Einstein Gave Black Holes a C-Minus. Strominger Still Bets the Farm on the Next Wrinkle

Lex Fridman opens with the Harvard Black Hole Initiative, a mix of theorists, experimentalists, and even philosophers, and asks Andrew Strominger for the big definition: what is a black hole, theoretically, experimentally, philosophically? Strominger's answer is a single cut. A black hole is a region of spacetime from which light can never escape. Therefore it is black. Many strange things follow. That is the starting point.

Light, he says, does not need a lecture. It is the stuff that comes out of the sun, the stuff that goes into your eyes, the stuff that vanishes when the lights go off and appears when they come on. He could give a mathematical definition. He thinks we already understand it intuitively. Black holes are the opposite. We do not understand them intuitively. They are very weird. Pictures from the last several years have shown the regions anyway. They are up in the sky, thousands or millions of them. We do not yet know how many.

Why the light stays in is still a matter of some debate. One explanation Einstein might have given is that light carries energy: photocells take sunlight and turn it into electricity. Anything with energy feels a gravitational pull, and the pull is proportional to mass. Pack enough mass into a small enough region and light cannot leave. On Earth, ignoring air friction, a rocket at eleven kilometers per second has escape velocity and could coast to the next galaxy. On the Moon it is seven. Reverse the logic and escape velocity becomes the speed of light. Relativity then says nothing can go faster, or the theory stops being consistent. In those massive regions, even light is stuck.

Fridman lingers on the speed limit itself. How wild was it, in Einstein's time, to decide the universe had a maximum speed and that the maximum was the speed of light? Strominger's reply is about the psychology of discovery, not the history of 1905. The best discoveries in physics seem completely obvious in retrospect. That includes his own, far lesser than Einstein's. He and his collaborators get confused, finally solve a problem, watch everything fall into place, then look back at months of discussion and literally cannot reconstruct how confused they were.

He cannot fathom how confused Einstein was at the start. He cannot even reconstruct his own confusion from two weeks ago. Beautiful ideas make it hard to get back into the earlier mindset. Einstein was confused about many things. Strominger's scorekeeping for a physicist is not how many you got wrong, and not the ratio of wrong to right. It is the number you got right.

Einstein wrote down the field equations in 1915. Karl Schwarzschild solved them three or four months later, in early 1916, and found the black-hole solution. About twenty-five years later Einstein published a paper arguing that black holes did not exist. Strominger has read it. If a student in his general-relativity course wrote the same thing, he would not pass them. A C-minus. Einstein also went back and forth on gravitational waves, and Strominger recalls a mid-1930s paper claiming they did not exist, born of confusion about what a coordinate transformation is. That confusion, he says, has persisted. A hundred years later they think they are on the edge of solving it.

He explains coordinates with a weather map. You number one set of stations; someone else numbers another. At the end of the day you should draw the same map. That is coordinate invariance. If you are telling a driver how to stay as dry as possible from here to California, the route should not depend on whose stations you used. The labeling of points is an artifact, not the physics. It turns out that is almost true, but not quite. Subtlety showed up in the 1950s: when spacetime has edges, how you label the edges gets very tricky, in space or in time. Einstein did not have it right.

He had already been excited about an earlier version of general relativity in 1914. It was only partially coordinate invariant. It was wrong. It gave the wrong answer for the bending of light by the Sun, off by a factor of two. An expedition went out to measure it during World War I and was captured before it could. That gave Einstein four more years to clean his act up, by which time he had gotten it right. The most beautiful theory in the history of the subject had an intermediate version that was false, and one reason the correct version arrived is that an observation never happened.

Why didn't Einstein believe his own equations? Strominger thinks the reasoning was ultimately wrong, but the Schwarzschild solution does contain something alarming. Behind the horizon, in a region nobody can see and live to tell about, there is a singularity. Cross the horizon and you go into it, get crushed, and that is the end of everything. Singularity, in this usage, just means Einstein's equations break down. The numbers become infinite. Write them down, put them on a computer, and when the machine hits that point it crashes.

He thinks that is a really good thing. Maxwell's theory and Newton's never do this. You can solve a lot of them exactly, even if you cannot solve the three-body problem. There was never any reason to think those equations were exact, even if Maxwell and Newton perhaps fell for the trap. Some people still think some of the equations we have written down are exact. Strominger's view is that there is no exact equation. Everything is an approximation. Newton's theory is not wrong; it had incredibly small corrections. Why they are so small is a puzzle.

