A veteran of the Great War, Friedmann was a mournful man whose appearance—he had a drooping mustache, small round glasses, and an expression that seemed to say he expected things to go wrong—matched his depressive nature. Late in 1914, a few months after the war had started, Friedmann wrote to his favorite professor, Vladimir Steklov, at St. Petersburg University, “My life is fairly even, except such accidents as the explosion of an Austrian bomb within half a foot, and falling down on my face and head. But one gets used to all this.” Friedmann had decided to train as a pilot, which, in an atypical burst of optimism, he was doing because he had been assured “it is no longer dangerous.” Steklov wrote back that this was an exceptionally bad idea.
There’s a gap in the existing correspondence, but soon Friedmann was thanking the professor’s wife for the warm clothing she’d sent him, which he found exceptionally useful, given his regular flights high in the frozen winter air. The professor’s counsel had been ignored. He also thanked Steklov for sending him some interesting differential equations to look at, although he apologized for his lack of rigor in the solutions he quickly sent back, noting that it was hard to carry out proper investigations in his circumstances. He did, however, describe to Steklov the calculations he came up with to find the best release positions for the bombs he ended up dropping on the vast enemy fortress at Przemy´sl with an accuracy that impressed, if also disturbed, its Austrian and German occupants.
Friedmann noted, too, that he was being ordered up for dogfights against the German air fleet, which, he said, was part of an army “with excellent organization and equipment,” in contrast to “the lack of either in ours.” Once, a German plane unleashed its new fast-firing machine guns at Friedmann. His only defense was an elderly carbine, which had to be lifted up and held at arm’s length before, with a mighty bang, it would release a single bullet. (“The distance between our airplanes being extremely small . . . it gives you a terrible feeling,” he wrote.) When his missions were done, he received the St. George Cross for bravery.
Surviving the war, as well as the revolution, counterrevolution, and counter-counterrevolution in Russia—not to mention poverty, lack of food and fuel, and epidemics—he came across Einstein’s papers around 1920. By then, Friedmann was teaching at the Institute of Railway Engineering, as well as part time at the Geophysical Observatory in the city that had recently been St. Petersburg and now was Petrograd. Very quickly he saw what he was convinced was a flaw in the relativity papers. But how could he, in desolate Russia, convince the great German professor of what he suspected?
Back in 1917, when Einstein realized that his G=T equation might predict that the universe was changing size, he had inserted the lambda term (Λ). What Friedmann found in 1922 was that Einstein’s original equation—the raw G=T, with nothing added—contained thousands, indeed millions, of scenarios for intriguing universes.
He began to explore them.
FROM EINSTEIN’S ORIGINAL G=T equation, Friedmann came up with a startling array of possibilities for how space and the “things” in it might change over time. In some of the scenarios he unveiled, a universe would steadily grow, like a sphere that inflated forever. Yet there were also scenarios—all contained in the mathematics of the original equation—in which the universe only pumped up in volume to a finite size before it then started collapsing, as if its substance was hissing out through some escape valve. Everything that mankind or other intelligent beings in such a universe had created would be annihilated.
There were yet other scenarios, in which a universe’s crash wasn’t final after all. Instead, after collapsing down to a single point, it would then begin to rebound back out. Everything that civilizations had built before would be utterly crushed, but the raw material would still be there to start again. Friedmann did some rough calculations: these “pulsations,” he found, might recur over periods of about ten billion years.
This wasn’t the first time humans had imagined such a sequence of death and rebirth. As Friedmann wrote, it “brings to mind what Hindu mythology has to say about cycles of existence,” a reference to the belief that the universe has already been created, destroyed, and re-created many times. He added that, of course, his solutions could be seen only as conjecture and were not yet supported by the known facts of astronomical experience.
