Sean Carroll: Einstein’s most radical thought

Einstein is underrated as a physicist because the history of physics selectively credits a small number of individuals while obscuring the reality that all very smart people, including Isaac Newton, were talking to other people and building on collective intellectual work.

“I like to say that Einstein is if if anything underrated as a physicist, which is hard to imagine given how highly he is rated. When we tell the history of physics, we try to keep things straight and we can't remember everything. So, we kind of give a lot of credit to a relatively small number of individuals, Einstein being one of them. The messy reality of it is that all of these very smart people, including Isaac Newton, were talking to other people.”

Einstein is underrated as a physicist despite his exceptionally high reputation because the historical narrative simplifies complex intellectual evolution by attributing discoveries to a small number of individuals rather than to broader collaborative networks of thinkers.

“I like to say that Einstein is if if anything underrated as a physicist, which is hard to imagine given how highly he is rated.”

Einstein initially rejected Minkowski's spacetime formalism as unnecessary mathematical abstraction, refusing to adopt mathematical tools that didn't serve his physics intuition, though he later changed his mind when he recognized spacetime's utility.

“Einstein himself was not impressed by this move. Einstein was a hilarious character because he was a physicist's physicist. He was very mathematically adept... but he wasn't in it for the math. He was in it for the physics. So, he learned as much math as he needed. And when Bikovsky says, 'I have some new math that unifies space and time based on Einstein's theories,' Einstein himself's like, 'I don't need that. That's like extra mathematical nonsense.' He soon changed his mind because it turns out that move from space and time being separate to being combined is super useful going forward.”

When a fundamental physical framework is reconceptualized, one must go back to all previous successful applications and ask whether they still work—this backward-compatibility check is essential and often reveals new insights.

“You have to go back to everything that was a success in your previous way of doing things and say, 'Does it still work?'”

Once a theory is formulated into equations, the equations become autonomous; they are 'smarter than we are' in the sense that they can produce predictions and solutions that their originator did not anticipate or intend.

“But the thing is once you use that intuition, Einstein used his ideas about gravity disappearing in small regions of spaceime to invent general relativity. But then you have the theory, then you have general relativity, then you have equations. And the equations don't care what your intuition is. I like to say that the equations are smarter than we are.”

Halley, the astronomer, and his colleagues (including Hooke, Wren, and others) socially pressured Newton to formulate and publish his gravitational theory by asking him to solve the mathematical problem of planetary motion, demonstrating the social context enabling scientific progress.

“And another one was Halley, the astronomer who discovered comet. And they basically cajjoled who was a young stver at the time to go up to Cambridge from London visit Isaac Newton and say could you please solve this math problem for us what happens if you have a planet moving in an inverse square law gravitational force and of course Newton said oh I already did that it's a it's an ellipse and so Halley said would you please write that up so that we can share it and Newton eventually wrote the Prancipia Mathematica the most important book in the history of physics”

Historical narratives often overstate the 'great man theory' by attributing breakthroughs solely to individual genius while obscuring the collaborative and institutional context that enabled those breakthroughs, leading to a misleading understanding of how science actually progresses.

“We sometimes get the wrong impression about the great man theory of science or physics because look, Isaac Newton and Albert Einstein did a lot and they deserve a lot of credit. But think about the difference between the development of quantum mechanics for example versus general relativity. General relativity was Einstein's great accomplishment and it was really his accomplishment. No one else was even really competing with him that much at the time.”

The inverse square law of gravity was not Newton's unique insight but was discussed by multiple contemporaries including Christian Huygens in the Netherlands and Robert Hooke; none of them had Newton's mathematical skill, and it took social pressure from Halley and others for Newton to write up his solution, resulting in the Principia Mathematica.

