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When Einstein Tilted at Windmills

The young physicist’s quest to prove the theories of Ernst Mach.


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Illustration by Jasu Hu

When they met, Einstein wasn’t Einstein yet. He was just Albert Einstein, a kid, about 17, with a dark cloud of teenage angst and a violin. Michele Besso was older, 23, but a kindred spirit. Growing up in Trieste, Italy he had shown an impressive knack for mathematics, but he was kicked out of high school for insubordination and had to go live with his uncle in Rome. Einstein could relate. At the Swiss Polytechnic, where he was now a student, his professors resented his intellectual arrogance, and had begun locking him out of the library out of spite.

Their first encounter was on a Saturday night in Zurich, 1896. They were at Selina Caprotti’s house by the lake for one of her music parties. Einstein was handsome—dark hair, moustache, soulful brown eyes. Besso was short with narrow, pointed features and a thick pile of coarse black hair on his head and chin. Einstein had a look of cool detachment. Besso had the look of a nervous mystic. As they chatted, Einstein learned that Besso worked at an electrical machinery factory; Besso learned that Einstein was studying physics. Perhaps they recognized something in each other then: They both wanted to get to the truth of things.

Besso would go on to become a sidekick, of sorts, to Einstein—a sounding board, as Einstein put it, “the best in Europe,” asking the right questions that would inspire Einstein to find the right answers. At times, though, he would seem to be something more—a collaborator, perhaps, making suggestions, working through calculations.

At other times he’d be the perfect fool—a schlemiel, Einstein called him. Like the time Besso was sent on a job to inspect some newly installed power lines on the outskirts of Milan but missed his train and then forgot to go the following day. On the third day he finally made it to his destination, but by that time he’d completely forgotten what he was supposed to be doing there in the first place. He sent a postcard to his boss: “Instructions should be wired.”

If Besso never seemed to know quite what he was doing, it wasn’t for a lack of smarts. “The great strength of Besso resides in his intelligence,” Einstein would write, “which is out of the ordinary, and in his endless devotion to both his moral and professional obligations; his weakness is his truly insufficient spirit of decision. This explains why his successes in life do not match up with his brilliant aptitudes and with his extraordinary scientific and technical knowledge.”

Still other times, Besso would play the role of Einstein’s conscience—urging him to work things out with his future wife, Mileva, or to be a better father to his sons. Besso took care of those sons on Einstein’s behalf when Mileva was sick. “Nobody else is so close to me, nobody knows me so well,” Einstein would write in 1918.

But there was something uncanny about Besso. Over the coming years, he would always show up at exactly the right moment, the perfect deus ex machina, handing Einstein books, innocently offering suggestions, prodding him, goading him, nudging him onto the right path, as if he had a plan. “I … watch my friend Einstein struggle with the great Unknown,” he would write, “the work and torment of a giant, of which I am the witness—a pygmy witness—but a pygmy witness endowed with clairvoyance.”

That Saturday night, though, all of that lay in the future. For now, they became fast friends—best friends, really. They talked for hours on end. For his first act of camaraderie, Besso handed Einstein two books, insisting that he read them. They were the works of Ernst Mach, the final actor in this three-man play.


Perhaps you’ve heard of Ernst Mach. Mach 1, Mach 2, Mach 3, that Mach. His name is a unit of speed, and—despite his beard—a brand of razors. He was a physicist, a physiologist, a philosopher. A little bit of everything, really. You could find the young Mach in the Austrian countryside carefully observing nature—staring at a leaf or a shadow or a cloud with the utmost concentration and scrutiny, then scrutinizing his scrutinizing, noting his every sensory glitch and glimmer, building a taxonomy of tricks that our eyes can play. He collected bugs and butterflies. He tested the reactions of various materials—in trying to see whether camphor would ignite, he burned off his eyelashes and eyebrows. But it was when he was 15 years old that a single moment changed everything.