With his friends’ support, he wrote up his findings in a brief paper, and after the best linguist in his group had improved his German—which was about on a par with Einstein’s French—he daringly sent the paper to the most prestigious physics journal in the world, Zeitschrift für Physik. The journal quickly accepted it, in 1922. He assumed that Einstein would love the paper, for he was showing that the original 1915 equation—the simple G=T, without the random brake of the lambda—contained these extraordinary results. And if he did, Einstein would finally be able to get rid of the new term.
To the shock of Friedmann and his friends, when they managed to get hold of the next issues of the Zeitschrift für Physik later that year—not easy in postrevolutionary Russia—they saw that Einstein had sent in a rebuttal! The Russian’s findings were unacceptable, Einstein wrote. Nor was this mere bias. Einstein had gone through Friedmann’s calculations and found a flaw. “The results . . . contained in [Friedmann’s] work,” Einstein’s published letter stated, “appear to me suspicious. In reality it turns out that the solution given in it does not satisfy [my] equations.”
Friedmann was distraught. A comment like that was death to any hopes he had for further academic advancement. How could the great man do this to him? It would be too presumptuous to write a letter of complaint to the journal. Instead, Friedmann and his friends decided it would be more tactful to write to Einstein at his Berlin address. And that, again no doubt getting help for his mediocre German, Friedmann laboriously did.
Friedmann’s letter to Einstein was polite but clear: “Allow me to present to you the calculations I have made . . . Should you find the calculations presented in my letter correct, please be so kind as to inform the editors of the Zeitschrift für Physik about it. [P]erhaps in this case you will publish a correction to your statement.”
There was no response—but not for the reason Friedmann would have feared.
Earlier in 1922, when the Jewish foreign minister of Germany, Walter Rathenau, was assassinated—to the glee of conservatives across the country—Einstein realized that serious danger was beginning for prominent Jews. Already a Working Party of German Scientists for the Preservation of a Pure Science had been formed to fight Einstein’s ideas. Their inaugural meeting had been held at the Philharmonic Hall in Berlin, with swastikas displayed in the hallway and anti-Semitic brochures on sale in the lobby. A few of the Einstein haters had some academic affiliation, but most were poorly educated. “Science, once our greatest pride, is today being taught by Hebrews!” the housepainter and failed art student Adolf Hitler complained.
Alexander Friedmann, early 1920s. “Allow me to present to you the calculations I have made,” he wrote to Einstein, not knowing where his overture would lead.
To give the situation time to cool, Einstein took up a long-standing invitation to undertake a lengthy tour by steamship. By the time Friedmann’s letter arrived, he had already left Marseille for Japan, where he wrote to his sons, “Of all the people I have met, I like the Japanese most . . . They are modest, intelligent, considerate, and have a feel for art.” Friedmann’s letter wasn’t forwarded to him. Yet even when Einstein got back to Berlin the next year, he didn’t respond.
Einstein’s failure to reply was partly attributable to the vast correspondence he had begun to receive after being awarded the Nobel Prize. The letters arrived in volumes that made his previous nightmare of the roaring postman seem tame. But something else was going on—something that only the mix of fame and pride could explain.
When Einstein had first inserted the lambda term into his G=T equation back in 1917, he believed he was doing something wrong. The Creator could not have first made the
universe to be close to absolute simplicity—to have two mathematical terms, G and T, so simply explain everything about the overall structure of the universe—and then reveal it to be so different that only the addition of an arbitrary constant could make the laws of creation work.
But despite his forebodings, Einstein had reworked his equation, and now he was stuck. His reputation was at stake, for now all physicists knew his equation in that modified form. His pride was in play, too. He had done this to himself, after great soul-searching. He couldn’t easily admit that he’d been weak—and wrong.
That’s why he had so quickly skimmed Friedmann’s paper hunting for some flaw. Then once he’d found a flaw—or thought he’d found one—he’d shown no interest in returning to the topic.
