Believe the Schrödinger Equation. The Cost Is Extra Worlds

This is Lex Fridman's second conversation with Sean Carroll, focused on quantum mechanics and the many-worlds interpretation in Carroll's book *Something Deeply Hidden*. Fridman starts where the book starts: Isaac Newton and classical mechanics. You can throw a rock and predict its flight. The theory still works. Newton himself, Fridman notes, found a human-level reading of it absurd, especially action at a distance. How does the Earth know there is a Sun ninety-three million miles away pulling on it?

Carroll says the religious worry was slightly different, and almost nobody mentions it. Newton was smart enough that he nearly invented chaos theory. He could explain a planet around the Sun, but he knew that once Jupiter and Saturn were included, the solar system would go out of whack. His solution was that God would intervene now and then to put the planets back on track. The worry about gravity was the other one: how the Earth knows about the Sun. Newton literally said he would leave that for future generations, because he did not know the answer.

Those generations did figure it out. Around 1800, Pierre-Simon Laplace showed that Newtonian gravity can be rewritten as a field theory. Empirically it is the same theory, with the same predictions, but the Sun no longer reaches across the void: a gravitational potential field between Sun and Earth obeys Laplace's equation. Einstein's general relativity keeps the field and adds a speed limit. Shake something here and the gravitational impulse radiates at the speed of light — a gravitational wave, now detected. Carroll does not want physicists to presume the answer must look one way or the other. If action at a distance turned out to be the best description, he would use it. When we are guessing at unknown laws, intuition is a guide, not a veto.

Fridman presses on whether a field that is everywhere is something we understand or merely something we trust because it predicts so well. Carroll's answer depends on what *understand* means. He thinks he understands Fermat's last theorem even though his intuition does not go where Andrew Wiles had to go to prove it. He thinks he has a pretty good intuitive grasp of fields filling spacetime — gravity, electromagnetism, the Higgs — though quantum field theory keeps making the intuition worse. Intuition, he says, is trainable. He has different intuitions than he had as a baby.

Noam Chomsky's harder claim is that cognitive abilities are evolved and biologically capped. Carroll allows limits on visualization. When Edward Witten proves a theorem about hundred-dimensional spaces, he is not picturing them; he is doing the math, and that does not stop him from understanding the result. Carroll's rough, lightly educated guess is that there is a threshold of abstraction at which a mind becomes something like a Turing machine, able to hold and manipulate formal symbolic structures. Dogs and cats have not made that leap. Humans have. Once you are there, he is not sure there are limits on understanding the scientific world. There are limits on calculation — nobody takes cube roots of million-digit numbers in their head — but that is not a limit of understanding.

Is the universe simpler than it appears, forever out of reach? Of course it is possible. The harder question is whether we have any reason to think we are close to the limit. Ask the world's greatest thinkers five hundred years ago whether they were approaching the edge of the natural world. They did not even have classical mechanics, let alone quantum mechanics. They were nowhere near how well they could do. Carroll sees no reason it is different for us. Of all the worries that keep him awake, the human mind's inability to rationally comprehend the world is low on the list. Eyes do not see atoms or cells either; we got there anyway, by combining senses with cognitive capacity, and he sees no hard boundary that would stop quantum mechanics from being understood the same way.

Asked for the most beautiful idea in physics, Carroll names conservation of momentum. Aristotle, in his *Physics*, made an obvious point you can still demonstrate at a table: push a bottle, it moves; stop pushing, it stops. That fact is indisputably true of everyday environments, and Aristotle blew it up into a picture of natures, teleology, and places things wanted to be. You were shoving them away from where they belonged, so they returned. It took a thousand or fifteen hundred years for people to say that if it were not for dissipation, air resistance, and friction, the natural thing is to move forever in a straight line at constant velocity.

That shift, Carroll says, is why the idea is beautiful. It replaces a vocabulary of *why* — purpose, cause, nature — with patterns. Give him the state of the world today and he can predict the future and reconstruct the past. It is impersonal and instantaneous, not aimed at future goals. Even more than classical or quantum mechanics, that is the insight that gets modern science off the ground: you do not need natures and purposes. You need patterns. The first person he knows to say that a projectile in vacuum would move at constant velocity was Ibn Sina, in the Persian golden age around the year 1000. Ibn Sina did not like the conclusion. He used it the way Schrödinger later used the cat: surely you do not believe there is really a vacuum, because then things would keep moving forever. He still got the conservation of impetus right, six hundred years before Newton.