“when Isaac Newton first understood that the inverse square law of gravity predicts that planets move in ellipses around the sun. So, number one, he's building on prior progress, right? It was Johannes Kepler who argued that planets do move in ellipses and came up with sort of some phenomenological rules about that. But the thing is that it wasn't only Isaac Newton who had this idea of the inverse square law. Christian Huygens in the Netherlands show that there's a relationship between how fast things move and the strength of the force pulling on them. Robert Hook, who was going to become a famous British scientist and helped found the Royal Society in London. He and his friends batted around the idea that maybe gravity is described by an inverse square law. It's just that none of them were quite as mathematically adept as Isaac Newton... one of Hook's friends was Christopher Ren, the architect who built St. Paul's Cathedral. And another one was Halley, the astronomer who discovered comet. And they basically cajjoli who was a young stver at the time to go up to Cambridge from London visit Isaac Newton and say could you please solve this math problem for us... And Newton eventually wrote the Prancipia Mathematica the most important book in the history of physics so even the Great discoveries made by individuals come about because of a social context.”

Einstein took a decade (1905–1915) to develop his hypothesis about curved spacetime into the complete mathematical formulation of the general theory of relativity, demonstrating that conceptual breakthroughs require substantial mathematical and intellectual work.

“It's a it's a good idea to have. It takes you a lot of effort and a lot of mathematical work to figure it out. So 10 years later in 1915, Einstein finally completes what we call the general theory of relativity.”

James Clerk Maxwell synthesized the work of Faraday, Ampère, and others to create a unified theory of electromagnetism, showing that electric and magnetic fields pervade the universe and interact according to his equations.

“It started in the 1800s with the invention of electromagnetism. It was James Clark Maxwell who put the whole story together after work by people like Faraday and Aier and so forth. And what he realized is there's two fields pervading the universe, an electric field and a magnetic field.”

For decades, physicists attempted elaborate schemes to resolve the contradiction between Newtonian mechanics and Maxwell's electromagnetism, including hypotheses like the luminiferous aether, before Einstein's 1905 solution.

“So for a long time, for decades, people physicists bashed their heads against this problem. They came with very elaborate schemes to get rid of it.”

Einstein discovered that gravity cannot be incorporated into special relativity as a force sitting on top of spacetime; instead, gravity must be understood as a feature of spacetime geometry itself.

“And what he realized is that gravity is not a force on top of spaceime. It's a feature of spaceime itself.”

Einstein hypothesized that spacetime geometry is curved and dynamical, warping in response to the presence of mass and energy, and that curved spacetime—not a force—explains gravitational phenomena.

“Maybe that geometry is curved. Maybe it's not like a flat tabletop like ukitian geometry. Maybe it's warped and bent and dynamical and changes in response to the existence of mass and energy and things like that.”

Einstein's immediate appreciation of Schwarzschild's solution shows Einstein's intellectual honesty and openness to others' work, saying 'I should have figured that out myself'—demonstrating that even great physicists recognize their limitations.

“And this was brilliant. And Einstein loved it right away. He got the fact, oh yeah, you know, I should have figured that out. You're right.”

Understanding how different layers of physical reality depend on each other—from quantum field theory to chemistry to biology—is essential to scientific understanding, even as each layer must be studied on its own terms.

“So, I think it's incredibly significant how the different layers of reality depend on each other... We can both appreciate that these different levels depend on each other while appreciating also that to study them and to understand them, we need to take each level seriously for its own sake.”

Even with Newton's profound insight into the inverse square law of gravity and the mathematical framework to describe planetary motion, his work built on prior discoveries by Johannes Kepler, Christian Huygens, Robert Hooke, and others who had grasped elements of gravitational theory.

“If you go back to the time of Isaac Newton, when Isaac Newton first understood that the inverse square law of gravity predicts that planets move in ellipses around the sun. So, number one, he's building on prior progress, right? It was Johannes Kepler who argued that planets do move in ellipses and came up with sort of some phenomenological rules about that. But the thing is that it wasn't only Isaac Newton who had this idea of the inverse square law. Christian Huygens in the Netherlands show that there's a relationship between how fast things move and the strength of the force pulling on them. Robert Hook, who was going to become a famous British scientist and helped found the Royal Society in London. He and his friends batted around the idea that maybe gravity is described by an inverse square law.”

Newton's mathematical adeptness surpassed that of his contemporaries—Huygens, Hooke, and others understood gravitational concepts but lacked Newton's mathematical facility to solve the problem completely—showing that even breakthrough discoveries require both conceptual insight and technical execution.

