The Equation Was Smarter Than Einstein

Carroll opens book one of *The Biggest Ideas in the Universe* by walking readers to Einstein's equation rather than around it. The cleanest on-ramp, he tells Fridman, is special relativity in 1905: Einstein showed you could drop the ether, keep the speed of light as a maximum, and still have the equations of physics make sense. The last elegant step was not Einstein's. In 1907 his former professor Hermann Minkowski realized that space and time should be blended into a single four-dimensional thing, spacetime, with no hard split between them.

Einstein first dismissed the move as mathematicians over-formalizing. Then he saw the implication: if spacetime is a real thing, it can have properties, including geometry. It can curve from place to place. That was what let him solve gravity. He had been trying to shoehorn Newton's inverse-square law into the new relativistic framework, and it would not fit. The final leap was to say gravity *is* the curvature of spacetime. Carroll calls that statement "basically general relativity."

If you want a case for Einstein's greatness, Carroll says, point at two things. In the miracle year of 1905 he wrote three papers on wildly different subjects, any one of which would have made a physicist famous: special relativity, Brownian motion as proof of atoms, and the photoelectric effect, which was really the invention of the photon. The other credential is general relativity itself, a decade of work from 1905 to 1915, overlapping with a refrigerator design and other projects, and overlapping with rivals who also tried relativistic theories of gravity.

The solution was not a crank you could turn. Einstein's happiest thought, in modern language, was that a quiet rocket accelerating at one *g* is indistinguishable from standing on Earth. A clever person might have stopped there. Einstein reasoned onward: if gravity is not detectable the way electromagnetism is — positive and negative charges respond differently to a field, but everything responds to gravity the same way — then it cannot be an ordinary force. It has to be a feature of spacetime. He did not know the math of curvature, so he sat down with the papers and taught himself differential geometry. There were no MOOCs and no AI helpers.

Asked how space differs from time in general relativity, Carroll says it is almost the difference between X and Y on a sheet of paper. There is one important exception. In space, the shortest distance between two points is a straight line. In spacetime, the time you measure along a trajectory is analogous to distance along a curve, except the dependence runs the other way. The *longest* time between two events is a straight line. Zigzag through spacetime and you take less and less time to go from A to B.

That is the twin paradox without the folklore. Two people start the same age; one goes out near light speed and comes back younger, because that twin did not take the shortest-distance path through spacetime. Locally, though, time is never funny. Your neurological signals, your heartbeat, and your wristwatch all suffer the same fate at the same rate. Time always ticks at one second per second for you. What can differ is how other people's clocks look from far away.

Fridman asks how to make sense of observed reality versus the objective world underneath. Carroll is "a huge believer in objective reality," but he thinks people are casual about the middle step. We start and end with observations, yet in between sits a theory. If the theory fits the data, is simple, and makes sense on its own terms, we should attribute some reality to the entities that play an important role in it — provisionally, until a better theory comes along.

A black hole is a sharp test of what we observe versus what the theory says is there. If Fridman stands outside and Carroll falls in, waving, the outside observer sees the infaller slow down and redshift until there is a last photon, after which the falling person fades from view. That picture treats them as test particles. If the infaller has mass of his own, the hole moves out to swallow him. You never quite *see* someone cross, because a last-minute change of heart is always possible from the outside.

As smart as Einstein was, Carroll says, he never figured out black holes, and he could have. "It's kind of embarrassing." General relativity arrived in 1915. Two years later Karl Schwarzschild derived the solution that represents a black hole. No one recognized it for what it was until the 1950s, with David Finkelstein and others. Part of the delay is understandable: between 1915 and 1955 the liveliest work in physics was particle physics and quantum field theory. Still, Carroll thinks that if the universe hands you a mysterious exact solution, someone should have put in more effort.

