The Hunt for Vulcan

by Thomas Levenson

  There is a strange magic to the term “the scientific method.” At a minimum, it asserts a particular kind of authority: here is a systematic approach, a set of rules, that when followed will reliably advance our understanding of the material world. Such knowledge, though, is always provisional, a seeming weakness that is the real strength of science: every idea, every generalization, every assumption is subject to question, to challenge, to refutation.

  That’s how the scientific method is usually taught. Every high school student confronts some version of Feynman’s description. The process of science rides down railroad tracks: you “Construct a Hypothesis” to “Test with an Experiment” (or an observation), and then you “Analyze Results” and “Draw Conclusions.” If the results fail to support the initial hypothesis, then it’s back to step one.

  Laid out like that, the scientific method can be seen as a kind of intellectual extruder. Set the dials with the right question, pour data into the funnel, and pluck knowledge from the other end. And, most important: when that outcome fails to match reality, then you go back to the beginning, work the dials into some new configuration, try again.

  This isn’t just cartoon stuff either, a caricature told to children who may never dive more deeply into science than a Coke-Mentos volcano. Even for those who penetrate into more and more advanced ideas and approaches, the same message gets dressed up in more formal language. Here’s a typical “Introduction to the Scientific Method” aimed at college students: “The scientific method requires that a hypothesis be ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests…”—pretty much exactly what sciencefair contestants are told. The explanation goes on, though, to echo Feynman’s point: “No matter how elegant a theory is, its predictions must agree with experimental results if we are to believe that it is a valid description of nature. In physics, as in every experimental science, ‘experiment is supreme.’ ”

  In other words: when a long-anticipated outcome fails to materialize, more than a single prediction lies in peril. If gravity waves don’t show up in ever more acute CMB measurements, then at some point the strand of inflation theory that requires them will be in trouble. Along those lines, once Vulcan refused to appear, decade after decade, what should have been done about that icon of the scientific revolution, Isaac Newton’s theory of gravity?

  Within the myth of the scientific method, there should have been no choice about the next move. “Experiment is supreme”…“Observation is the judge.” We hold this truth to be self-evident: the hard test of nature trumps even the most beloved, battletested, long-standing idea.

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  Does history behave like that? Do human beings?

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  No. Real life and cherished fables routinely diverge.

  After July 1878, almost all of the astronomical community abandoned the idea that a planet or planets of any appreciable size existed between the Sun and Mercury. But that broad consensus did not lead to any radical reassessment of Newtonian gravitation.

  Instead, a few researchers tried to salvage the core of the idea with ad hoc explanations for Mercury’s motion. The historian of science N. T. Roseveare has catalogued the struggle, dividing it into two main strands. Simon Newcomb followed his recalculation of Mercury’s orbit with a review of the “matter” alternatives—Vulcan-like explanations that depended on coming up with a source of mass that for some good reason remained undetected but could generate enough gravitational tug to produce the perihelion advance. He took Vulcan itself as clearly refuted, but he catalogued a number of more subtle suggestions: perhaps the sun was sufficiently oblate—fat around its middle—that such an unequal distribution of matter could solve the problem. Alas, the record of solar observation persuaded Newcomb that our star is pretty nearly spherical (as it is). Other proposals—matter rings, like those around Saturn, or enough of the dust that was known to exist near the sun—fell to a variety of other objections. After more than a decade of thinking about the problem, Newcomb came to his uncomfortably necessary conclusion: within the framework of the inverse square law of gravity, there was no plausible trove of matter near the sun that could account for the motions of Mercury.

  With that, if science as lived matched the stories scientists tell about it, Newtonian theory should have been for the chop. In the fairy-tale version of the search for knowledge, Newcomb’s verdict—that there was a persistent, unrepentant anomaly current theory could not explain—would compel researchers to question its status as “a valid description of nature.”

  In any myth there’s at least a hint of some deeper truth, and so, as matter-based ideas fell, Newton’s version of gravity did come under a bit of scrutiny. One astronomer suggested that Newton’s law might be only an approximation: gravity could vary by masses involved and inversely with the distance between them to a power of 2…plus just a tiny amount: .0000001574. That would bring Mercury’s motion into perfect agreement with the math, but there were several obvious objections. For one, it was such a messy move: why would the inverse exponent for gravity “choose” to be so close to a perfect integer, and yet refuse to settle on exactly two?

  To be sure, nature sometimes just is, in ways that can seem both arbitrary and unlovely. Even now, there are several numbers in fundamental theories of the large and small that are set by observation. In some cases they are just as odd—or weirder still—than an inverse 2.0000001574 power law. For example, the fine-structure constant, a number involved in describing the ways charged particles (like electrons) interact, is known by observation to be 7.2973525698 × 10-3. There is nothing in any theory that offers any explanation for why that number should take that particular value. It’s just the way the universe does that particular job. To Richard Feynman, this was cosmic bad taste: “All good theoretical physicists put this number up on their wall and worry about it….It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.”