“It's just that none of them were quite as mathematically adept as Isaac Newton.”

General relativity was primarily Einstein's individual achievement, with limited competition or parallel development from others, making it an exception rather than the typical pattern of scientific discovery.

“General relativity was Einstein's great accomplishment and it was really his accomplishment. No one else was even really competing with him that much at the time.”

Subsequent developments in particle physics including Fermi theory of beta decay, fermion/boson distinction, Yang-Mills gauge theories, parity violation, Higgs mechanism, and the Standard Model involved many physicists (Fermi, Bose, Yang, Mills, Lee, Yang, Wu, Higgs, Goldstone, Nambu, Weinberg, Salam, Wilczek, Gross, Politzer, Gell-Mann, Zweig, etc.), demonstrating the deeply collective nature of twentieth-century physics.

“Enrico Farmy invents a theory that explains how neutrons and muons can decay called the Fairmy theory of beta decay. Vermy and Bose invent the idea of firmians and Bzons. Yang and Mills generalize the idea of electromagnetism to other symmetry groups and propose that this is an origin of the strong and weak nuclear forces. Lee and Yang say that maybe there is violation of par in the weak nuclear force... CS Woo detects experimentally that this is in fact true. Peter Higgs and Franco and Robert Brow and Philip Anderson and others use the idea of symmetry breaking which have been pioneered by Jeffrey Goldstone and Yoshiro Namboo to explain why the nuclear forces are short range. Steven Weineberg fits the final pieces of the puzzle together along with Abdul Salam to understand the unification of the electromagnetic and weak nuclear forces. Frank Wilchek and David Gross and David Pitzer do an analogous thing for the strong nuclear force by understanding confinement. Why quarks are stuck inside protons and neutrons. Murray Galman puts together by inventing the idea of quarks along with George Swag.”

Two years after Einstein's 1905 paper, mathematician Hermann Minkowski, who had been one of Einstein's professors, proposed that the correct interpretation of special relativity is to view space and time as a unified four-dimensional spacetime rather than separate entities, a mathematical reformulation Einstein initially dismissed as unnecessary but later recognized as useful for further development.

“it wasn't until two years later when Herman Minkovsky, who was a mathematician who had been one of Einstein's professors, said, you know, the right way to think about Einstein's theory is to say that space and time aren't separate anymore. to imagine there's one thing called spacetime and different people, different observers moving in different ways through the universe will divide it up into space and time differently... Einstein himself was not impressed by this move... he wasn't in it for the math. He was in it for the physics. So, he learned as much math as he needed. And when Bikovsky says, 'I have some new math that unifies space and time based on Einstein's theories,' Einstein himself's like, 'I don't need that. That's like extra mathematical nonsense.' He soon changed his mind because it turns out that that move from space and time being separate to being combined is super useful going forward.”

Einstein's equations of general relativity are so complex that Einstein initially believed no one might ever solve them, but Carl Schwarzschild, a German astronomer who attended Einstein's lectures in Berlin, taught himself general relativity, solved the equations for the gravitational field around the sun, and returned from World War I to present the solution to Einstein, who immediately recognized its brilliance.

“Once Einstein writes down his equation, anybody can solve it. And indeed, Einstein himself looked at his equation and goes, I don't know if anyone's going to ever go to solve this. This is too complicated looking. It's too intimidating. But a bunch of other people were not intimidated. Most famously, most quickly, Carl Schwarziel, who was a German astronomer who sat in on lectures that Einstein gave in Berlin. He taught himself general relativity. Came back from the Eastern Front in World War I and said, 'Professor Einstein, I've solved your equations. I've solved them for the gravitational field around the sun, and now we can use that to predict the motions of planets and things like that.' And this was brilliant. And Einstein loved it right away. He got the fact, oh yeah, you know, I should have figured that out. You're right.”

The development of electromagnetism in the 1800s revealed a conflict between Maxwell's equations and Newton's mechanics: Maxwell's equations predicted a special velocity (the speed of light), while Newtonian mechanics allowed all velocities to be equivalent, leading physicists to struggle for decades with reconciling this inconsistency.