In May 1923, however, one of Friedmann’s colleagues, Yuri Krutkov, managed to track Einstein down in the Netherlands, through a colleague of Einstein’s who had once taught in Russia. Krutkov confronted him, politely but insistently, and proudly recounted to his sister what happened next. On Monday, May 7, he said, he was reading Friedmann’s paper in the Zeitschrift für Physik along with Einstein. And then, on May 18, “at 5 o’clock . . . I defeated Einstein in the argument about Friedmann. Petrograd’s honor is saved!”
Einstein had the decency to look back through the Russian’s work and admit he’d overreacted: Friedmann hadn’t, in fact, made any mathematical mistakes. He wrote to the journal editors to set matters right: “In my previous note I criticized [Friedmann’s work ‘On the Curvature of Space’]. However, my criticism . . . was based on an error in my calculations.”
The retraction was impressive, if curt. Nonetheless, back in Russia Friedmann knew he had to get Einstein properly on his side if his new scenarios were ever to be taken seriously. But how? The only way would be to give Einstein more proof. There wasn’t any astronomical evidence to prove his assertions yet, but perhaps there was another way.
AS FRIEDMANN RACKED his brain to think of how to convince Einstein that the addition of the lambda had been unnecessary, the Russian used a method of imaginative problem solving that would have looked familiar to his German colleague. Specifically, he went back to the way that tiny beings who lived on a flat surface—our Flatland creatures again—couldn’t step back and see their whole world. But they could do various calculations on that world, or take journeys there, which could give them the information they needed.
Friedmann imagined what would happen if one of the research centers in this flat world sent out a traveler to check what their universe was really like. He imagined such a traveler as being like a little postage stamp. If the traveler kept to a straight line and proceeded in one direction, Friedmann wrote, it would be able to look at the landscape it passed. Clearly that would alter as the traveler moved along. He would see other landscapes, other cities. But then his surroundings would begin to look more and more familiar, and finally he would find himself back at his hometown—but arriving from the side opposite to the one he had started from!
Friedmann noted: “On returning to the starting point, the traveler would find, through observations, that the point which he reached coincided completely with the point from which he had started.” That’s how he would be able to prove that the sphere—the “universe”—he lived on was actually finite. If, however, the traveler never found the cities becoming familiar again, he would know that his world didn’t bend back on itself. This would be proof that his universe was not a sphere.
Just as with Flatland, and with our imagined Finnish skaters, Friedmann was suggesting an analogy for our own, much larger, three-dimensional universe. If we could send out emissaries to make measurements of the universe—using advanced exploratory vessels sometime in the future or just telescopes today—we could use those measurements to work out what the underlying shape of the universe was like. That would help determine which of the scenarios Friedmann had found locked within Einstein’s simple G=T equation described our world and which did not. Although we couldn’t actually make the lengthy journey Friedmann imagined, if our universe was truly flat, then enormous rectangles measured out in the solar system would have four right angles inside. If it were curved like a sphere—in a way we couldn’t see with our naked eye, of course, or even imagine with our limited brains—then the giant rectangles that were measured out wouldn’t be flat like that, but would show inner angles that splayed ever so slightly wider than 90 degrees. As the curvature went up or down, so these angles would change as well.
Friedmann knew himself to be physically feeble, and surviving in early 1920s Russia had done little to overturn his habitual depression. But yet, he had somehow survived bombing raids over Austrian fortresses and dogfights with the German air force. He had mental strength, and he also believed that he and Einstein shared a vision. The German physicist had spoken of small-scale local measurements to understand large spaces, after all. Perhaps if Friedmann managed to traverse the continent of Europe and see the great man in person, they could—together—go further.
And so, in the summer of 1923, Friedmann decided that he would imitate the miniature traveler he had imagined and journey alone to Berlin. If he met Professor Einstein in person, perhaps he could get Einstein to trust the original equation from 1915.