  Even so, simplicity, elegance, and above all, consistency have proved to be pretty great ad hoc measures of theoretical insight, even if they give no guarantees. An inverse-not-quite-two law was ugly enough that very few researchers took it seriously. The idea finally went away in the 1890s when it was shown to account for Mercury’s motion, but not that of the earth’s moon.

  A few more attempts to tweak Newton followed. Some added another term to the classic inverse square law to better fit theory to nature, and others explored the idea that the speed of a body might change its gravitational attraction. None gained significant support from either physicists or astronomers, and they all would collapse under a variety of fatal flaws.

  By the turn of the twentieth century, most researchers had given up. There was still no explanation for Mercury’s behavior—but no one seemed to care. There was so much new to think about. X-rays and radioactivity had opened up the empire of the atom. Planck’s desperate creation of the quantum theory was about to transform the study of both energy and the fundamental nature of matter. The decades-in-the-making confirmation that the speed of light (in a vacuum) was truly constant was beginning to hint that extremes of speed might produce some very interesting effects. Henry Adams at the Paris Exhibition of 1900 marveled at the practical applications of the new science of electricity. In 1903, the Wright brothers’ experiments on a beach in North Carolina would usher in an age in which, among much else, long-pondered and very difficult questions in physics—like the motion of air over a surface—took on literally life-and-death significance.

  And through it all, good old Newtonian theory worked a treat, pretty much all the time. Its laws of motion described the experience of the real world close to perfectly, and, if Mercury acted up a little (so little! those few arcseconds per century!), comets and Jupiter and falling apples and just about everything else that could be observed proceeded on their way in calm agreement with the rules laid down in the Principia.

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Amid all this—the tumult of the new and the excellence of the old—Vulcan itself dwindled into a mostly forgotten embarrassment, the physical sciences’ crazy uncle in the attic. There it sat (or rather, didn’t), hooting in the rafters. No one seemed to hear. Mercury’s perihelion still moved. The gap between fact and explanation remained.

  That would change—but only after a young man in Switzerland started to think about something else entirely, nothing to do with any confrontation between a planet and an idea. There was a question he’d begun to ask. One way we now reframe his problem is to ask how fast gravity travels from here to there, from the sun, say, to Earth. But that’s not the way it struck him on an autumn afternoon in 1907 as he stared out his window on the top floor of the patent office in Bern.

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  *1 To call something a fundamental particle is to say that it is a chunk of reality that cannot be broken up into any smaller components. Another example of such a particle would be the photon —the quantum, or finest possible subdivision of light across the entire spectrum of electromagnetic energy.

  *2 In current theory, a particular kind of nothing called the false vacuum. False vacuums are regions of space-time that appear to be truly empty of phenomena, but through the effects of quantum mechanics can be populated, seemingly from nowhere, by subatomic particles or energy fluctuations.

  “THE HAPPIEST THOUGHT”

  November 1907.

  Albert Einstein was always a conscientious employee. He had been a model civil servant since 1902, when the Swiss national patent office took a chance on the then-unemployed recent graduate with a bachelor’s degree in physics. In 1905 he had experienced what would later be called his annus mirabilis, his miracle year—really just six months—when, to a much greater extent than most realize, he laid the foundations of the twentieth-century revolution in physics. Almost instantly, he was transformed: no longer a mere amateur, stealing time to calculate at his government desk, he became a full participant at the highest level of international physics. And yet, he was still a bureaucrat. In 1906 his superiors promoted him to Technical Examiner Second Class—undoubtedly the most famous patent clerk in Europe.

  He still did his job and did it well, delivering an extremely competent day’s work for a day’s pay. He reviewed the documents and technical drawings that crossed his desk. He wrote his evaluations, doing his part to maintain the legal framework for invention. Even so, he couldn’t keep himself from pausing every little while to think about what truly moved him. So it was one day in 1907, he found himself staring out the window. Across the way, he saw a man fixing something on a roof. His imagination took over. In his mind’s eye, that suddenly luckless roofer slipped, slid, fell—and there it was, what Einstein would call “the happiest thought of my life.” It had just come to him that “if a man falls freely he will not feel his own weight.”

  A man crashing to his death would seem to be an odd image to evoke joy in anyone. And that treacherous roof was a very long way from the limb of the sun and the realm Vulcan had been supposed to roam. Even so: there stood an anonymous laborer, unaware of the mental play going on in the office across the way and, equally unknowing, about to take on a vital role in settling the fate of an undiscovered planet.

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  Of course, the work to come did not emerge wholly formed from that first insight. Einstein’s greatest discovery built on an earlier one from his almost ridiculously profligate outpouring in the first half of 1905, when he produced four papers spread across huge swaths of theoretical physics. The first emerged from what might seem like a surprisingly narrow investigation into a phenomenon called the photoelectric effect, originally observed in 1887. A better picture of the phenomenon came at the turn of the century, through the work of the great experimentalist (and horrible man) Philipp Lenard. Lenard studied what happened when he varied the intensity of the electromagnetic radiation—light—striking a metal target. The expected result, based on Maxwell’s description of light as a field of waves, was that a bigger wave (brighter light) should impart more energy to the electrons. But Lenard found that while dimming or adding light altered the amount of current produced—the number of electrons emitted—it didn’t affect the energy of each individual electron as it left a metal surface. That varied only with the color of light he chose, its frequency or wavelength. Ultraviolet radiation, for example, imparted a bigger kick than did longer wavelengths—lower frequency visible colors. Lenard, who won a Nobel Prize for his experiments, couldn’t explain this fissure between theory and observation. In 1905, with no formal training beyond his undergraduate degree in physics, Einstein did.