“It started in the 1800s with the invention of electromagnetism. It was James Clark Maxwell who put the whole story together after work by people like Faraday and Aier and so forth. And what he realized is there's two fields pervading the universe, an electric field and a magnetic field. People were very happy at the existence of electromagnetism. They started thinking about what it all meant. And what they realized is that the sort of way that space and time are treated in Maxwell's theory of electromagnetism is different than the way they are apparently treated in Newton's theory. In particular, Maxwell's equations predicted a special velocity... Every velocity is created the same [in Newton]. Maxwell says there is something called the speed of light... How can it possibly be the case that everyone measures the same speed for light even if they're moving with respect to each other? So for a long time, for decades, people physicists bashed their heads against this problem.”

The history of physics ideas does not follow a lockstep pattern with the history of individual physicists; different people develop different ideas at different times from different sources, making scientific discovery inherently messier than simplified historical narratives suggest.

“It's always interesting to see the evolution of ideas which is not exactly lock step with the evolution of people. Different people have different ideas. They have different ideas at different times. They get them from different sources. That's the messy human reality of doing science.”

The evolution of ideas in physics does not lock step with the evolution of people; different people have different ideas at different times and get them from different sources.

“It's always interesting to see the evolution of ideas which is not exactly lock step with the evolution of people. Different people have different ideas. They have different ideas at different times. They get them from different sources. That's the messy human reality of doing science.”

Different layers of reality depend on each other: quantum field theory and atoms form the foundation, which governs chemistry through electromagnetic interactions, which in turn enables biology, demonstrating a ladder of emergent complexity where each level depends on lower levels but must be studied on its own terms.

“I think it's incredibly significant how the different layers of reality depend on each other. And we know one layer really, really well, the layers of particles and forces at the level of quantum field theory and atoms and things like that... leads to the layer of chemistry and atoms. The stability of the chair that I'm sitting on ultimately comes down to the rules of quantum field theory. Those atoms and molecules come together with electricity and magnetism to make all of chemistry, which is a pretty big deal. Chemistry comes together to make biology and so up on the ladder. We can both appreciate that these different levels depend on each other while appreciating also that to study them and to understand them, we need to take each level seriously for its own sake.”

The many-contributor model of quantum mechanics development is actually much more characteristic of how physics is usually done than the single-person-inventing-everything model implied by the great man theory.

“This idea that there are many people contributing and many different parts of the pieces need to put together is actually much more characteristic of how physics is usually done than the single person inventing everything all by themselves.”

Einstein attempted to create a version of Newton's theory of gravity compatible with special relativity but found it impossible, which forced him to realize that gravity is not a force on top of spacetime but rather a feature of spacetime itself—specifically, spacetime geometry that is curved and dynamical, responding to the presence of mass and energy.

“The biggest success of Newtonian classical mechanics was gravity. The famous inverse square law of gravity... And that simple rule plus the framework of Newtonian mechanics is enough to match exactly what you see in the sky... It's enough to launch a rocket and get it to the moon. So Einstein comes along and says, 'Well, okay, can I make a version of Newton's theory of gravity that is compatible with my new theory of special relativity?' And after trying, he said, 'No, I can't. You have to do something much more dramatic.' And what he realized is that gravity is not a force on top of spaceime. It's a feature of spaceime itself... Maybe that geometry is curved. Maybe it's not like a flat tabletop like ukitian geometry. Maybe it's warped and bent and dynamical and changes in response to the existence of mass and energy and things like that.”

The difference between general relativity (primarily Einstein's accomplishment) and quantum mechanics (developed through contributions from dozens of physicists including Planck, Einstein, Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger, Dirac, and others) demonstrates that the 'great man theory' is not characteristic of how physics is usually done; quantum mechanics involved many necessary pieces from many contributors.