Aristotle already knew his theory had a problem: an arrow goes a long way before it stops. His patch was an elaborate story in which the arrow pushed air aside and the air ran around to shove it from behind. Thought experiments like that, bouncing against experience, eventually produced the opposite claim: take the air away and the arrow goes on by itself. Theory and experiment, Carroll says, have always been that give and take. Galileo played a large role and still did not quite get momentum conservation right. The idea is so against everyday life that it took centuries to sink in.

Math, roughly, is the logical structure of all possible worlds. Physics is our actual world — *world* in the broadest sense, all of reality, which might be a multiverse or the many worlds of quantum mechanics and still be one physically contiguous world with rules. Eugene Wigner asked about the unreasonable success of mathematics in physics. Carroll thinks the question is slightly wrong. Any other possible world could be described mathematically; it might just be a mess. The surprising fact is that the math is so simple you can write it on a T-shirt: enormous compression that seems to hold in the real world. He is not sure that fact has a deeper explanation. The existence of the world at all, and the specific laws we have, may at some level just be how it is.

What is fundamental and what is emergent is easier to order than to finish. Atoms and molecules are more fundamental than cells and organs; quantum fields are more fundamental than atoms and molecules. Whether that bottoms out, nobody knows. A table has height, width, material, solidity, weight — a useful description. There is another description in atoms strung together. Smash the table and the atomic language still works; the table language does not. The more fundamental the theory, the broader its domain of validity. Carroll guesses the world does eventually reach a place you cannot ask beneath.

What would Newton make of *Something Deeply Hidden*? It would take a long time for any of it to make sense, Carroll says, even though the book gives him a shout-out. Newton was the greatest scientist who ever lived, and he invented calculus in his spare time. He was also, in some sense, still a premodern thinker. The cosmologist Rocky Kolb has said that Galileo, though earlier, was more modern: bring Galileo to the present, give him six months, and he would be in your office telling you what your latest paper got wrong. Newton wrote more about the Bible and alchemy than about physics, and he might have had mental blocks against seeing the world this way — or he might have asked for the textbooks, been left alone for a few months, and caught up. Einstein is the other obvious book reviewer Carroll would want. Older philosophers — Hume, Kant, Aristotle — would be fascinating, but unfair. Catch them up on what we know and they would be different people.

Quantum mechanics is the paradigm that replaced classical mechanics in the early twentieth century, in a way we are still coming to terms with. Classically, an object has a location and a velocity; know those for everything and you know what the world will do. Quantum mechanics has an analogue: a quantum state, or wavefunction, governed by an equation. The wavefunction is a vector in a huge-dimensional space rather than a position and a velocity; the equation is Schrödinger's, not Newton's. Those are details. The real break is a second set of textbook rules about what happens when you look. Classically there were no rules about observing. In the textbook, measurement is fundamental. An electron in an atom is a spread-out cloud, but when you look you see a particle with a location. The state changes at once, and that change affects what the electron does next. Carroll is careful: we do not agree on what quantum mechanics says. That is the textbook view.

Atoms were a chemist's idea before they were a physicist's. In the 1800s, two forms of tin oxide had exactly twice as much oxygen in one as in the other, never one-and-a-half times. John Dalton's hypothesis was tin atoms and oxygen atoms in one-to-one and one-to-two ratios. Chemists were quickly convinced. Physicists took longer; Boltzmann had a hard life in Germany, where atoms were unpopular. Rutherford later showed atoms could be broken further: a nucleus of protons and neutrons, almost all the mass, with electrons about eight hundred times lighter doing almost all the chemical and electrical work. The solar-system cartoon cannot be right. An orbiting electron would radiate and spiral into the nucleus in 10^-11 seconds, a hundred-billionth of a second.

Light, already understood as a wave, had been shown to have particle-like properties. Maybe the electron, the obvious particle, had wave-like properties. A bunch of people reached the same conclusion: do not think of the electron as a point in orbit; think of it as a spread-out wave. They named this the wavefunction — Carroll's verdict is that it is the dopiest name in the world for one of the most profound things in the universe. There is a number at every point in space, the value of the electron's wavefunction there. And there is only one wavefunction. Two electrons do not each have one; they share a combined wavefunction. There is one for the entire universe at once.