“On a bright summer day in the open air, the world with my ego suddenly appeared to me as one coherent mass of sensations,” he later wrote. He felt, in that moment, there was no reality sitting “out there,” independent of his sensations, and likewise that there was no self sitting “in here,” independent of its sensations. He grew certain that there could be no real difference between mind and matter, between perceiving subject and perceived object. “This moment was decisive for my whole view,” he wrote.

It must have been an unsettling feeling for Einstein, proving the very thing he had set out to disprove.

From that day forward, he vehemently rejected any form of dualism: the idea that the external world was made up of substantial material objects—things—while the mind was made of something else, so that the world we experience in consciousness is a mere copy of an actual world that lies forever hidden from us. Instead he grew convinced that mind and matter were made of the same basic ingredient. It couldn’t be a physical ingredient, he argued, because how would bare matter ever give rise to subjective experience? But it couldn’t be a mental ingredient either, he said, because he was certain that the self was equally an illusion. The only way to unite mind and matter, he decided, was to presume that they were made not of objective atoms, and not of subjective qualia, but of some neutral thing, an “element,” he called it, which in one configuration would behave as material substance and in another as immaterial mentation, though in itself it would be neither and nothing.

“There is no rift between the psychical and the physical, no inside and outside, no “sensation” to which an external “thing,” different from sensation, corresponds,” he wrote. “There is but one kind of elements, out of which this supposed inside and outside are formed—elements which are themselves inside or outside, according to the aspect in which, for the time being, they are viewed.” These elements “form the real, immediate, and ultimate foundation.”

Mach’s view—neutral monism, it would later be called—required that every single aspect of reality, from physical objects to subjective sensations, be purely relational, so that whether something was “mind” or “matter” was determined solely by its relations with other elements and not by anything inherent to itself. It was a radical idea, but it seemed plausible. After all, Mach said, science is based on measurement, but “the concept of measurement is a concept of relation.” What we call length or weight, for instance, is really the relation between an object and a ruler, or an object and a scale.

It dawned on Mach, then, that if we could rewrite science solely in terms of what can measured, then the world could be rendered entirely relational—entirely relative—and the mind and universe could be unified at last. But that was going to require a new kind of physics.


By 1904, Don Quixote had become one of Einstein’s favorite books.

Two years earlier, an unemployed Einstein had put an ad in the newspaper offering physics tutoring for three francs an hour, and a philosophy student named Maurice Solovine had shown up at his door. They started talking about physics and philosophy and didn’t stop; the whole tutoring thing never even came up. Soon Conrad Habicht, a mathematics student, joined the conversation, and the three young bohemians formed something of a book club for highbrowed degenerates. They read works of philosophy and literature and discussed them, sometimes until one in the morning, smoking, eating cheap food, getting rowdy and waking the neighbors. They met several nights a week. In mockery of stuffy academia, they dubbed themselves the Olympia Academy.

Besso was in Trieste working as an engineering consultant, but he came when he could, and as Einstein’s closest friend, he was made an honorary member of the Academy. Under Besso’s influence, the Olympians read and discussed Mach. Eventually Einstein landed a job at the Patent Office in Bern, and in 1904 he got Besso a job in the same office, so they could work side by side. In the evenings, the Academy read Don Quixote. It struck a chord with Einstein—later, when his sister Maja lay dying, he would read it to her. As for the Olympia boys, who can say whether they noticed it then: how Besso had become the Sancho Panza to Einstein’s Quixote. When Solovine and Habicht left, it was just Einstein and Besso, walking home together from the patent office, discussing the nature of space and time and, as always, Mach.

Pennies for Your Thoughts: In general relativity, the spacetime of each local observer seems flat, like the surface of a penny. And, in the absence of gravity, all of spacetime is indeed flatPhoto by Hannah K. Lee.

Mach’s plan to unite matter and mind required that every last bit of world be rendered relative, with nothing left over. But there was one stubborn obstacle standing in the way: According to physics, all motion was defined relative to absolute space, but absolute space wasn’t defined relative to anything. It just existed, self-defined, like the basement level of reality—it wouldn’t budge. Mach knew of this obstacle, and it rankled. He criticized Newton’s “conceptual monstrosity of absolute space”—the idea of space as a thing unto itself. But how to get around it?