“think about the difference between the development of quantum mechanics for example versus general relativity. General relativity was Einstein's great accomplishment and it was really his accomplishment. No one else was even really competing with him that much at the time. But quantum mechanics mock plunk points out that you need to fiddle with the equations to make the right prediction for black body radiation. Einstein himself says, 'Oh, I can understand why light jiggles loose electrons sometimes.' Rutherford builds experiments and he detects that there are nuclei inside atoms. Neils Boore says, 'I can explain the different sizes of the orbits of the electrons in the atoms.' Louis De Bruy says it's even better if you imagine that those electrons are waves rather than particles. Berner Heisenberg says I can invent a theory using matrices that explains exactly what's going on. Maxourne and Pascal Yordon say we can improve the mathematics of Heisenberg's theory to make it more general. Irwin Schroinger comes along and says we can replace the matrices by waves. And then Maxourne comes again and says actually these are useful for predicting probabilities. Wolffegong Powley says there's something called spin and that affects what the electrons can do in an atom. Paul Durac says, 'I can invent an equation for the electron that predicts what it will do and fits it in with relativity.' Durac's equation also predicts an anti-particle of the electron. Carl Anderson goes and discovers the antiparticle of the electron and also discovers the muon. Enrico Farmy invents a theory that explains how neutrons and muons can decay called the Fairmy theory of beta decay. Vermy and Bose invent the idea of firmians and Bzons. Yang and Mills generalize the idea of electromagnetism to other symmetry groups and propose that this is an origin of the strong and weak nuclear forces. Lee and Yang say that maybe there is violation of par... The fact that a right-handed interaction does not happen at the same speed as the left-hand interaction... CS Woo detects experimentally that this is in fact true. Peter Higgs and Franco and Robert Brow and Philip Anderson and others use the idea of symmetry breaking... Steven Weineberg fits the final pieces of the puzzle together along with Abdul Salam to understand the unification of the electromagnetic and weak nuclear forces. Frank Wilchek and David Gross and David Pitzer do an analogous thing for the strong nuclear force by understanding confinement. Why quarks are stuck inside protons and neutrons. Murray Galman puts together by inventing the idea of quarks along with George Swag. And that's only getting us up to 1970.”

If William Shakespeare had never existed, his plays would never have been written, but if Albert Einstein had never existed, general relativity would still have been invented, likely without much delay, because physics progresses through the contributions of multiple brilliant people in the right place and time, not through irreplaceable individuals.

“I suspect that if William Shakespeare had never existed, Shakespeare's plays never would have been written. But I'm pretty sure that if Albert Einstein had never existed, general relativity would still have been invented. Indeed, I don't think it would have taken that much longer. It's something about the progress of physics that there are super duper smart people who are making these advances, but they're also in the right place at the right time.”

Maxwell's equations of electromagnetism treat space and time differently than Newton's mechanics do, creating an apparent tension between the two theories.

“What they realized is that the sort of way that space and time are treated in Maxwell's theory of electromagnetism is different than the way they are apparently treated in Newton's theory.”

Maxwell's equations predict the existence of a special velocity—the speed of light—at which electromagnetic waves travel, contradicting Newton's principle that no velocity is special in the universe.

“In particular, Maxwell's equations predicted a special velocity. There's no special velocity in Newtonian mechanics. Every velocity is created the same. Maxwell says there is something called the speed of light. It is the speed at which waves in the electromagnetic fields move.”

Hermann Minkowski, a mathematician who had been Einstein's professor, provided crucial mathematical insight two years after Einstein's 1905 paper by proposing that space and time should not be viewed as separate entities but as a unified four-dimensional spacetime.

“And in fact, it wasn't until two years later when Herman Minkovsky, who was a mathematician who had been one of Einstein's professors, said, you know, the right way to think about Einstein's theory is to say that space and time aren't separate anymore. to imagine there's one thing called spacetime and different people, different observers moving in different ways through the universe will divide it up into space and time differently.”

Empirically, everyone observes the same value for the speed of light regardless of their own motion relative to each other, yet this contradicts the expectation from Newtonian relativity that velocities should add linearly.

“And naively you look at the equations and everyone measures the same value for the speed of light. It's a constant of nature. How can it possibly be the case that everyone measures the same speed for light even if they're moving with respect to each other?”