In the textbook, you square the wavefunction to get the probability of finding the system at a location. For two electrons there is still only one wavefunction, giving the probability of observing both at once. You can set it up so you do not know where either will be seen, yet you know they will be seen in the same place: if this one is here, the other is doing a certain thing. That conditional is entanglement, and classical mechanics has nothing like it. A common mistake is to think entanglement tracks distance. Two electrons can be fully entangled or fully unentangled anywhere in the universe. Quantum fields are a different story. Empty space is full of vibrating fields, and nearby field degrees of freedom are highly entangled, distant ones not. The gravitational field at this spot is still here even if you cannot see it. Drop something.

Hilbert space is the space of all possible quantum wavefunctions, for the universe or for a system. It is an abstract mathematical space, infinite-dimensional or merely enormous, with no immediate connection to the three-dimensional space we live in. A dimension there is just how many numbers you must be given to specify the state. Classically, position is three numbers; add velocity and you have six-dimensional phase space; add orientation and you add more. Entropy, in one useful sense among several, measures how much we do not know. You know the volume, temperature, and pressure of a bottle of water, not the position and velocity of every molecule. The bigger Hilbert space is, the higher the entropy of the system can be.

Carroll does not want his comfort to decide what the world is like, and infinity is a tricky case: multiply it by two and you still have infinity. His slogan is that only three numbers are simple — zero, one, and infinity. Three hundred and eighteen is a bizarre number; you need a lot of bits to say which it is. Once you have three hundred things you might as well have infinitely many, unless you can say when to stop. Infinity, in that sense, is a very natural number of things to exist. It also pops up whether we like it or not. Write a five-line program and ask how long it runs. Some of them run forever. You did not go looking for infinity. It arrived.

Carroll's personal feeling is that measurement and observers will not play a fundamental role in the ultimate laws. That is where the evidence has pointed so far. It would be infinitely cool if observation or mental computation did; he does not think so, and he is not spending much time on the possibility. The textbook's obsession with looking is a reason to find a better interpretation. His favorite, many-worlds, says two things. First, you the observer are just a quantum system: a bunch of atoms, a wavefunction, Schrödinger's equation, nothing special. Second, when you think you are measuring, you are becoming entangled. The electron is still in all those locations, but now part of the wavefunction says the electron was here and you think you saw it here, and another part says it was there and you think you saw it there. Those parts, once they exist, no longer talk to each other. They are, in effect, separate worlds.

Hugh Everett III, a Princeton graduate student in the 1950s, did therapy more than anything else. You do not need extra rules about looking. Listen to the Schrödinger equation: you have a wavefunction, you become entangled, the different versions of you stop interacting. Accept it. The cost is a bunch of extra worlds. The full theory is even thinner: there is a wavefunction of the universe, and it obeys the Schrödinger equation all the time. That is it. All the work is mapping that onto what we observe — carving the wavefunction into non-interacting worlds, and distinguishing a system from its environment. The environment is every degree of freedom you are not tracking: individual molecular velocities, photons, air in the room. Worlds split whenever a system in superposition becomes entangled with that outside world. No observer need be present.

How many worlds? Finite or infinite, it is a very big number. Whether Hilbert space is finite is secretly tied to gravity and cosmology, a part still being struggled with. In 1998 we learned the universe is accelerating. If that continues, a horizon forms: things recede faster than light, from our point of view, and never come back. Inside that horizon only finitely many things can happen — a finite-dimensional Hilbert space, with a guess at the dimensionality of ten to the ten to the one hundred and twenty-two. The age of the universe is something like 10^17 or 10^18 seconds; particles in the universe, maybe 10^88. Once you branch that many times you run out of room. Roughly, that corresponds to the universe expanding, emptying, cooling, and becoming empty space literally forever.

People who hear that the universe duplicates reasonably ask where the energy came from. Nobody who understands the equation worries about energy conservation, Carroll says; the equation is perfectly clear. It is better to think of a pre-existing universe splitting into two skinnier ones. Draw a vector of length one at forty-five degrees; you can write it as the sum of two shorter arrows along the axes, each of length one over square root of two. One arrow becomes two, the length is the same, you have only changed the description. The wavefunction of the universe is a big vector. Branching is that kind of decomposition. On other questions, such as where probability comes from, he admits legitimate puzzles. On energy, we know the answer: it is conserved.

