*Einstein’s Unification*, Jeroen van Dongen (Cambridge University Press, 2010).

Albert Einstein was a charmingly blunt man. For instance, in 1952 he wrote a letter to his friend and fellow physicist Max Born where he admits that even if the astronomical data had gone against general relativity, he would still believe in the theory:

Even if there were absolutely no light deflection, no perihelion motion and no redshift, the gravitational equations would still be convincing because they avoid the inertial system...

It is really quite strange that humans are usually deaf towards the strongest arguments, while they are constantly inclined to overestimate the accuracy of measurement.

In a few short sentences Einstein completely repudiates the empiricist spirit which has ostensibly guided scientific inquiry since Francis Bacon. He doesn’t care what the data says. If the experiment hadn’t been run, he would still believe the theory. Moreover, should the data have *disconfirmed* his theory, who cares? Data are often wrong.

This is not, to put it mildly, the official story of how science gets made. In the version most of us were taught, the process starts with somebody noticing patterns or regularities in experimental data. Scientists then hypothesize laws, principles, and causal mechanisms that abstract and explain the observed patterns. Finally, these hypotheses are put to the test by new experiments and discarded if they contradict their results. Simple, straightforward, and respectful of official pieties. The Schoolhouse Rock of science. Or as Einstein once described it:

The simplest idea about the development of science is that it follows the inductive method. Individual facts are chosen and grouped in such a way that the law, which connects them, becomes evident. By grouping these laws more general ones can be derived until a more or less homogeneous system would have been created for this set of individual facts.

See? It’s as easy as that. But then, Einstein finishes that thought with: “[t]he truly great advances in our understanding of nature originated in a manner almost diametrically opposed to induction.”

Was Einstein a *science-denier*? I’m obviously kidding, but this is still pretty jarring stuff to read. How did he get this way? *Einstein’s Unification* is the story of the evolution of Einstein’s philosophical views, disguised as a story about his discovery of general relativity and his quixotic attempts at a unified field theory. It’s a gripping tale about how Einstein tried to do science “correctly,” experienced years of frustration, almost had priority for his discoveries snatched away from him, then committed some Bad Rationalist Sins at which point things immediately began to work. This experience changed him profoundly, and maybe it should change us too.

Like many, I was taught the ethical meme that Einstein failed his math classes.1 This is completely false. Einstein was really, really good at his math classes. What is true is that when he got to university his interest in *pure* mathematics started to wane, and he instead got obsessed with the opposite extreme: scientific experimentation, and even the design of laboratory instruments. In his *Autobiographical Notes*, Einstein writes, “I really could have gotten a sound mathematical education. However, I worked most of the time in the physical laboratory, fascinated by the direct contact with experience.” That “direct contact with experience” line is a dead giveaway, because these were the years when Einstein became a fanboy of Ernst Mach.

Mach is one of those guys who was incredibly famous and impressive in his day, but is now totally forgotten.2 His jobs included physicist, philosopher, psychologist and social reformer, and he made a splash at all of them. He was also a radical empiricist who believed that the only things worth talking about were the things we can see, touch, or otherwise measure. His fanaticism eventually led him in a bit of philosophical horseshoe theory to anti-atomism: atoms, being inaccessible to the senses, were an example of the “metaphysics” he wanted to expunge from science. Mach's views on the philosophy of science were enormously influential on an entire generation of American and European empiricists and positivists — particularly the Vienna Circle. Einstein described Mach’s philosophy like this:

Science is nothing else but the comparing and ordering of our observations according to methods and angles which we learn practically by trial and error... As results of this ordering, abstract concepts and the rules of their connection appear... Concepts have meaning only if we can point to objects to which they refer and to the rules by which they are assigned to these objects...

He [Mach] conceived every science as the task of bringing order into the elementary single observations which he described as 'sensations.'

Or, more succinctly: “Mach's system studies the existing relations between data of experience: for Mach, science is the totality of these relations.”

One of the reasons leftists loved Mach’s epistemology was that it offered liberation from the oppressive legacies of religion, ideology, and inherited privilege. Because if science, properly understood, meant the generalization and codification of knowledge directly from sensory data, then there was a real hope that it could produce discoveries that are neutral, objective, and accepted by all of humanity. Again, as Einstein put it:

[Mach] tried to show how concepts arose out of experience. He took convincingly the position that these conceptions, even the most fundamental ones, obtained their warrant only out of empirical knowledge...