Einstein's 1905 insight was to reject the assumption that electromagnetic waves travel through a medium (luminiferous aether), and instead treat electromagnetic waves as fundamental phenomena whose constancy of speed should be taken at face value rather than explained away.

“And it was Einstein, Albert Einstein in his great paper in 1905 who first said you should get rid of the idea of these waves traveling through a medium. You should think of the electromagnetic waves as really being the thing that exists. And when the equations tell you everyone measures the speed of light the same, that's because they do. Take that seriously.”

Taking the constancy of light speed seriously requires a complete reconceptualization of what space and time are—a radical revision of the framework of physics that subsumed centuries of Newtonian assumptions.

“All you have to do is entirely rejigger your thoughts about what space and time are.”

In spacetime, different observers moving at different velocities through the universe will divide spacetime into space and time components differently; there is no objective absolute fact about what is happening at a distant location at a given moment—simultaneity is relative to the observer.

“Different people, different observers moving in different ways through the universe will divide it up into space and time differently. There's no objective true fact about when I snap my fingers now what's happening light years away. That's going to depend on who's doing the observing and who's doing the measuring.”

The transition from separate space and time to unified spacetime was a radical reworking of physics' foundational framework that had been stable for hundreds of years under Newtonian assumptions.

“That was a radical reworking of the framework of physics. You know, Newton's idea of separate space and separate time, absolute and agreed upon by everyone, had been there for hundreds of years.”

Einstein's own uncertainty about whether anyone could solve his general relativity equations demonstrates their mathematical complexity and the non-obvious nature of their solutions.

“Einstein himself looked at his equation and goes, I don't know if anyone's going to ever go to solve this. This is too complicated looking. It's too intimidating.”

Karl Schwarzschild, a German astronomer, solved Einstein's general relativity equations for the gravitational field around the sun shortly after returning from the Eastern Front in World War I, demonstrating that the equations, though intimidating, were solvable.

“But a bunch of other people were not intimidated. Most famously, most quickly, Carl Schwarziel, who was a German astronomer who sat in on lectures that Einstein gave in Berlin. He taught himself general relativity. Came back from the Eastern Front in World War I and said, 'Professor Einstein, I've solved your equations. I've solved them for the gravitational field around the sun, and now we can use that to predict the motions of planets and things like that.'”

Quantum mechanics developed through contributions from many physicists: Planck recognized quantization; Einstein explained the photoelectric effect; Rutherford discovered the nucleus; Bohr explained electron orbits; de Broglie introduced wave-particle duality; Heisenberg developed matrix mechanics; Schrödinger developed wave mechanics; Dirac unified them and predicted antimatter, and many others.

“But quantum mechanics mock plunk points out that you need to fiddle with the equations to make the right prediction for black body radiation. Einstein himself says, 'Oh, I can understand why light jiggles loose electrons sometimes.' Rutherford builds experiments and he detects that there are nuclei inside atoms. Neils Boore says, 'I can explain the different sizes of the orbits of the electrons in the atoms.' Louis De Bruy says it's even better if you imagine that those electrons are waves rather than particles. Berner Heisenberg says I can invent a theory using matrices that explains exactly what's going on. Maxourne and Pascal Yordon say we can improve the mathematics of Heisenberg's theory to make it more general. Irwin Schroinger comes along and says we can replace the matrices by waves. And then Maxourne comes again and says actually these are useful for predicting probabilities. Wolffegong Powley says there's something called spin and that affects what the electrons can do in an atom. Paul Durac says, 'I can invent an equation for the electron that predicts what it will do and fits it in with relativity.'”

Einstein's solution to the Maxwell-Newton conflict was to reject the idea that electromagnetic waves travel through a medium and instead take literally Maxwell's equations that predict everyone measures the same speed of light, which required completely reconceptualizing space and time.

“It was Einstein, Albert Einstein in his great paper in 1905 who first said you should get rid of the idea of these waves traveling through a medium. You should think of the electromagnetic waves as really being the thing that exists. And when the equations tell you everyone measures the speed of light the same, that's because they do. Take that seriously. All you have to do is entirely rejigger your thoughts about what space and time are.”