Why the discomfort, then, if many-worlds is one of the cleanest ways to think about quantum mechanics? Carroll distinguishes two simplicities. There is simplicity in the theory itself: many-worlds wins, with only a wavefunction and the Schrödinger equation. Then there is simplicity in mapping the formalism onto the world we see. Newtonian physics scores high; the bottle is there, the center of mass is there. General relativity is harder. Quantum mechanics is very hard. Many-worlds is the version where that mapping is hardest. All the work of elaborating it is that mapping. Being bugged by the distance from experience is legitimate. You should give the skepticism up if there are no alternatives and the theory keeps working. Right now there are alternatives, built to sit closer to what we observe directly.

A debate among interpretations could fill a twelve-person stage. Carroll still sees only three frontrunners. Everett's many-worlds: a wavefunction that always obeys Schrödinger. Hidden-variable theories: the wavefunction is real but not everything; the simplest extra ingredient is particles, pushed around by the wave. Quantum systems look like waves and particles because, on this view, both are involved. That is easy for non-relativistic particles and becomes much harder in quantum field theory and quantum gravity. Spontaneous-collapse theories: every particle has a tiny chance per second of collapsing, so small it might take hundreds of millions of years for one particle, but a table has far more than a hundred million particles, all entangled, so one collapse brings the rest along. Roger Penrose has an induced variant: collapse when the gravitational difference between two parts of the wavefunction gets too large.

A fourth category is epistemic: the wavefunction is only a tool for predicting experiments, not a map onto an element of reality. Two people can assign different wavefunctions to the same system because they know different things. The trouble is the follow-up: predicting about what? Those interpretations decline to say. The other camps treat the wavefunction as real. Fridman would love to see the debate on stage; Carroll points to a World Science Festival session moderated by Brian Greene, with David Albert for collapse, Shelly Goldstein for hidden variables, and Rüdiger Schack for epistemic approaches.

Carroll finds many-worlds compelling for two reasons. It is the simplest, the most austere, pure quantum mechanics, and he would rather work hard on the map to reality than complicate the formalism. The more practical reason is modern physics: quantum fields, quantum gravity, holography, spacetime doing strange things. Every other version brings classical baggage. Hidden variables want locations in space; collapse theories want a classical stage. Change the system and you start from scratch. Many-worlds is plug-and-play: tell him the theory and he can give you its many-worlds version. When the classical description of gravity and spacetime breaks dramatically, start from the most quantum theory you have and try to build spacetime up.

Einstein put general relativity in final form in 1915 and 1916: gravity is the curvature of spacetime, a classical field everywhere. We also have an algorithm for taking a classical theory and quantizing it. That is how quantum electrodynamics arrived, after infinities that Feynman, Schwinger, and Tomonaga taught us to handle, and that Kenneth Wilson later said we should not have worried about. The same instinct said: start with classical general relativity and quantize it. Gravity's infinities are more stubborn. There is also evidence that quantum gravity is not a field theory at all, but something with nonlocal features we do not understand, a clue from black holes, Hawking radiation, and information conservation. If the fundamental theory is not even local, you do not know which classical precursor to quantize. The next sensible move, Carroll thinks, is to start intrinsically quantum and look for a classical limit.

Locality is the answer to Newton's old question. What happens to the field at this point depends directly only on the points next to it, and those on their neighbors, so influence can cross space through local steps. That idea is built into every field theory, including classical general relativity. Black holes strain it. Hawking showed in the 1970s that they radiate and eventually evaporate. If you make a black hole from certain stuff and evolve the system with the Schrödinger equation, you should be able to predict what it turns into. There are good arguments that this cannot happen while preserving locality: information seems to be spread out in a nonlocal way. Holography is the slogan for that. From the outside, the information that fell in looks smeared over the horizon, a two-dimensional surface encoding the three-dimensional interior.

Complementarity, a word borrowed from Niels Bohr, rides along with holography. There is no unique way to describe what happens inside a black hole. An infalling observer sees something fairly normal until the singularity; an outside observer sees information on the horizon. Both descriptions can be accurate and sound incompatible, the way you can measure position or momentum but not both at once. Carroll feels liberated. Space is just a good approximation, and that was always going to be true once you quantized gravity. We are only beginning to face the dramatic implications. He does not think anything weird has happened to quantum mechanics itself. Ordinary notions of spacetime are what fail. Many-worlds was not invented because extra worlds were cool. It was invented to account for what we already observe: wavefunctions that look spread out, then located when we look. Hopping from branch to branch is physically forbidden. There is already a copy of you over there. Leave them alone. The fear of missing out is the downside; acceptance is part of the deal.