The useful picture is not of an object but of a region of spacetime. Once you enter, you cannot leave. Escaping is exactly as hard as traveling faster than light, because they are the same requirement. In principle you do not notice crossing the event horizon, the point of no return. Meanwhile spacetime collapses toward a singularity in your future. For a hole about the mass of the Sun, the trip from horizon to singularity takes about a millionth of a second. And the singularity is not at the middle of space. Because space and time are one, it is a moment of time — a Big Crunch in your future, the time-reverse of the Big Bang's expansion from a past singularity.

In classical general relativity, the information that made you is lost to the outside world: it is still inside, but unreachable. In the 1970s Stephen Hawking showed that black holes radiate, lose mass, and eventually evaporate. Once the hole is gone you can no longer say the information is hidden behind it. Either it was destroyed, or it was transferred into the Hawking radiation. Most people who work on the problem believe information is conserved, a feature of both general relativity and quantum mechanics on their own. Nobody is close to observing the radiation. Larger holes are colder; Sagittarius A*, a few million solar masses, is so cold its radiation will never be seen. "We don't have any nearby," Carroll says. "Allegedly," Fridman replies. "As far as we know."

Fridman is confident the universe is thick with civilizations we simply cannot see. Carroll is not placing heavy bets. He would not have expected Earth to be special, and he can imagine microbial life that never becomes complex, or intelligent beings with better things to do than knock. The simplest explanation for the silence, he still thinks, is that they are not there. Even if "life finds a way," it might typically take a hundred billion years, in which case we would be alone. He puts less credence on a Great Filter that kills every technological species, because the filter would have to work every single time.

John von Neumann already pointed out that you do not need to send the aliens themselves. You build self-reproducing probes. The galaxy looks huge until you remember it is tens of thousands of light years across and billions of years old. You do not need a high fraction of light speed to fill it. Radio SETI, Carroll argues, is a poor bet for the same reason of time. Why would a billion-year civilization waste energy beaming at random? A signal would also pass you by. Humans have been listening for a century or two; a long-lived culture would have to hit that window exactly.

The efficient move is to send probes, park them in other solar systems, and wait for intelligence to arise. That is the *2001* monolith hypothesis. "I would be less surprised to find sort of quiescent alien artifact in our solar system than I would to catch a radio signal from an intelligence civilization." If the probe met us, he doubts language would be the long-term problem: there is logic, math, and a shared physical world. You can point at a rock. He is more worried about biosignatures in exoplanet atmospheres. Small molecules prove little, because non-life can make them too. Long molecules are the kind of thing life would produce.

Hawking assigned black holes a finite entropy, and the working belief — already speculative — is that this is the most entropy a region of spacetime can hold. You might guess that information capacity scales with volume, because bits take up space. For a black hole it scales with the area of the event horizon. That mismatch is the seed of the holographic principle: the information in the hole can be thought of as living on the two-dimensional horizon rather than in the three-dimensional interior. Gerard 't Hooft and Leonard Susskind sketched the idea; it became a full theory in the 1990s with Juan Maldacena's AdS/CFT correspondence, in which an N-dimensional theory without gravity casts a hologram into an (N+1)-dimensional world that looks like gravity.

Everyday objects are nowhere near that density. Quantum field theory says you and I are mostly empty space; books, CDs, and RAM encode information by volume at a "super duper low" density. A black hole is information-dense and also extremely high entropy. Carroll's image: "a black hole is kind of like a very, very, very specific random number." It takes many digits to specify, and the digits tell you nothing useful. When the hole evaporates, the entropy of the radiation is higher than the hole's was, which is good, because entropy should go up — but the information is scattered to the four winds, the way a burned book's contents still exist in heat, light, and ash.

Fridman wants to know how old the infaller is "now." Carroll shuts the question down. "The whole point of relativity is to say there's no such thing as right now when you're far away. And that is doubly true for what's inside a black hole." You are not allowed to ask how fast their clock is ticking. Holography, as currently understood, does not force a new view of time; time "just goes along for the ride." Carroll is more skeptical than some colleagues that we are close to knowing how information gets out or how to quantize gravity. The surprise that would truly floor him is if quantum mechanics itself were superseded. There is no empirical reason to think it is wrong. Black holes are where that wrongness would show up.