For years it had been bugging Einstein that all attempts on an observer’s part to determine whether or not he was at rest relative to absolute space were doomed to fail. For every experiment he could think of, nature seemed to have a clever trick up its sleeve to hide any evidence of absolute motion. It was so downright conspiratorial that one might suspect, as Einstein did, that absolute space simply didn’t exist.

Following Mach’s lead, Einstein wanted to assert that motion was not defined by reference to absolute space, but only relative to other motion. Unfortunately, the laws of physics seemed to suggest otherwise. The laws of electromagnetism, in particular, insisted that light had to travel at 186,000 miles per second regardless of the observer’s frame of reference. But if all motion was relative, the light’s motion would have to be relative too—traveling 186,000 miles per second in one reference frame and some other speed in another, in blatant violation of electromagnetic law.

So Einstein went to see Besso. “Today I come here to battle against that problem with you,” he announced when he arrived.

They discussed the situation from every angle. Einstein was ready to give up, but they hammered away.

The next day, Einstein returned. “Thank you,” he said. “I’ve completely solved the problem.” Within five weeks, his theory of special relativity was complete.

What magic words had Besso uttered in that fateful conversation? It seems he reminded Einstein of Mach’s central idea: a measurement is always a relation.

Einstein and Besso discussed this—what two quantities we compare in order to measure time. “All our judgments in which time plays a part are always judgments of simultaneous events,” Einstein realized. “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.”

But how does one know that two events are simultaneous? Perhaps you’re standing still and you see two distant lights flash at precisely the same moment. They’re simultaneous. But what if you had been moving? If you happened to be moving in the direction of flash A and away from flash B, you’d see A happen first, because B’s light would take ever so slightly longer to reach you.

Simultaneity is not absolute. There’s no single “now” in which all observers live. Time is relative. Space, too.

It all dawned on Einstein then: It was possible for all observers to see light moving at exactly 186,000 miles per second regardless of their own state of motion. The light’s speed is a measure of how much distance it covers in a given amount of time. But time changes depending on your state of motion. So even if you’re moving relative to the light, time itself will slow down precisely long enough for you to measure light’s speed at the very one required by Maxwell’s equations.

Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” introduced the world to the theory of relativity, in which time and space can slow and stretch to account for an observer’s relative motions. It included no references whatsoever, but it ended with this final paragraph: “In conclusion I wish to say that in working at the problem here dealt with I have had the loyal assistance of my friend and colleague M. Besso, and that I am indebted to him for several valuable suggestions.”


Einstein proudly sent his work to Mach, and seemed almost giddy when Mach responded with his approval. “Your friendly letter gave me enormous pleasure,” Einstein replied. “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.”

Einstein had a long way to go, however, to see Mach’s vision through. The problem was that special relativity only relativized motion for observers moving at a constant speed. The question of accelerated observers—those who were changing speed or rotating—was far trickier. Within special relativity, there was no way to blame the force that comes with acceleration on relative motion. Absolute space lingered.

There’s no single “now” in which all observers live. Time is relative. Space, too.

In 1907, Einstein made a breakthrough. It was the happiest thought of his life, he would later say: In small regions of space, an observer would be unable to tell whether he was accelerating or at rest in a gravitational field. This suggested that it might be possible to do away with the absolute nature of acceleration—and with it absolute space—once and for all. Gravity, it seemed, was the secret ingredient that made all motion relative, just as Mach had wanted. And that gave a whole new meaning to the very nature of gravity: The path of an accelerated observer through spacetime traces a curve, so if acceleration was equivalent to gravity, then gravity was the curvature of spacetime. It would be some time before Einstein brought his general theory of relativity to fruition, but for now, he knew he was on the right track.