  What if, he asked, light could be understood not simply as a wave, but as a kind of particle, a quantum of light—what is now called a photon. Starting from that physical intuition, interpreting Lenard’s experiments becomes simple (though not easy). If light is made up of particles, then more photons (more light) would produce a bigger flux of electrons and hence more current—as observed. But the energy imparted to each of those electrons would depend on the energy of the photon that whacked it, not the total number of particles that struck the target. Once Einstein represented light as quanta in his equations, the calculation that followed reproduced Lenard’s results…and helped form the foundations of quantum mechanics, a set of ideas that is utterly intertwined with every facet of twenty-first-century life.*1

  That came in March. April brought Einstein’s proof of the existence and size of atoms and molecules, an exercise in statistical physics that remains the most frequently cited of his 1905 works, with applications that range from mixing of paint to Einstein’s own definitive explanation for why the sky is blue.

  He followed that up with a related analysis that solved the long-standing mystery of Brownian motion—first observed in the random motion of dust or pollen in water. That sounds like a sidelight, a minor result, except that Einstein’s method of accounting for the outrageously large number of molecular collisions required to produce the wandering track of a pollen grain was a significant step in building perhaps the single most powerful idea in twentieth- and twenty-first-century science: the recognition that the fundamental nature of reality in many of its facets is determined by the behavior of crowds that can only be understood in statistical terms, and not by direct links in a chain of cause and effect.

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  Einstein sent off the Brownian motion paper in the second week of May. With that he’d completed work that would have been the pride of at least two careers—and when he finally won his Nobel, the prize committee cited his account of the photoelectric effect instead of the more popularly celebrated work to come. But he had one more shot to fire. The last of Einstein’s “big four” papers arrived at the offices of Annalen der Physik on June 30, 1905. It came under a seemingly bland title, “On the Electrodynamics of Moving Bodies”—which masked the radical, almost subversive idea it contained, what we know as the special theory of relativity. It took him about six weeks to produce it, but once he was done, he was able to express his ideas in astonishingly simple, clear language, almost a story, in which he asks his readers to question what almost no one had ever paused to consider. What does it mean, he asked, to say that an event happens at a certain time? “If,” he wrote, “I say that ‘the train arrives here at 7’o’clock’ that means, more or less, ‘the pointing of the small hand of my clock to 7 and the arrival of the train are simultaneous.’ ” In other words—to describe any event in nature you need a rigorous concept of time: how it is to be measured and how any two people can come to agree on when anything may be said to have happened.

  From there, Einstein lays down the two pillars on which all the rest of his new idea will rest. One was the “relativity principle,” originally defined by Galileo. It holds that “the laws governing the change of state of any physical system do not depend” on whether someone observes that event from within a system or from the outside, looking in—as long as both vantage points “are in uniform motion relat
ive to each other.” That is: it doesn’t matter whether you are standing by the track or riding a train. Newton’s laws of motion (and any other natural laws, of course) behave the same way in both circumstances, even if, say, the path of a ball thrown on the train looks different to people watching from either vantage point.

  Einstein’s second axiom was that the speed of light in a vacuum must be a constant, identical for all observers throughout the universe. The problem with that idea—and this had troubled scientists for decades before Einstein—is that if the speed of light truly does remain constant for all observers, that would seem to contradict Newton’s ideas about motion. Here’s the difficulty: imagine that a person turns on a lantern and stands still, while another runs down its beam of light. If Newton were right, the person at rest should find light traveling at the usual number—very nearly 300,000 kilometers (186,000 miles) per second. But the person in motion should come up with a different answer: 300,000 kilometers per second, less the speed at which she runs, say twenty kilometers an hour.*2 To Einstein’s predecessors, that’s how a properly organized universe would behave. Yet stubbornly, throughout the last years of the nineteenth century, the measured speed of light never complied, no matter how precise the experiment, no matter the state of motion of the experimental apparatus.

  Einstein’s insight was to take seriously the implications of that evidence of a constant velocity for light. If the speed of light does not change with the motion of an observer, he argued, then to reconcile that fact with the rest of experience requires a change in the way one must think about the elements of speed—distance and time. Another thought experiment captures what he was trying to express: imagine a train traveling at a steady pace along a straight stretch of track, with one person equipped with a clock on the train at its midpoint, and another with an identical clock standing on the embankment. Now picture two bolts of lightning striking each end of the train at the instant that the watcher on the train passed her luckless counterpart, standing by the tracks amid the storm. So here’s the question: do both observers agree that the two bolts of lightning hit the train at the same time?