...he more or less believed science to consist in a mere ordering of empirical material; that is to say, he did not recognize the freely constructive element in the formation of concepts. In a way he thought that theories arise through discoveries and not through inventions.

In other words, if science is just a process of induction without any “freely constructive element,” then it’s basically mechanical. That means there’s no way the scientist can inscribe his or her biases into a finished theory — if somebody else had been the one to produce it, it would have come out exactly the same. This in turn makes science the perfect, value-free, objective standard of everything. Golly, wouldn’t that be great!

Einstein read Mach's *Science of Mechanics* while he was in college, and said it was what first shook his faith in Newtonian physics. Later, once Einstein put his own name on the map, he started a lengthy correspondence with the great man himself. The only surviving letters are from Einstein to Mach, and they address him in a fawning tone: “You have had such a strong influence upon the epistemological conceptions of the younger generation of physicists that even your opponents today... would have been called Mach followers by physicists of the kind that was typical a few decades ago.” When he heard that Mach approved of the new theory of special relativity, Einstein practically bubbled: “Your friendly letter gave me enormous pleasure... I am very glad that you are pleased with the relativity theory... Thanking you again for your friendly letter, I remain, your student, A. Einstein.”

So no surprise that Einstein initially described special relativity in Machian, operationalist terms. His 1905 paper is practically overflowing with mentions of measuring sticks, clocks, and observers taking various sorts of readings. Here’s an example sentence from that paper: “If, for instance, I say, ‘That train arrives here at 7 o’clock,’ I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.’” That may sound awkward to us, but actually this is just abiding by the orthodox Machian take that ‘metaphysical’ concepts such as space and time only have meaning when they enter into our sensorium. And the love was reciprocated: the neo-positivists of the Vienna Circle all *loved* special relativity.

This is also the period when Einstein was most down on math. His friend and biographer Abraham Pais said that when Einstein first learned of Hermann Minkowski's elegant geometric reformulation of special relativity,3 he dismissed it as “*überflüssige Gelehrsamkeit*” — “superfluous learnedness.” In 1912 Einstein praised Paul Ehrenfest as “one of the few theorists who has not been robbed of his natural mind by the mathematical epidemic!” And when Max Abraham made an early attempt at developing a relativistic theory of gravity, Einstein immediately pounced on the idea that Abraham had allowed himself to be bamboozled by mathematical elegance. In a letter to Michele Besso he writes

Abraham’s theory has been created out of thin air, i.e. out of nothing but considerations of mathematical beauty, and is completely untenable. How this intelligent man could let himself be carried away with such superficiality is beyond me. To be sure, at the first moment (for 14 days!) I too was totally ‘bluffed’ by the beauty and simplicity of his formulas.

There was a lot wrong with Abraham’s theory, so it’s a little weird that Einstein chose to attack it on these grounds. But it makes total sense once you realize that, to a committed Machist, an overreliance on formal and aesthetic considerations was the cardinal methodological sin leading to the broken theory.

There you have a picture of where Young Einstein was at: philosophically an orthodox Machist and career-wise going from win to win. So naturally, when he set out to cap his successes by building his own relativistic theory of gravitation, he was gonna avoid all that highfalutin’ math stuff that doomed Abraham’s theory, and just stick to physical considerations. Little did he know that would nearly be the worst decision of his entire life.

Let’s go back to Newton’s second law, which says that force equals mass multiplied by acceleration. This is very intuitive — it means that a given force will accelerate a light object much more than a heavy one, so if you give the same sized shove to a ping pong ball and a minivan, the ball will move a lot faster than the van.4 If you want to calculate the acceleration, you divide the force the object is experiencing by its mass. You see this all over the place in physics textbooks — say you want to calculate how fast something will move when you attach it to a horizontal spring and then let go (Hooke’s law) or when you give it an electric charge and then stick it next to something with an opposite charge (Coulomb’s law) — the term for the acceleration always has a factor of 1/m, the reciprocal of the object’s mass. Again, this makes total intuitive sense, if there’s more stuff to move, then it’s harder to move it.

But there’s one sort of force that *doesn’t* work this way. Newton’s law of universal gravitation says that the gravitational attraction between two objects is proportional to both their masses, like this:

You see how the term for the force already has a copy of “m” in it? That means when we go to calculate the acceleration and divide by “m”, we don’t get a “1/m” term, instead it just cancels out, and there’s no dependence on the mass at all! This results in the quite unintuitive fact that gravitational acceleration doesn’t depend at all on an object’s mass, as Galileo famously demonstrated.