The first sign something was off with Newton was Mercury's perihelion. Urbain Le Verrier, in 1859, compared theory and experiment and found that the long axis of Mercury's ellipse goes around the Sun once every 233 centuries instead of every 231. The difference is tiny. The labor behind the measurement is hard to imagine now, and Le Verrier could not have known what the discrepancy would be good for. It was still the first crack. Corrections to electromagnetism, Strominger adds, show up when you get super accurate: without quantum mechanics, the electron in a Bohr atom would spiral into the proton and the atom would collapse.

Hit the singularity and you know Einstein's gravity needs an improvement, one that should involve quantum effects. The theory was invented for weakly curved things like the solar system, and it has turned out to be incredibly robust near black-hole horizons. Newton's gravity had regimes where it failed. Maxwell's electromagnetism had regimes where quantum effects greatly modified the equations. General relativity, all on its own, drove a system that started out fine into a configuration where Einstein's equations no longer applied. The theory predicts its own demise. The edges, Strominger says, keep physicists in business.

Fridman recalls a TED talk in which Strominger treated the clash between quantum mechanics and relativity as something wonderful. Strominger is sure, though many people would disagree, that now is the most wonderful time to be a physicist. The classical sigh in the field is to wish it were 1920, with quantum mechanics just understood and the periodic table falling into place. That seed was so rich it took a whole century to sort, with experiments, observations, and computers for visualization. He would not trade.

The seed of general relativity was itself an incompatibility. Maxwell's electromagnetism forbids anything faster than light. Newton's gravity is transmitted instantaneously across the entire universe. A friend in another galaxy with a sensitive gravitometer could, in that world, watch you bounce a cup of coffee up and down in Morse code and get the message at once. That is not self-consistent. Resolving the contradiction is how Einstein arrived at a new vision of the universe. The trap is that lots of contradictions are merely technical: you set the equations up wrong, you mistranslated the formalism. From inside, you are never very sure which kind you have.

The tension between quantum mechanics and general relativity, for him, is the deep kind. Pauli noticed it in the 1950s. Hawking, in the early 1970s, gave it a much more visceral form. People have been hurling themselves at it, trying to reduce it to a technicality, and nobody has succeeded. The attempts have thrown off unexpected relations between quantum systems and applications in other fields. A contradiction that has survived seventy years of digestion is, itself, a signal.

Fridman asks for quantum gravity, the Standard Model, quantum mechanics, general relativity, and the unification efforts, five questions at once. Strominger starts with the Standard Model. It describes everything except gravity with astonishing accuracy. It is, he says, the most accurate theory in the history of human thought. Theory and experiment have been successfully compared to sixteen decimal places. They have that stenciled on the door where he works.

Electromagnetism was tamed first, then unified with the weak interaction, which you need serious tools even to see. Then the strong interaction, which binds quarks into protons. The forces between them are mediated by Yang-Mills theory, a beautiful mathematical generalization of electromagnetism in which the analogs of the photons themselves carry charge. Every particle the Standard Model predicted has been observed. The last piece was the Higgs, found a little over a decade before this conversation. Around the edges sit dark matter, neutrino masses, and measurements that are not yet perfect. He does not expect anything very new conceptually in the completion of that theory, and nothing contradictory, because the gaps are so small.

The buzzword he throws Fridman for the bar later is renormalizable quantum field theory. All of those forces fall under that rubric. Gravity will not put that suit on. Quantum gravity is the effort to make the two dance. The one fully consistent model Strominger is willing to name, the one that tames gravity and reconciles it with quantum mechanics, is string theory and its cousins. We do not know whether, in any sense, it describes the physical world. We do know it is a consistent reconciliation, and one able to incorporate particles and forces like the ones we see. It has not been ruled out as a unified theory of nature. In his view, there is also no reasonable chance of a yes-or-no experiment in the foreseeable future. Some people would disagree.

The basic idea emerged in the early 1970s: replace the notion of a particle with a little loop of string. Strings are softer. If there were a big particle on the table and you hit it, you might bruise yourself. If there were a string, you would probably just push it around. The infinities in quantum field theory come from particles hitting each other, a jarring effect. Throw strings at each other and it is a little more friendly. He has never described it that way before, he says, but it is scientifically accurate. The mathematics behind it is not hand-waving. It is precise.