In principle you can rewind. Knock over a glass of Bordeaux on a white tablecloth and, if the world were classical and you were lucky, every molecule of wine might hop back into the glass when you lift it. It will not happen. The quantum case is the same: possible in principle if you had the entire wavefunction, never in practice once you have Avogadro's number of particles. Quantum mechanics is no help with time travel. Information is conserved, so a Laplacian demon could run the clock backward; none of us is that demon. The arrow of time is not different in many-worlds. In both thermodynamics and Everett, the fundamental laws are reversible. Special initial conditions fourteen billion years ago do the work: low entropy near the Big Bang, entropy increasing ever since; and, in quantum mechanics, a wavefunction that started with one branch and has been branching ever since. Same arrow. Carroll did not say time is emergent. He said the arrow is. You can have time without an arrow — Earth going around the Sun forever, a movie that looks the same backward. Space, by contrast, may well be emergent: the fundamental description is a vector in Hilbert space, and three-dimensional space is a good approximate story you have to recover.

Tests of many-worlds are indirect. Experiments looking for spontaneous collapse, if they found it, would rule the interpretation out. Hidden variables come with a theorem that seems to say the predictions always match many-worlds; Carroll is a little skeptical and has not internalized it, so there may be loopholes. Otherwise it is quantum mechanics all the way down. Science journalism, he notes, has a cottage industry of pieces announcing that quantum mechanics is more astonishing than ever. It is still the quantum mechanics of 1926. Emergent spacetime is in a much more primitive state. There is not yet a safely written-down, respectable, honest theory, so experimental predictions we have not thought of are entirely possible — at huge distances, or high speeds, or high energies. Light of different wavelengths traveling at different speeds would be a dramatic violation of known physics. It is not a firm prediction. The theories are not mature enough to speak firmly.

Can quantum mechanics teach us about the human mind? The short answer is not really. Minds are pretty classical. Carroll does not think entanglement is crucial to how the mind or consciousness works. The word *quantum* is used for everything besides quantum mechanics. If panpsychists are right and consciousness is fundamental, is that possible? It is possible. He does not ponder it. He is a thorough physicalist: no separate mental states or properties, all of them emergent, like spacetime. Spacetime is already hard enough. That we do not yet understand consciousness is not surprising.

Carroll's podcast *Mindscape* is one of Fridman's favorites, not only for physics but for the episodes where Carroll leaves his expertise and asks real questions. The selfish origin story is a stack of unread books and no time; interviewing authors forces him to read. The method worked. He is now slightly annoyed that people write such long books. He is still learning to interview: the questions are good, the give-and-take is a skill, and the happy medium sits between barely talking and talking half the time. He learns more from the episodes that have nothing to do with physics or philosophy — Wynton Marsalis on jazz, a master sommelier on wine, Will Wilkinson on partisan polarization and the urban-rural divide, psychologists on cognitive dissonance. Scott Derrickson, who directed *Doctor Strange*, walked him through making a blockbuster and, as an evangelical Christian, through the nature of reality. Carroll wants more highly educated theists who know the theology; he has not quite arranged them yet.

He has zero interest in booking a target to be slapped down — no flat-Earthers, no charlatans. He will happily bring on people he disagrees with, but only people from whom the audience can learn something interesting. With David Chalmers he puts the disagreement on the record and does not dwell, because Carroll has an episode every week and the guest is on once. With Philip Goff, who wanted the fight, they really got into it. Debate is fun when there is intellectual respect. Fridman asks a harder sorting question: someone who accepts natural selection but says the Cambrian explosion cannot be understood in current Darwinian terms — box-breaker or dressed-up crank? Carroll does not have a satisfying answer. The further from his expertise, the harder the call. He would talk to people he respects who know the field, and he notes that physicists, and biologists too, can be too dismissive of alternatives.

He gets heat all the time. Mix up the topics is the point of the show, and every episode someone names the other person he should have booked instead. Fridman hopes he keeps doing it. The through-line of the physics half is the same attitude Carroll asked for at the start. Newton disliked action at a distance and did not throw out the equations. Many-worlds is the version of quantum mechanics that asks you to dislike extra worlds and still believe the Schrödinger equation. If a theory keeps working and the alternatives keep adding machinery, the job is to get better at mapping the math onto the world we see — not to demand that the world look like the living room.