It’s unintuitive because gravity is the *only* thing that acts this way. When you hit an object, its mass matters a lot. When it falls, its mass doesn’t matter at all. I don’t think most teachers do a good enough job drawing our attention to how *extremely weird* this is — but it’s weird enough that the Aristotelians got it wrong for centuries!

General relativity was Einstein’s characteristically audacious response to this weird coincidence. He conjectured that the reason gravitational forces were unlike all the other forces was that they don’t actually exist, but instead are just phantoms of our experience, nothing more than the state of being in an accelerated frame of reference. So to formalize this, he needed a theory where doing a coordinate transformation to a uniformly accelerating reference frame would generate a homogeneous gravitational field. Ideally, the theory should also extend the principle of relativity – that is, the requirement that the laws of physics appear the same to all observers – from the comoving frames satisfied by the theory of special relativity to frames accelerated with respect to one another.

The most mathematically natural way for a theory to nail all these requirements was simply for it to be ‘generally covariant’ — that is, for the equations of the theory to remain unchanged in their form under arbitrary transformations of the coordinates. No empirical or observational data imposed this requirement: it could only be justified on the philosophical grounds that coordinate systems are not part of the true ontology of nature, or on the grounds that they allowed the theory to be expressed in a simple, aesthetically pleasing form. Both justifications should have sounded heretical to a committed Machist, but nevertheless when Einstein set out to discover general relativity, he went looking for a theory that was generally covariant.

Van Dongen’s book gives a beautiful overview of Einstein’s thought process as he set off down this intellectual path. I’d love to give a gloss of that story here, but after a few minutes of typing Christoffel symbols into the Substack editor I decided that was insanity. So instead I’ll just say that if you’re into math or physics and interested in *how* the Einstein Field Equations came to be, you should read that section of this book. What’s important for our purposes is that along the way, Einstein became wrongly convinced that a theory based on the Riemann and Ricci curvature tensors could not possibly revert to the Newtonian account of gravity in the limit of sufficiently weak fields.5 This was a super-important quality of a good theory: it had to explain the successes of Newtonian mechanics by agreeing with the old calculations on all the low-energy observations and experiments done up to that point in history.

So having incorrectly concluded that his mathematically natural and generally covariant approach wouldn’t work, Einstein switched to trying to generalize directly from the Newtonian equations. This didn’t go well either. Again, I would love to tell you the gory details of how it didn’t go well, but that would make 95% of you close the tab in disgust, so instead I’ll refer you again to this book and just tell you that after Einstein and his buddy Grossman hammered away at it for a few months, they came up with a field equation setting the stress-energy tensor equal to this monstrosity:

So by mid-1913 Einstein had derived two different candidate field equations for general relativity: one that was mathematically natural and generally covariant, but which he (incorrectly) believed didn’t yield the correct approximation in the Newtonian limit; the other physically motivated and visibly related to the Poisson equation, but not covariant. Forced to choose between these two candidates, Einstein sided with physics over mathematics, and published the non-covariant equations with Grossman under the title “*Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation,*”6 now commonly known as the 'Entwurf' (outline) theory. He would regret this choice to the end of his life.

The new theory ran into problems almost immediately: in June, Einstein used the *Entwurf* equations to compute the precession of the perihelion of Mercury, and came up with a value that was off by a factor of 2.4.7 A worse blow came at the end of September, when Einstein realized that flat Minkowski space transformed to a rotating coordinate frame was not a solution to the *Entwurf* field equations. This embarrassment finally shattered Einstein’s confidence in the theory, and set him furiously backpedaling. His correspondence from this period reveals a man teetering on the brink of despair. Not only had he finally figured out that he’d spent the past two years charging down a blind alley, but his lonely journey had suddenly turned into a race — and one that it seemed Einstein might very well lose.

A few months earlier, in June of 1915, Einstein had given a lecture on his *Entwurf* theory to an assembly of mathematicians at Göttingen. Attendees included the geometer Felix Klein (yes that Felix Klein) and the legendary David Hilbert. Everybody loved the basic idea — especially Hilbert, who put up Einstein in his guest room and peppered him with questions. Now, just as Einstein was realizing that the *Entwurf* was fatally flawed, he received word that Hilbert had made a major breakthrough.