With postdoc Oliver Friedrich, Carroll tried to drag holography toward data. Quantum field theory is local: something can happen at every point. Holography says there is less room than that. One reconciliation is that the extra field-theory states are not quite orthogonal. In a huge Hilbert space you can pack many more almost-perpendicular vectors than the dimension would suggest. If neutrinos are not exactly orthogonal, a high-energy neutrino traveling across the universe might dissolve into other neutrinos. Nearby you would see many; from far enough away, fewer. IceCube, strings of 360-degree photodetectors a mile down in Antarctic ice, is the detector. Ice is denser than air and still transparent, so nature built a neutrino observatory. IceCube's counts die at exactly the energy where their cutoff sits. That does not confirm the prediction. It means the experiment loses sensitivity at the same place.

After 1998, when observations showed the universe is not only expanding but accelerating, cosmologists reached for Einstein's cosmological constant or some more complicated dark energy. Carroll, more at home with particle physicists than most cosmologists, thought the popular models were wildly unnatural. Particle physics lives at small lengths and fast times; a new field that changes once every billion years should set off alarm bells. Interaction with other particles would speed it up. The way to protect it is a symmetry that stops the new field from talking to the others. That keeps the dynamics slow and also makes the field harder to detect.

There is one loophole he could not close, leftover from his first paper: an interaction with photons that rotates their polarization as they travel, a birefringence of a couple of degrees if you roughly fit the data. Cosmic microwave background measurements are now on the edge of detecting it or ruling it out. There is a claim of a detection; it is not very significant. If Carroll were betting, he thinks it will go away. The paper was "Quintessence and the Rest of the World." Quintessence is a dynamical dark energy field; "the rest of the world" is every other particle you have to keep it from touching.

Critics treat dark matter and dark energy as physicists inventing invisible stuff to save the math. Carroll's first reply is Neptune. Newtonian gravity was excellent; the outer planets were slightly off; one more planet in a specific place explained it; people looked and found it. "That was the first successful example of finding dark matter." Dark matter, as hypothesized, is a particle that interacts with us very weakly. We know how much there is, roughly where it is, and some of its properties. Dark energy is different: uniformly spread, apparently unevolving, the same energy in every cubic centimeter from moment to moment. The leading candidate is Einstein's cosmological constant, strictly 100 percent constant. The data require it to be at least 98 percent constant, so 100 percent works.

The second reply is personal: physicists would love it if it were not dark matter, because a new particle is "the most boring thing in the world." Carroll tried to unify dark matter and dark energy by modifying gravity. Both become important where gravity is very weak — late in cosmic history, and in the outskirts of galaxies — which is the opposite of the usual field-theory rule that new effects show up when fields are strong. He added a term that said, roughly, the *less* matter and energy, the *more* curvature. The equations could possibly help with cosmic acceleration. They did not help with dark matter at all. "It didn't work." He still wrote the paper after two collaborators independently had the same idea. You listen to the equations and the data, even when the cooler story loses.

Carroll once opened a general-relativity textbook by calling GR the most beautiful physical theory ever invented, and he will stand by that. Quantum mechanics is less pretty in the form we teach: the Copenhagen interpretation is "a god awful mess." Many-worlds is beautiful in a different sense — fewer ingredients, one equation, a shot at covering everything. Classical mechanics describes this particle and that particle separately. Quantum mechanics, as Einstein pointed out in 1935, gives you entanglement: a single state for two particles, and ultimately a single wave function of the universe. The job is to carve tables and chairs out of it.

The teaching experiment is Stern–Gerlach: an electron's spin is clockwise or counterclockwise, nothing in between. Quantum mechanics lets you prepare a superposition of both, and that is not ignorance. It truly is both until you measure. Copenhagen says the measurement collapses the state, and you get probabilities without a story of when, why, or what caused the collapse. That is the measurement problem. Many-worlds replies that you cannot describe only the electron. You have to include yourself, because you interact with it in order to look.