Excited, Einstein wrote a letter to Mach informing him of his progress and the publication of his newest paper. A new theory of gravity was underway, he said, and as soon as he could prove it correct, “your inspired investigations into the foundations of mechanics … will receive a splendid confirmation.” In other words: I’ve done what you wanted. He published his theory of general relativity in 1915; the next year, Mach died.

Einstein wrote a long and moving obituary, glowing with praise for Mach’s scientific vision, with its central point, as Einstein wrote, that “physics and psychology are to be distinguished from each other not by the objects they study but only by the manner of ordering and relating them.” He argued that Mach himself was close to coming up with the theory of relativity, and wrote, with palpable admiration and innocence, that Mach “helped me a lot, both directly and indirectly.”

That, however, was the apogee of the kinship between Einstein and Mach’s philosophy. Einstein would eventually disavow the pure relativism of his mentor, and even to split from his Sancho. The rift begins with a most unlikely event: words from beyond the grave.


In 1921, Mach’s book The Principles of Physical Optics was published posthumously, and contained a preface written by the author around 1913, shortly after Einstein had sent him the early paper on general relativity.

“I am compelled in what may be my last opportunity, to cancel my views of the relativity theory,” Mach wrote. “I gather from the publications which have reached me, and especially from my correspondence, that I am gradually becoming regarded as the forerunner of relativity … I must as assuredly disclaim to be a forerunner of the relativists …”

Mach had likely seen what Einstein would only later come to terms with—that the so-called general theory of relativity did not live up to its name. General relativity was an unprecedented intellectual feat—but it didn’t make everything relative, as Mach had dreamed. In the final version of the theory, the equivalence between acceleration and gravitation, which had seemed to make all motion relative, turned out to hold only for infinitesimally small regions of space. Patching together local regions into one big universe produced misalignments at their edges, like flat tiles on a round globe. The misalignments revealed the curvature of spacetime—a global geometry that couldn’t be transformed away by a mere change in perspective. Each local region—a self-consistent, relative world—turned out to be the tiny tip of an enormous, four-dimensional iceberg, forever hidden from sight and decidedly not relative.

It must have been an unsettling feeling for Einstein—watching his theory gather steam and speed away from him, proving the very thing he had set out to disprove. The problem was that, according to the theory, spacetime geometry was not fully determined by the distribution of matter in the universe, so that even if you removed everything observable, some extra ingredient still remained—spacetime itself, dynamic yet absolute. It created an unbridgeable divide between the physical world and the mind, inviting, in its realist stance, a whiff of pure belief, even mysticism—the belief in a four-dimensional substratum, the paper on which reality is drawn, though the paper itself is invisible.

Einstein continued to push Mach’s view for several years after publishing general relativity in 1915, living in total denial of the fact that his own theory went against it. He tried everything under the sun to mold his theory into the shape of Mach’s philosophy—making the universe finite but unbounded, adding a cosmological constant—but it just wouldn’t fit. “The necessity to uphold [Mach’s principle] is by no means shared by all colleagues,” he said, “but I myself feel it is absolutely necessary to satisfy it.”

So when Einstein first read Mach’s preface, it must have stung. We can hear his hurt in a comment he made at a lecture in Paris in 1922, shortly after Mach’s preface was published. Mach was “un bon mecanicien,” Einstein said bitterly, but a “deplorable philosophe.” He would no longer claim that his theory was one of Machian relativism, and by 1931 he would abandon Mach’s views completely. “The belief in an external world independent of the perceiving subject is the basis of all natural science,” he wrote. When asked how he could believe in anything beyond our sensory experience, he replied: “I cannot prove my conception is right, but that is my religion.” And in 1954, a year before his death: “We ought not to speak about the Machian Principle anymore.”

What Mach had never known—couldn’t have known—was that his true devotee had never been Einstein. It was Besso.


Besso, that pygmy witness endowed with clairvoyance, saw exactly where Einstein’s departure from Mach would soon lead him astray: in the realm of quantum mechanics.