This combination of stresses provoked one of the most productive months in Einstein’s life. Over the course of November 1915, Einstein threw away the *Entwurf* theory, started again nearly from scratch, and derived the correct gravitational field equations plus many of their consequences. How did he accomplish this feat? By returning to the mathematically elegant and generally covariant approach based upon the Riemann curvature tensor which he had previously abandoned, and pursuing its consequences without regard to its seeming failure to generalize existing physical theories. As Einstein himself put it in the opening of his first November paper:

I completely lost trust in the field equations I had chosen and looked for a way to restrict the possibilities in a natural manner. Thus I went back to the requirement of a more general covariance of the field equations, which I had left only with a heavy heart when I worked together with my friend Grossmann. In fact we had then already come quite close to the solution of the problem...

In a few short weeks, Einstein arrived at a linearized version of what we now call the Schwarzschild metric. This allowed him to compute the correct value for the precession of Mercury’s perihelion. Finally, on November 25th, he submitted the final and correct version of the equations for publication.

It wasn’t a moment too soon. Einstein wrote to Fokker that the discovery had given him heart palpitations. We might suspect another reason for those palpitations: Hilbert. He and Einstein exchanged a flurry of letters in the middle of November in which each discovered that the other had essentially completed the theory. Hilbert submitted his own paper on relativity on November 20th, five days before Einstein. Recent scholarship tends to the view that Hilbert’s theory of gravitation was incomplete when he submitted this draft, and that his claim to priority ought to be dated from a later revision, or perhaps from the galley proofs dated December 6th. Even so, that means that after dawdling with an obviously broken theory for two years, Einstein won the race for priority by a week and a half. Given the circumstances, I think we can forgive the heart palpitations.

Shall we check back in on Einstein’s views on the scientific method? Remember that as a young man, Einstein was an acolyte of Mach and a believer that induction from a mass of empirical evidence was the only legitimate scientific method. But now, his tone had changed: “[Mach's] point of view is wrong, and in fact what Mach has done is make **a catalog, not a system**.” In a letter to Ehrenfest, he put it bluntly: “Inductive means will never get you to a sensible theory.”

Einstein himself attributed these changes to his experiences with general relativity. In a letter to his collaborator Walther Mayer he said, “One should look for the mathematically most natural structures, without initially being bothered too much about the physical, as this brought the desired result in gravitation theory.” And in a letter to his friend Cornelius Lanczos (yes, that Cornelius Lanczos):

Coming from skeptical empiricism of somewhat the kind of Mach’s, I was made, by the problem of gravitation, into a believing rationalist, that is, into someone who seeks the only trustworthy source of truth in mathematical simplicity.

These letters, besides showing Einstein losing faith in Mach and positivism,8 also hint at the new philosophical system he was beginning to work out: one based around mathematical simplicity. Einstein saw mathematical simplicity as providing a prior constraint on the process of theory formation, or as he put it to Lanczos, “the physically true is logically simple, that is, it has unity in its foundation.” If that’s true then an ugly theory9 cannot possibly be a description of the underlying reality, and can therefore be rejected. Beauty is a heuristic that filters out invalid theories and lets scientists save time. It certainly would have saved Einstein a lot of time, since there’s no way the *Entwurf* would have passed the aesthetic test.

Why did Einstein believe that the truth must always be mathematically simple? In his 1933 Herbert Spencer lecture *On the Method of Theoretical Physics* he proclaims, “Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.” The most important word in that sentence is ‘experience.’ Einstein had been a committed philosophical positivist, and it was *experience* that caused him to change his mind: experience as a theoretical physicist, but especially the experience of discovering general relativity, where promising but ugly ideas failed again and again and the truth turned out to be as simple as possible.

He gives two examples in that speech, the first is one we’ve already seen:

The physical world is represented as a four-dimensional continuum. If I assume a Riemannian metric in it and ask what are the simplest laws which such a metric can satisfy, I arrive at the relativistic theory of gravitation in empty space.

But it wasn’t just general relativity.

If in that space I assume a vector-field or anti-symmetrical tensor-field which can be derived from it, and ask what are the simplest laws which such a field can satisfy, I arrive at Maxwell's equations for empty space.