The year 1923 wasn’t quite as bad a time to travel as when Freundlich had led his astronomical expedition to the Crimea just as World War I broke out, but it wasn’t much better. Inflation had already begun in Weimar Germany. “There is a wild currency orgy,” Friedmann wrote home. In the course of less than a week, a dollar could jump from being worth one million marks to being worth four million. There were poverty and food shortages, albeit not the level of shortages that Russians were living with. Even the German landscape seemed to show how far Friedmann was from home, and he was especially disoriented to see how neatly arranged German forests were, with all the trees that made them up seeming to have been planted in straight lines. There’s a photograph of Friedmann from this time: the hangdog expression and drooping mustache as always, yet sporting his best double-breasted jacket and an odd beretlike cap balanced on his head; holding a sprawling mess of papers under his left arm; awkwardly gripping his shirt with his right hand, Napoleon-style, as if he doesn’t quite know what to do with it; trying to smile.
He actually made it to Berlin, and even to Einstein’s street . . . but then: “August 19th: My trip is not going well—Einstein . . . has left Berlin on vacation. I don’t think I will be able to see him.” Two weeks later, he wrote his friends again, saying that he still hoped to see Einstein. But it was not to be. At least, though, near the end of his trip to Germany, just before returning to Russia, Friedmann did visit another man who understood the disappointments life can bring. For on September 13, 1923, Friedmann made his way to the Potsdam Observatory, where he met Freundlich. The men got on, sharing their thoughts about how the universe was structured. “Everybody was much impressed by my struggle with Einstein, and my eventual victory. It is pleasant for me.”
Einstein hadn’t been far away, probably at his country home outside Berlin. But even if Freundlich had told him that Friedmann was around, he probably wouldn’t have made the trip back to the city. He still had too much invested in the “fix” he’d made in 1917. He’d now almost convinced himself, in fact. After all, how could any Creator—or even just the rules of physics—set up a universe that would so wildly break from equilibrium? For if Friedmann was right and Einstein’s original equation did show that the universe was expanding, eventually there would just be a vast aloneness of burnt-out stars and lifeless planets steadily moving farther and farther apart. That was too awful to imagine: all mankind’s strivings ending up so lost. On the other hand, if one of Friedmann’s other scenarios held and Einstein’s original equation showed our universe was collapsing, then sometime in the future, the night sky would shine with a terrifying brightness as all the stars above came tumbling toward us. That also was too unpleasant to believe.
In the o
riginal typed draft of the retraction he’d prepared for the Zeitschrift für Physik, Einstein had written that despite Friedmann’s mathematical correctness, the vast range of solutions described were ones “to which a physical significance can hardly be ascribed.” He then thought better of that phrase and scratched it out. But he wanted Friedmann to be wrong.
The confusion was exhausting for Einstein. It would be wonderful to find clear evidence that could release him once and for all and determine if the warpings in space that his original equation predicted would do what Friedmann proclaimed or not. But that would require measuring locations in the most distant reaches of space and seeing if the stars there were speeding away, or standing still, or falling toward us. Measuring objects so far away seemed impossible. Stars might be enormous furnaces, but at their great distances they appear on earth as just tiny pinpricks of light, without observable movement of any kind.
If only someone could find a way to identify what the stars, so remote from the earth, were really doing.
INTERLUDE 3
Candles in the Sky
In his journal, the Italian explorer Antonio Pigafetta recalled the moment he decided to strike out for the unknown:
“Finding myself in Spain in the year of the Nativity of our Lord, one thousand five hundred and nineteen, at the court of the most serene king . . . I deliberated . . . to go and see with my eyes a part of the very great and awful things of the ocean.”
Pigafetta’s decision led to his sailing with Ferdinand Magellan in 1519, in a flotilla of ships intended to reach the Spice Islands of East Asia by an unprecedented route: heading west across the Atlantic, then finding a way around or through the American continent into a new ocean that was imagined to be there. If all went well, they would circle the earth—the first time any humans had done so.
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