As Einstein came to grips with Mach’s rejection of relativity, the world of physics was rocked by quantum theory, a revolution Einstein had helped to spark but now refused to join. While he was making peace with an absolute spacetime—an absolute reality—quantum mechanics was rendering the world even more relative. The theory suggested that the outcomes of measurements could be defined only in relation to a given experiment: An electron might be a wave relative to one measuring apparatus and a particle relative to another, though in itself it was neither and nothing. In the words of Niels Bohr, the purpose of the theory was “to track down, so far as it is possible, relations between the manifold aspects of our experience”—relations and nothing more. In other words, quantum theory picked up Mach’s program right where Einstein left off, a point that both Bohr and Besso were quick to emphasize.

When Einstein, complaining about a colleague’s work, joked to Besso that, “He rides Mach’s poor horse to exhaustion,” Besso replied, “As to Mach’s little horse, we should not insult it; did it not make possible the infernal journey through the relativities? And who knows—in the case of the nasty quanta, it may also carry Don Quixote de la Einsta through it all!”

“I do not inveigh against Mach’s little horse,” Einstein responded, “but you know what I think about it. It cannot give birth to anything living.”

The truth was, Einstein’s belief in a hidden reality had lain dormant for years, ever since he was a little boy—4, maybe 5—and his father had come to his bedside and handed him a compass. Einstein had held it in his hand, and found himself trembling in awe. The way the needle quivered, tugged northward by some invisible force, overwhelmed him with the feeling that “something deeply hidden had to be behind things.” Now he glimpsed it again in the mathematics of general relativity. With Mach’s approval moot, the awe he’d felt as a boy returned to him. When Besso tried to steer him away—toward Mach, toward the quantum— Einstein reproached his faithful squire: “It appears that you do not take the four-dimensionality of reality seriously.”

The reinvention of Einstein as a young iconoclast who embraced Mach’s view and ran with it, determined to create a theory of pure relativity despite his natural realist leanings—was it actually Besso’s doing? Had the squire steered his master? In the short story “The Truth About Sancho Panza,” Franz Kafka suggests that this reversal is, in fact, the key to Cervantes’ tale. Don Quixote, he wrote, was Sancho Panza’s own creation, an alter ego invented to carry out some inner vision Panza himself was ill equipped to face. “I owe to you the scientific synthesis that without such a friendship one would never have acquired—at least, not without expending all one’s personal forces,” Besso wrote to Einstein—as if to say, thanks for working out that theory for me. But the synthesis was incomplete. Having guided Einstein to water, Besso appears to have failed to make him drink.

Besso never gave up on luring Einstein back to Machian relativity. But Don Quixote had abandoned the knighthood for good, leaving Sancho to fend off the windmills for himself. In Princeton, New Jersey, his hair now white and wild, Einstein sat at a cluttered desk and struggled with reality while physics marched on without him. In Geneva, Switzerland, in the University mathematics library, his wiry beard now blanched with time, Besso sat hunched over his own pile of books, and worked—quietly, mysteriously—alone.

Amanda Gefter is a physics writer and author of Trespassing on Einstein’s Lawn: A father, a daughter, the meaning of nothing and the beginning of everything. She lives in Cambridge, Massachusetts.

Additional Reading

Bernstein, J. Quantum Profiles Princeton University Press, Princeton, NJ (1990).

Blackmore, J.T., (Ed.) Ernst Mach—A Deeper Look: Documents and New Perspectives Springer Netherlands (1992).

Einstein, A. The Collected Papers of Albert Einstein Princeton University Press, available for open access at The Digital Einstein Papers: http://einsteinpapers.press.princeton.edu/papers

Einstein, A. “How I Created the Theory of Relativity”; 1922 lecture given at Kyoto University; transcribed by Ono, Y.A. and published in Physics Today 35, 45 (1982).

Holton, G. Mach, Einstein and the search for reality. Daedalus 97, 636-673 (1968).

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This post originally appeared on Nautilus and was published December 1, 2016. This article is republished here with permission.

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