Einstein saw the same pattern playing out in physics again and again, and everywhere he looked he saw simple theories that were correct and correct theories that were simple. It’s tempting to joke that Einstein came to abandon inductivism through a process of meta-induction, but in fact this is exactly what happened! The unifying theme across all of Einstein’s philosophical meanderings was a blunt pragmatism, and ultimately he went with what worked and what got results…even when it turned out that what worked was the airiest and most rareified sort of philosophical Platonism like this:

I have learned [...] from the theory of gravitation: no collection of empirical facts however comprehensive can ever lead to the formulation of such complicated equations.

A theory can be tested by experience, but there is no way from experience to the construction of a theory.Equations of such complexity as the equations of the gravitational field can be found only through the discovery of a logically simple mathematical condition that determines the equations completely or almost completely. Once one has obtained those sufficiently strong formal conditions, one requires only little knowledge of facts for setting up a theory...

Or in a letter to Louis de Broglie:

I have however long been convinced that one shall not be able to find this substructure in a constructive way from the known empirical relations between physical things, because the required mental leap would exceed human powers. I have arrived at this opinion not only because of the fruitlessness of the efforts of many years, but rather also through the experiences with the gravitational theory. The gravitational equations could only be found by a purely formal principle (general covariance), that is, by trusting in the largest imaginable logical simplicity of the natural laws.

So is the problem with inductivism just that human beings aren’t smart enough to work backwards from a mass of data to a compact and unified theory that would explain that data? Could a superintelligent AI do better? Einstein actually went on to make a deeper, more fundamental criticism of inductivism. The real problem is that there are too many degrees of freedom, too much underdetermination. That is, there are *many* different possible theories, all of which are compatible with a body of evidence. This brute reality crushes Mach's dream of liberating science from the bias, prejudice, and ideology enabled by “free conceptual construction.”

Moreover, Einstein observes that scientific training tends to obscure this crucial fact:

[E]ven scholars of audacious spirit and fine instinct can be hindered in the interpretation of facts by philosophical prejudices. The prejudice — which has by no means disappeared — consists in the belief that facts by themselves can and should yield scientific knowledge without free conceptual construction… Such a misconception is possible only because one does not easily become aware of the free choice of such concepts, which through success and long usage, appear to be immediately connected with the empirical material.

It's easy to see what he's referring to: science pedagogy has a tendency to emphasize the completed, polished form of theories. Students are rarely exposed to the messy and sometimes irrational process of their creation, and they are certainly not encouraged to wonder what alternative formalizations could have explained the evidence equally well.

In his Herbert Spencer lecture, Einstein gave a clear example of this sort of underdetermination: celestial mechanics itself!

The natural philosophers of those days were, on the contrary, most of them possessed with the idea that the fundamental concepts and postulates of physics were not in the logical sense free inventions of the human mind but could be deduced from experience by “abstraction” — that is to say, by logical means. A clear recognition of the erroneousness of this notion really only came with the general theory of relativity, which showed that one could take account of a wider range of empirical facts, and that, too, in a more satisfactory and complete manner, on a foundation quite different from the Newtonian.

Many would say that this is a wonderful example of scientific progress. After all, general relativity explains all of the observations that Newtonian mechanics does and more. But, as someone who actually attempted to generalize Newton’s laws, Einstein is less sanguine. He observes that far from being a straightforward extension of classical mechanics, general relativity is a completely different *kind* of theory with different principles, different internal logic, and even a different ontology. For Einstein, the fact that two so totally dissimilar pictures of the universe can both match with observations to such a high degree of accuracy is cause for wonder...and despair:

But quite apart from the question of the superiority of one or the other, the fictitious character of the fundamental principles is perfectly evident from the fact that we can point to two essentially different principles, both of which correspond with experience to a large extent; this proves at the same time that every attempt at a logical deduction of the basic concepts and postulates of mechanics from elementary experiences is doomed to failure.

If there are two completely distinct descriptions of the universe, both of which agree with measurement to a high degree of accuracy, then how many others are there? And if we found another one which matched general relativity to an accuracy beyond what our instruments could measure, how would we decide between them? You might object, “if two theories are indistinguishable by observation and experiment, then they are equally valid and it doesn’t matter which one we pick.” But come on, while some philosophers might say that, nobody actually believes it.