Once you replace particles by strings, the infinities go away, and you get a consistent theory of gravity without them. That can sound trivial until you remember the timing. People had already spent fifteen years searching for any theory that could do this. String theory was found kind of by accident, and the subject is full of accidental discoveries. In the 1970s it was still treated as a toy model on paper, interesting for putting quantum mechanics and general relativity together, but unable to describe some of the idiosyncratic features of our universe, in particular parity violation.

Parity violation is the bar trick after renormalizable quantum field theory. Look in the mirror across the room. The universe in the mirror is not identical. Show a smart enough person a photograph that includes both you and the mirror, and in principle she can tell which half is the real world, though she would need precise measurements, and a grainy photo might not suffice. The real world is not parity invariant. String theory was thought unable to tolerate that. In the mid-1980s it was learned that not only could it, but if you did things the right way you could construct a string world that reconciled quantum mechanics and general relativity and looked more or less like the one we live in. That is not a prediction of our world. It means the hypothesis that string theory describes our world cannot be ruled out from the get-go. It is also still the only proposal for a complete theory that would. Nobody will believe it until there is a direct experiment. Strominger does not even believe it himself, which he treats as the right mental place for a physicist.

Fridman asks whether string theory is dead, and whether Strominger would bet all his money on its future. Strominger calls the framing a logical error. It is not right or wrong, dead or alive. It is a stepping stone. The analogy he likes is Yang-Mills theory, invented in the 1950s because Chen Ning Yang and Robert Mills thought its symmetry described the relationship between the proton and the neutron. That motivation was completely wrong. The math describes everything else in the Standard Model. They had some of the right pieces, not the others, and not quite in the right context. It had a kind of inevitability and eventually found its place.

Einstein's 1914 general relativity is the same pattern. He had understood the equivalence principle and spacetime curvature. He was missing pieces. Technically you would have to say that version was wrong, and technically you would have to say Yang and Mills were wrong. Odds are we keep finding new wrinkles, including in what we now call string theory, which technically is not quite right either. We are always going to be wrong, he says, but hopefully a little bit less wrong every time.

He would bet the farm. The phrase means more than it used to, because he actually has a farm, and they just renovated it. His wife spent five years on the renovation. Before that, the line was looser. Now it really means something. The bet is that a hundred years from now, string theory will be viewed as a stepping stone toward a greater understanding of nature. It solved the infinities problem, and later it also solved Hawking's puzzle about what is inside a black hole. Put in one assumption and get five things out. You are probably not doing everything right. You are doing something right. There have been a lot of signposts like that.

Fridman brings up Strominger's work with Cumrun Vafa and the holographic principle. Strominger was a black-hole person first, a reluctant string theorist who started reading the papers because people claimed they had quantum gravity. The more he read, the more interested he got. The phrasing was mathematically clumsy. It was all correct. That often happens: people live inside a problem, dream it, and begin to see inner relationships and a beauty that is really there. They are not deceived. An outsider glancing at it cannot grasp it.

In 1985, understanding of string theory was almost all about weakly coupled waves of strings colliding. Nobody knew how to describe a big thing like a black hole. You could show that in some limit the theory reproduced Einstein, with corrections, but you could not do any better with black holes than Einstein and Schwarzschild had done. Then you put the equation on Hawking's headstone together with the one on Boltzmann's. There are not many equations that make it onto headstones. Together they give a formula for the number of gigabytes in a black hole. In Schwarzschild's description the black hole is literally a hole in space, with no place to store them. Wheeler, Bekenstein, and Hawking drove the point home: unless a black hole can store a large number of gigabytes, quantum mechanics and gravity cannot be consistent.

Einstein's and Schwarzschild's black holes cannot store information. Stuff flies in, hits the singularity, and is gone. Einstein's theory is not exact, and string theory tells you the corrections, so there should be another description in which you can see where the gigabytes live. What Bekenstein and Hawking showed is that physics is inconsistent unless a black hole stores a number of gigabytes proportional to its area, divided by four times Newton's constant times Planck's constant. Area, not volume. That is the holographic principle. The universe, Fridman says, is so weird.

What does the principle actually mean? Is there a projection? Strominger had been writing an introduction to a paper just before walking into the conversation. The first sentence was "the as yet imprecisely defined holographic principle." Nobody knows exactly what it is. Roughly, it is the area claim they had just been circling. A three-dimensional region's information is set by the area of its two-dimensional boundary, and the field has been using the idea anyway. The foundations are being poured while people are already working inside the building.