longtime dream of theorists of explaining how space and time emerge from some more basic property of reality, in this case, bits of quantum information. The theorist John Wheeler, of Princeton, who had coined the term “black hole,” called this concept “it from bit.”
Taking this idea seriously, Dr. Maldacena and Dr. Susskind proposed that a similar kind of wormhole arrangement existed between the black hole in the AMPS case and its Hawking radiation. Instead of a tunnel snaking through hyperspace and opening at the maw of another black hole, the wormhole would split into a zillion spaghetti-like strands ending on each of the pieces of Hawking radiation. That would mean that Bob, the Hawking particle in the cartoon version of the theory mentioned above, might be light years away from the event horizon, but he would still be connected to the interior of the black hole, as if there were a doorway in New Jersey that opened up into a basement in Manhattan.
Because of this wormhole connection, Dr. Maldacena explained, “Ted and Bob are the same.” So the result is sort of like the happy ending of one of those screwball romantic comedies that involve mistaken identity and the handsome vagabond turns out to be the prince in disguise; Alice can marry Ted who is really Bob and the bonds of matrimony extend smoothly across the edge of the black hole.
Dr. Maldacena and Dr. Susskind admit that the wormhole hypothesis is still a work in progress. Few of their colleagues are convinced yet that it has been formulated in sufficient detail, let alone that it can solve the firewall paradox. “All I can say,” Dr. Susskind said in an e-mail on the eve of a firewall workshop next week at the Kavli Institute where wormholes and everything else will surely be scrutinized, “is that no one has a completely solid case and that certainly includes me. Time will tell.”
Dr. Polchinski said, “My current thinking is that all the arguments that we are having are the kind of arguments that you make when you don’t have a theory.” We need a more complete theory of gravity, he concluded.
“Maybe ‘space-time from entanglement’ is the right place to start,” he wrote. “I am not sure.”