In Einstein’s view, this underdetermination strikes a fatal and fundamental blow against inductivism. Even a superintelligent being with access to all relevant data and a perfect ability to think laterally and construct alternative theories to explain the data can’t work backwards to the “correct” theory if there’s more than one of them. And Einstein’s solution to this crisis is straightforward: since science *cannot* be “just the facts,” since there’s *always* some room for free conceptual construction, since “every true theorist is a kind of tamed metaphysicist, no matter how pure a ‘positivist’ he may fancy himself,” then what scientists need to do is put their cards on the table.

Every scientist has secret, pre-scientific criteria for choosing between equivalent theories. “If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don’t listen to their words, fix your attention on their deeds." For some of them it may be social fashion, for others it may be religion, for Einstein himself it was considerations of mathematical beauty and simplicity. Any of these can be fine, you just need to be honest with yourself and others about what you’re doing. The danger is when scientists keep their metaphysics to themselves, or, worse, pretend that they have no metaphysics at all and are solely guided by the evidence, because it’s then that they run the risk of being driven by passing scientific fashions and political fads rather than by reasoned and universal principles.

I was really into math and science as a kid, and that meant that everybody was always talking to me about Einstein. I’m older than many of my readers, and so you’ll just have to trust me that way back in the *twentieth century*, Einstein was culturally omnipresent in a way that he isn’t now. He was the avatar, the representation of “mathy, sciencey stuff,” with goofy hair and insipid out of context quotations, the whole works. Think of the cultural role that Neil deGrasse Tyson played in the 2010s — that’s kind of the niche Einstein was filling back before Neil deGrasse Tyson existed. Nonconsensually, mind you; Einstein was long dead, but they were still sticking his face on posters like the one above.

In addition to being into math and science, I was also a pretty worldly and cynical kid, so naturally I assumed that this guy that the entire world was foisting down my throat was a total phony. That isn’t a bad assumption: for instance, the kids these days are *absolutely correct* that Neil deGrasse Tyson is a giant phony. So I thought Einstein was too, or that at the very least he was seriously overrated. His status as “ultimate science man” meme among the normies seemed to be conclusive evidence that his true scientific stature couldn’t be all that great. I continued thinking this way for an embarrassingly long time. Even after learning about Einstein’s “miracle year,” even after drinking from the firehose of modern physics, I still thought of him as a pretty good physicist in an era with a lot of pretty good physicists.

It was reading Einstein’s philosophical and autobiographical writings that finally shook me out of this. Yes, he had many cringe and redditpilled views as a young man, and even kept a few of them as an old man, but are any of us truly without cringe? His non-scientific writings, both public speeches and private letters, are also full of astonishingly clear and incisive examples of thinking. You read any of them and it’s immediately clear that this man was very clever. But more impressive than that is his sheer intellectual forcefulness, brashness, and charisma. It’s immediately clear that this guy was a force of nature, totally fearless, and possessed of a well-deserved arrogance.

Maybe it was that same arrogance that enabled him to march to the beat of his own drum? The thing I finally learned, decades after seeing it, was that that stupid Apple ad was actually correct despite itself. Einstein came by even his dumbest opinions honestly, after careful and deliberate thought. The man had zero fear about rejecting what “all the smartest people” believed about science, the logical positivism of Mach, and embracing instead a most retrograde sort of Platonism. Let him be an inspiration to all of us quacks and eccentrics. It’s a dangerous game to play, but it turns out that if you’re as smart as Einstein you can get away with it.

Why do we tell people this? Is it supposed to somehow encourage them or make them feel better? If you think about it, shouldn’t it kind of do the *opposite? *If you need encouragement, read this instead.

Like Charles Maurice de Talleyrand-Périgord, or, for a much lamer example, Isaiah Berlin.

Minkowski was the guy who showed that if you consider the universe to be a four-dimensional manifold with an unusual metric, then special relativity is just natural kinematics.

Conversely, if you want the ball and the van to take off with the *same* acceleration, you need to shove the van a lot harder — exactly “the ratio of their masses”-times harder.

Van Dongen’s explanation of *how* Einstein made this huge mistake is also super-interesting. Somehow Einstein became convinced that, in the case of a gravitational field created by a static mass, the field equations should produce a spacetime metric in which only the time-time diagonal component varies with spatial position, and all other components of the tensor are equivalent to their analogues in flat Minkowski space. This metric clearly reverts to the Poisson equation in the classical limit, but it’s not the only thing that does! Unfortunately it cannot possibly be a solution to the linearized field equations derived from the Ricci tensor plus considerations of energy-momentum conservation, since these would in general allow the other diagonal components to deviate from their values in flat space.