The Schrödinger equation is unambiguous. If the electron is clockwise, your brain should register clockwise; counterclockwise, counterclockwise. If it starts in a superposition, you and the electron entangle. Part of the universe's state says the electron was clockwise and you saw clockwise; part says counterclockwise and you saw counterclockwise. Everyone agrees on that step. Niels Bohr then says one part of the wave function disappears. Hugh Everett, a graduate student in the 1950s, said it stays. The reason nobody had taken that seriously is the naive implication: you would feel yourself in a superposition of both outcomes. No experimenter ever has.

Everett's move, which Carroll calls kind of genius, is that the problem is not the equation. You misidentified yourself in it. The clockwise branch, once it exists, is completely unaffected by the counterclockwise branch. They do not interact. Identify yourself as one of those people, not as the superposition of both. After the experiment there are two people. Where do the worlds go? "The worlds don't exist in space. Space exists separately in each world." If you cannot visualize that, so much the worse for you; the equations are clear. The best reason to be skeptical, Carroll thinks, is not data or location. Taking the Schrödinger equation that far requires a new philosophy of identity, probability, and prediction. He is sympathetic to methodological conservatives who call it a step too far. He also thinks they are wimping out.

On what the Big Bang was, and why it happened, Carroll is "more or less maximally uncertain." General relativity unambiguously predicts a past singularity of infinite curvature, energy, and expansion rate, which is a fancy way of saying the theory has broken down. There may have been a first moment, before which there were no other moments. There may have been time before that, evolving into our hot Big Bang by a process we do not understand. A first moment would fit hand in glove with time being emergent. If time is fundamental, it tends to go forever.

Is there an outside to the universe? It is legitimate to ask, and also legitimate that the answer is no. If the universe is the totality of everything, it would not have an outside; that is the simplest answer on the table. A related pitfall in cosmology is the principle of typicality, mediocrity, or Copernicus: assume you are a typical observer, then draw conclusions. Carroll thinks that move is hilariously presumptuous. By saying you are typical, you are saying typical observers are like you, which is not justified by anything.

Fridman keeps sneaking up on the question of how something came from nothing. Carroll's answer is that "why is there something rather than nothing?" does not have the kind of answer we ordinarily attach to why-questions. Ordinary why-questions are embedded in the universe; we answer them with features of the universe. The universe itself, as far as we know, is not embedded in anything bigger. Therefore it can just be. The simulation hypothesis? "Sure." Mindscape listeners tease him because any question that starts "do you think it's possible" gets a yes, short of adding two even numbers and getting an odd one. He sees no philosophical knockout objection, and also "absolutely no reason to take it seriously." People will build better virtual worlds; David Chalmers argues those events are as real as ordinary experience. Practically, realistic simulation is much harder than we naively think. Not a this-lifetime worry.

Carroll wants to eliminate the phrase AGI. Artificial intelligence is different from human intelligence. An agent we can build now or soon might be far better than humans at some things and far worse at others. Asking how close it is to human-like intelligence both misdescribes it and makes it harder to use well or to protect ourselves. He is a physicalist: he sees no obstacle in principle to a machine indistinguishable in thought from a person. That is not what large language models are trying to do. They predict text, and they leverage a human habit of attributing agency to anything that acts like us.

Driving to the recording, he ignored Google Maps to get coffee. The app nagged him to turn left while he turned right. "It is impossible as a human being not to feel a little bit sad that Google Maps is getting mad at you." It is not even a language model. Dan Dennett's paper on the intentional stance described the bias: we attribute more intentionality than is there. The first step toward clear thinking about AI is to notice that bias. Whether models succeed by building the same kind of world model we have, or by some other route, is still open. Either answer would be remarkable. The data are not yet clear.

He cites work Melanie Mitchell discussed at the Santa Fe Institute. A network trained on millions of real Othello games, fed only symbolic moves like "E5," was probed for a representation of the board. The probe beat chance, so the original authors claimed tentative evidence that the net had discovered the board from raw data. Mitchell's group asked how much of that "understanding" was built into the probe. At least half of the improvement was. An Othello board is vastly simpler than the world. Carroll was factually surprised by the recent rate of progress — "some kind of phase transition percolation has happened" — without that telling him the mechanism.