Dr. Bousso, who has been e-mailing with Dr. Maldacena, is skeptical that the wormholes will eliminate firewalls. “My own view is that it’s time to move on, accept, and actually understand firewalls,” he said. After all, he added, there’s no principle of nonviolence in the universe, except for Einstein’s equivalence principle, which says the black hole’s horizon is not a special place. But maybe it is, after all.
Meanwhile, Dr. Bousso said, the present debate had raised his estimation, “by another few notches,” of the “stupendous magnitude” of Dr. Hawking’s original discovery of the information paradox.
The firewall paradox,” he said, “tells us that the conceptual cost of getting information back out of a black hole is even more revolutionary than most of us had believed.”
全球的物理學家之間爆發了一場炙烈的論辯，爭論的焦點是， 如果你跳進黑洞——這頭令人膽寒，能吞噬物質、能量，甚至連光也不放過的引力怪獸——會發生什麼？當然，你不免一死，但怎麼死呢？是像天文學家和科幻作家 們幾十年來告訴我們的那樣，被強大無比的引力壓縮成比塵埃還細小的微粒？還是像一番驚心動魄的新計算似乎指出的那樣，被一道高能火牆瞬間燒死？
去年一年中，這場聽起來很可怕的辯論，製造了大量的論文和 博客文章，以及多場研討會。要緊的問題不是愛因斯坦的名望（他的名望已不可動搖），也不是我們手中的iPhone的效力，但或許是愛因斯坦的引力理論—— 廣義相對論的基石，我們對宇宙的認識都基於這一理論。或者一些其他的建立以sic久的自然法則也許會被放棄，但具體是哪一個，物理學家尚無一致意見。他們在這個 問題上的觀點反反覆復，幾乎每周都會改變一次，而且目前看來不會很快有定論。
加州大學伯克利分校(University of California, Berkeley)的理論物理學家拉菲爾·鮑索(Raphael Bousso)說：「我從來沒有感到如此震驚過，真不知道該期待什麼結果。」
「它表明我們對引力的認識存在缺陷，」位於加州聖芭芭拉市 的卡弗里理論物理研究所(Kavli Institute for Theoretical Physics)的理論物理學家約瑟夫·波爾欽斯基(Joseph Polchinski)說，他是引起這場困惑的理論家之一。
就像《愛麗斯漫遊奇境記》中的兔子洞一般，這裡充滿了現代 物理學中光怪陸離的神奇奧妙：黑洞；穿越時空的被稱為「蟲洞」的捷徑；還有量子糾纏(quantum entanglement)，它又有「鬼魅般的超距作用」這一稱呼，意思是相隔數光年之遠的粒子仍可表現得瞬息相聯。進入這個魔洞可能得到的回報無法預 料，也許會是我們對一個問題的新認識：我們究竟為什麼會覺得自己所在的宇宙有着時間和空間。這種新認識所能帶來的後果同樣無法預料。畢竟，假如一個世紀前 愛因斯坦不曾對牛頓力學宇宙觀中的不自洽之處感到困惑，我們今天也許就不會有能隨身攜帶的全球定位系統(GPS)，這個系統靠他的廣義相對論原理來計時。
黑洞是廣義相對論最為極端的理論預言。廣義相對論描述了物 質和能量如何讓時空幾何發生彎曲，就像一個很重的人睡在床上會讓床墊凹下去那樣。物質和能量過度集中在一處，可能導致太空的「凹陷」程度如此之大，以至於 其中的物質會像被魔術師的斗篷隱匿了起來似地消失掉，朝着被稱為「奇點」的無窮大密度點不斷地坍縮。1916年，有人向愛因斯坦指出這種可能時，他認為那 是一個荒謬的想法；但當今的天文學家認同這一觀點：宇宙中四處散落着這種漆黑的怪物，有很多這種黑獸潛藏在大多數星系的中心，它們的質量是太陽的數百萬乃 至數十億倍，許多是死亡恆星塌縮的產物。
此原理的一條推論是，當一位宇航員跨過名為「事件視界」的 不歸點、進入黑洞時，他自己不會感覺到有任何特殊的事情在發生。就像玩蹦極跳的人一樣，他會有失重感，這種感覺一直持續到他探底的時刻，這段旅程的時間可 以是幾秒鐘也可以是數年，要看黑洞有多大，他也會被潮汐力拉得像根麵條一樣，然後被碾壓成一粒微塵。用行話說來，事件視界之處「沒有戲劇」——至少從物理 學的角度來看，當然不是說知道自己再也不能回家時，所感受到的精神創傷。東西或人掉進去，被碾壓到無窮大密度而消失了，這就是對黑洞的傳統認識。
不過，1974年英國宇宙學家斯蒂芬·霍金 (Stephen Hawking)讓情況變得更有趣。他的研究結果震撼了世界，他發現，如果把描述亞原子行為、不符合常識的量子物理定律考慮進來的話，那麼黑洞也會泄漏出 粒子和輻射，而且最終會爆發，儘管恆星質量大小的黑洞走完這個過程所需的時間比宇宙目前的年齡還要長久。
把描述致使時空彎曲的引力的廣義相對論，與描述其中微觀奇 異行為的量子理論結合起來，是霍金的一項突破。不過，這裡面也有個大麻煩。霍金的結論是，來自一個黑洞的輻射會是完全隨機的，不包含任何有關落入其中物體 的信息。當黑洞最終爆發時，那些信息將在宇宙中徹底消失。霍金1976年戲仿愛因斯坦對量子理論隨機性的著名質疑說道，「上帝不僅和宇宙玩擲骰子，他有時 候還把骰子擲到看不見的地方。」