“Outline of a general theory of relativity and of a theory of gravitation”

Intriguingly, this mismatch doesn't seem to have bothered Einstein very much, since he continued to publicly express confidence in the theory for many months after discovering that it did not match the observational data. Indeed, in a 1914 letter to Besso we can see the first glimmerings of his later blasé attitude towards empirical confirmation:

Now I am fully satisfied, and I do not doubt any more the correctness of the whole system, may the observation of the eclipse succeed or not. The sense of the thing is too evident.

...

For the expert, this thing is not particularly important, because the main significance of the theory does not lie in the verification of little effects, but rather in the great simplification of the theoretical basis of physics as a whole.

Einstein was still publicly calling himself a disciple of Mach at this point, which gives his actions and this letter something of the flavor of heresy.

Anti-inductivism isn’t the only way Einstein was now opposed to Mach. We’ve seen a few times now how the mature Einstein was rather breezily unconcerned even when experimental data *directly contradicted* his theories.

One of these days I’m going to review Paul Feyerabend’s *Against Method*, but a key point he makes is that scientists stubbornly maintaining a theory in the face of empirical failure is very common, and moreover that it’s *good, actually*. A young theory might have some vital new insight, but get a few of the details wrong, such that it does a worse job at predicting the actual evidence. It’s vital for the progress of science as a whole that proponents of these theories be willing to bullheadedly ignore evidence and keep charging ahead, until later more accurate measurements bear it out or the theory successfully adapts.

What makes Einstein special then is not that he ignored experimental evidence when it was useful to do so, but that he *bragged* about it, as in this conversation recounted by Ilse Rosenthal-Schneider:

When I was giving expression to my joy that the results coincided with his calculations, he said quite unmoved, “But I knew that the theory is correct”; and when I asked, what if there had been no confirmation of his prediction, he countered: “Then I would have been sorry for the dear Lord – the theory

iscorrect.”

Remember “tweak theories are weak theories”!

"Mach is one of those guys who was incredibly famous and impressive in his day, but is now totally forgotten.² His jobs included physicist, philosopher, psychologist and social reformer, and he made a splash at all of them. He was also a radical empiricist who believed that the only things worth talking about were the things we can see, touch, or otherwise measure."

In 2018, I met Rainer "Rai" Weiss. It was a few months after he got the Nobel prize for LIGO--at least being the face attached to it. The husband of the librarian at my old high school in New Orleans had worked with Rai in the past and when he saw the accolade, he invited him to speak at the graduation. I attended it to hear Rai and I threw a dinner for him afterward, so I got to spend quality time asking him questions and generally shooting the bull with him. Great guy.

One of his main points was that Einstein had predicted the existence of gravitational waves, but he also predicted that, because they are so almost incomprehensibly small, they'd never be detected. LIGO proved the first to be correct--they're real, but the second to be wrong--LIGO found them. In fact, they pick up about fair number of them. Tens to hundreds of solar masses get turned into GW energy when black holes collide with one another and when black holes collide with neutron stars. That's an enormous amount of energy. The effect on the LIGO is a shrink/expansion of the kilometer-long interferometer arms of ~ 1/2000th the diameter of a proton. We're talking one part in about 10^24. That's a 1 followed by 24 zeroes. Not a surprise the Albert predicted it would never be measurable, but he hadn't anticipated engineering 100 years after the prediction.

Back at the dinner table...I'm sitting across from Rai, and next to the principal's wife, who asks animatedly about things like alternate universes. Rai pleasantly says that he thinks that physicists ought not to delve into unmeasurable fantasy things, like alternate universes. I ask him if he remembers pointing out that Einstein had predicted that GWs wouldn't be measurable either....

It was a light moment.

edited May 28An entertaining/enlightening read, as always! I have a question though:

> You might object, “if two theories are indistinguishable by observation and experiment, then they are equally valid and it doesn’t matter which one we pick.” But come on, while some philosophers might say that, nobody actually believes it.

… does nobody believe this? The strong form even seems obvious, if you have two theories which agree on every single prediction they make, even if they’re superficially different in some way, isn’t it the most natural conclusion that these are in fact the same theory, seen from different perspectives? It’s like a surjective mapping defining an equivalence clas, A->C, B->C => A~B.