Physics, he thinks, is low-hanging fruit for the energy and heat of computation. Existing machines are hilariously worse than brains; a laptop heats your lap and a brain does not. He is cautiously optimistic about fusion and quicker to mention solar, including in space, because space is bigger than Earth. Efficiency races scale: we get better at doing things, then invent new things to do faster than the efficiency gains, and keep making some things worse. Between nuclear and biological weapons, he agrees it is a little surprising we have not caused enormous devastation. That is also, he notes, exactly what you would say right before we went too far.

Complexity is what Carroll is thinking about now, rather than guessing new laws of physics. Einstein guessed right; Steven Weinberg guessed right; very few people do. Emergence of complexity from simplicity still looks pre-paradigmatic. Geoffrey West and others at Santa Fe have had real insights, but Carroll thinks the basics are not understood. His working cliché is that the key is information. Through cosmic history, subsystems figure out how to use information to survive, thrive, or reproduce. That is the fuel and the leverage, until heat death.

Cellular automata are a vivid classroom: start with a line of zeros and a single 1, apply a tiny rule, and Stephen Wolfram-style complexity explodes. Carroll likes the demonstration and does not think it is how physics works. Physics conserves information and is reversible. Cellular automata are not; they bake in an arrow of time. He wants complexity in the real world, with microscopic reversibility and macroscopic irreversibility from entropy. Entropy is hard to localize, but approximate numbers exist. The observable universe, before stars, planets, and black holes formed, had entropy around 10^88. The single black hole at the center of the Milky Way has entropy around 10^90. Most of the entropy in the universe today is in black holes.

An isolated system at very low entropy looks simple, because few arrangements look like that. At maximum entropy it looks simple again, smeared out. Entropy only goes up. Complexity starts low, rises, and falls. People sometimes think life is fighting the second law. "That is precisely the wrong way to think about it. We are surfers riding the wave of increasing entropy. We rely on increasing entropy to survive." A table holds itself up mechanically. You and I do not. We stay stable by ingesting food, water, and air, burning it, raising its entropy. We are non-equilibrium quasi-steady-state systems, using the universe's low-entropy fuel.

He wants a physics of how complexity is born as the universe runs from low entropy to high, and he thinks it comes in stages. Configurational complexity is Kolmogorov's question: how much information specifies the setup. Then subsystems start burning fuel. A planet and a main-sequence star can look similar as spheres of density; the star is macroscopically stationary only because it is burning fuel underneath. Life is another stage, where information is gathered and used. Later still comes imagination: you and I run shoddy simulations of hypothetical futures; bacteria do not. There is an argument that what separates humans from other species is the ability to imagine counterfactuals. Northwestern engineer Malcolm MacIver's theory puts a cognitive shift at the water's edge. Underwater, light dies in meters and you move at meters per second, so evolution optimizes decisions under a second. On land you can see stars. A new mode opens: not a lookup table, but *what if I did this?* That, eventually, is the birth of imagination.

Carroll has been blunt about panpsychism, the claim that consciousness is everywhere, a fundamental aspect of reality. Philip Goff has almost single-handedly revived it in the popular imagination; David Chalmers remains panpsychism-curious. The argument is that physics might someday map every neuron and still fail to say what it is like to see red or taste sweet. First-person experience is supposed to lie outside physics, so you posit "mind," then either become a dualist or put mind prior to matter. Carroll the physicalist does not buy the gap. What it is like to be you is a way of talking about the atoms and neurons that make you up, the way hardness and brownness are words we attach to a table. He claims no special insight into how consciousness works. He sees no reason to change the laws of physics to account for it.