粒子物理學家對此表示強烈反對，稱霍金的觀點違背了現代科 學和量子理論的一個基本原則，那就是信息總是被保存下來。比如說，從燒一本書產生的煙與火的成分里，原則上應該能判斷出這本書是基督教《聖經》還是古印度 《愛經》(Kama Sutra)。這些物理學家辯稱，黑洞釋放出的火苗和煙圈按理也應該包含信息。長達30年的論爭因此拉開了帷幕。
而這正是身在聖芭芭拉的四位研究人員給自己下的任務，他們 中的艾哈邁德·艾爾姆赫里(Ahmed Almheiri)、唐納德·馬洛爾夫(Donald Marolf)、和詹姆斯·薩利(James Sully)來自加州大學聖芭芭拉分校，而波爾欽斯基則來自卡弗里研究所。這個自稱「AMPS」(取自四人姓氏的首字母)的團隊做出了讓自己都吃驚的發 現：從已知的物理定律出發，會得出自相矛盾的「火牆悖論」。
落入黑洞時被燒成灰燼，當然與愛因斯坦「沒有戲劇」的論斷 相矛盾。如果這個結論是對的，那麼你在進入黑洞的蹦極之旅中，早在遠離觸底的地方就沒命了。如果火牆存在，那將會意味着，視界是一個很特殊的地方，而不是 廣義相對論所認為的那個什麼東西都沒有的空間。火牆的存在將動搖愛因斯坦原理的基石，也動搖他的引力理論的基石，因此會動搖建立在廣義相對論之上的現代宇 宙學的基石。用鮑索的話說，這相當於給科學家們提供了一本「地獄菜譜」。如果火牆說正確，那麼處於現代物理學核心地位的三個概念中有一個就必須是錯的。要 麼是信息畢竟可以丟失，要麼是愛因斯坦的等效原理有問題，要麼是描述基本粒子和基本力如何相互作用的量子場論是錯的，需要修正。
火牆論據所依賴的是量子物理中更詭異的一個東西，即被稱為 「糾纏」的作用。正如愛因斯坦、鮑里斯·波多爾斯基(Boris Podolsky)和內森·羅森(Nathan Rosen)在1935年所指出的，量子理論預言，一對粒子可以有這樣一種關聯方式，不管兩個粒子相距多少個光年，測量其中一個粒子的某種特性，比如自旋，會立刻影響到另一個粒子的測量結果。
愛因斯坦曾用這種「鬼魅般的超距作用」來暗示量子力學的荒 謬，但如今，這種實驗每天都在實驗室中進行。你不能靠它來用比光速還快的速度傳遞信息，因為只有當兩個做實驗者相會，比較各自的結果時，才能看到這種關 聯。但是，糾纏在量子計算和密碼學中起關鍵作用，而且現在看來，糾纏在解釋霍金輻射中隱含的信息如何逃離黑洞上，也很關鍵。
與此同時，物理學家有比以往任何時候都多的理由相信，信息 不可能消失。1997年，普林斯頓高等研究院的胡安·M·馬爾達塞納(Juan M. Maldacena)發表過一篇赫赫有名的論文，把大自然描繪成一種全息圖，其中，比如有關一個三維空間內部發生什麼的信息，是編碼在這個空間的二維界面 上的量子方程中的，就像一個3D圖像被編碼在你的銀行卡上面那樣。
加拿大不列顛哥倫比亞大學(University of British Columbia)的年輕理論物理學家馬克·范拉姆斯東克(Mark Van Raamsdonk)喜歡用一個更嚇人的比喻來描述這個概念，即控制類似於《黑客帝國》(Matrix)的視頻遊戲的芯片。（請自己選擇可怕的音樂伴奏。）
馬爾達塞納常把宇宙比喻為一個湯罐頭，星系、黑洞、重力、 恆星等，包括我們在內，是裝在罐頭裡的湯，而描述這些物質的信息像是貼在罐頭外面的標籤。你可以把它想像成用罐頭包裝的引力。代表標籤的方程是確定性的， 方程中沒有能讓信息遺失的餘地，這也就意味着，宇宙內部的信息必須被保留。
1935年，愛因斯坦和羅森發現，至少在數學上，黑洞可以 成對出現，它們由太空中的捷徑連接起來，這種捷徑當時被稱作愛因斯坦-羅森橋，現在被稱作蟲洞。雖然科幻小說作者和星際探索者有過諸多夢想，但用我們目前 已知的所有方法都無法穿越蟲洞，這就排除了穿越時間旅行和其他違背相對論的可能性。
其實，這些理論學家說的是，如果沒有糾纏現象，時空就根 本不會有結構。或者正如馬爾達塞納所說，「鬼魅般的超距作用創造了時間和空間。」如果真是這樣，這一深刻見解是朝着理論學家的一個長久的夢想邁出的一步。 他們夢想解釋空間和時間如何由已有的一些更基本的性質所產生，在糾纏理論中，更基本的性質是量子信息。普林斯頓大學的理論物理學家約翰·惠勒(John Wheeler)是「黑洞」這個詞的發明者，他把這個概念稱為「時空源於比特」。
把蟲洞概念進一步延伸，馬爾達塞納和蘇斯金德提出，在 AMPS理論的黑洞和霍金輻射之間存在一種類似蟲洞安排。這種安排不是那種蜿蜒穿越超時空、在另一端與黑洞內部相連的隧道，而是分裂成千絲萬縷的類似於意 大利麵條的連接，每個連接都連到霍金輻射的一個碎片上。這就意味着，在前文中提到的卡通版理論中，雖然霍金粒子鮑勃也許與事件視界相去數個光年之遠，但他 仍與黑洞的內部相連，就好像是在新澤西州有一扇門，打開它能直接通到曼哈頓的一間地下室似的。
馬爾達塞納和蘇斯金德都承認，他們的蟲洞假說並不完善。同 行中幾乎沒人相信這個假說的描述足夠詳細，更不用說用它來解決火牆悖論了。一個火牆研討會下周將在卡弗里研究所(Kavli Institute)舉行，屆時人們肯定會給蟲洞以及所有的理論挑刺兒。蘇斯金德在研討會開幕前給記者的一封電子郵件中表示：「我只能說，還沒有任何人能 給出一個完全紮實的理論，當然也包括我。任何理論只能靠時間來檢驗。」
鮑索一直在用電子信跟馬爾達塞納交流，他對蟲洞能消除火牆 的提法有懷疑。他說，「我本人的看法是，結束爭論的時候到了，我們應該接受火牆的概念，從而開始真正了解火牆。」他補充說，畢竟宇宙中沒有非暴力原則，除 了愛因斯坦的等效原理之外，該原理說黑洞的視界不是一個特殊的地方。但也許它是一個特殊的地方。