He almost never uses the word illusion. Illusion means you think you are perceiving something that is not there, like an oasis in the desert: walk up, and you were wrong. That is different from something emergent or non-fundamental that is still real. The table is real even though it is made of atoms. Consciousness and free will, he says, are just as real as tables and chairs. Donald Hoffman's claim that spacetime itself is an interface-illusion gets a split verdict. The respectable part is structural realism: Newtonians two hundred years ago could predict sunrise without quantum mechanics or relativity; the words of the fundamental story changed, the prediction pointed at something true. Calling that an illusion is wrong. Belief in God, by contrast, he does call an illusion — a reasonable one at the time, but a substantive claim that went beyond what we could verify and later failed.

He calls himself a poetic naturalist. Naturalism: all that exists is the natural world, the world we learn about by doing science. The poetic part is a warning against being fundamentalist about what that world is. Newtonian spacetime and Einsteinian spacetime tell different stories; if you want to fly a rocket to the Moon, you still use Newton. Many ways of talking latch onto something real and causally efficacious, and those ways get some reality. Tables remain real even though the deeper description is a quantum field theory wave function. The second job of the "poetic" is normative language: this painting is beautiful, that action is wrong. Those claims are not fixed by the phenomena and cannot be killed by a crucial experiment. They can be subjective without being arbitrary.

Science will not settle morality or meaning. A full theory of the mind would help explain why people hold the beliefs they do. It would not justify those beliefs as right or wrong. That is a real limit. You first decide what your goals are; then science can help you reach them. "If your goals are horrible, science has no problem helping you achieve them. Science is happy to help out." Dictators who wave science as moral authority are confusing an instrument with a verdict.

Fridman wants the method behind the output. Carroll has no sacred two-hour morning block. His strategy is to ignore interruptions and email, and the usable hours move around; some days and weeks, writing never happens. His wife Jennifer, also a science writer, free-writes a pile of "I think this" and then compresses. He sits silently for a long time and then writes something close to a final draft. A lot of the work happens in his head before it hits the page. *The Biggest Ideas* trilogy is an experiment: equations in public, aimed at the sixteen-year-old he once was. Book two, *Quanta and Fields*, is quantum field theory and particle physics. Book three, in progress, is *Complexity and Emergence*. The point is not to speculate. It is to say things that will still be true in five hundred years.

Mindscape started with over-preparation: anticipate the guest's lecture, then tug it out with leading questions. He now keeps a sketchy list of big questions he actually cares about and tries to have a real conversation. The hard constraint is one day of his life per episode, on average — research, invite, record, edit, publish. Young brilliant guests often cannot wander past their papers; some older ones have only canned answers. The sweet spot is broad enough to leave the specific papers, not so practiced that the answers are dead. Fridman reaches for the edge of chaos. Ask Me Anything episodes, questions from Patreon and audio for everyone, get picked by a selfish standard: which ones does he have interesting answers for? He will talk food, movies, politics, and religion. People never ask for relationship advice, which he keeps offering.

When people call you arrogant, he says, 99.999 percent of the time they mean they disagree. Atheists get the charge constantly, which he finds rich coming from people who think God exists and loves them. His advice is to specify the substantive disagreement and not to psychologize. Maybe you are right about their motives; a response to what they actually said would be more interesting. He once drew a two-by-two "Grid of Disputation": agree or disagree, respect or don't. All four quadrants are full. Everyone's favorite was embarrassing allies — people who agree with you and for whom you have no respect. As a society we are bad at disagreeing. We go straight to insults.

Why is general relativity so beautiful to teach? It starts from clear assumptions and goes extraordinarily far. Carroll has a talk that builds, in an hour, from no math to Einstein's equation. The punchline is that the equation is much smarter than Albert Einstein. Einstein did not know about the Big Bang, gravitational waves, or black holes. His equation did. That Einstein never won a Nobel for general relativity is, Carroll says, a tragedy. He should perhaps have won four: the photoelectric effect, because it invented the photon (Planck's 1900 chunks were how radiation was *dispensed*, like a coffee maker; Einstein in 1905 said light itself is quantized); special relativity; general relativity, separately, and not only because they were pretty but because they were experimentally verified. Edwin Hubble never won for the expanding universe. The prize is probably a net good for the world, because it points at good science, and a net negative for science, because it makes people want to win it.