The Nobel Prize may be the most prestigious award in science, but the new Fundamental Physics Prize is by far the world's most lucrative scientific award, instantly making its first winners this August multimillionaires. But the size of the payout isn’t the only difference between the two prizes: Unlike the Nobel, the Fundamental Physics Prize can be awarded for research that has not yet been verified by experiment. Is it foolhardy to extol work later findings might prove wrong?
The Fundamental Physics Prize is the brainchild of Russian tycoon Yuri Milner, a one-time physics graduate student turned billionaire investor in internet companies such as Facebook, Twitter, Groupon and Zynga. Milner personally selected the inaugural class of nine winners, each of whom received $3 million, roughly three times as much as a Nobel grant.
Although some of the work recognized by this year’s awards has been experimentally verified (for example, the principles of quantum computers are firmly grounded in experiment), others, like string theory, which compares elementary particles to loops of vibrating string, and the holographic principle, which suggests that our three-dimensional reality is a projection of information stored on a far-off two-dimensional surface, live further out on a theoretical limb.
Ideas like these may not get experimental verification any time soon, either. Take string theory. As Fundamental Physics Prize winner Ashoke Sen, a string theorist at the Harish-Chandra Research Institute in India, explains, "Unfortunately the strings are so small that the energy required for seeing these structures is huge, much larger that what we have achieved in the present day accelerators.”
Yet many physicists (including, unsurprisingly, some Milner honorees) argue that unverified ideas, and even ideas that are unverifiable with today’s technology, are prizeworthy—even if future tests should prove them wrong.
"Many of the most important developments in physics involve subjects for which there is little hope of experimental verification anytime soon," argued cosmologist Alan Guth at the Massachusetts Institute of Technology, one of the winners of the Milner prize. Guth invented the theory of cosmological inflation, which suggests our universe expanded staggeringly just a sliver of a second after it was born. This rapid expansion that would help explain, among other things, why the cosmos is so extraordinarily uniform on large scales, with only very tiny variations in the distribution of matter and energy.
In fact, two of the greatest theoretical breakthroughs of the 20th century—Albert Einstein's theories of special and general relativity—were never honored by a Nobel Prize, said Stanford cosmologist Andrei Linde, another winner of the Fundamental Physics Prize. These ideas changed the world by showing that mass and energy are equivalent and that gravity is a result of mass curving the fabric of space and time. Although Einstein was awarded the Nobel Prize in 1921, he was given the prize not for relativity but for describing how light was composed of discrete packets of energy now called photons, because the Nobel committee felt that relativity had not at the time been verified.
"More recently, we have the case of the Higgs particle, with almost 50 years between the theoretical advance and the experimental verification," Guth added. "If this kind of theoretical work is not respected, then progress in fundamental physics would suffer tremendously."
Even if theoretical research does lead to a dead end, it can help inform what ultimately prove to be successful ideas, said theoretical physicist Nima Arkani-Hamed at the Institute for Advanced Study in Princeton, New Jersey, a winner of the new prize who has investigated ideas such as extra dimensions of reality and new theories regarding the Higgs particle.
"One of the great developments in physics in the 20th century was the Standard Model of particle physics, which explains particles such as electrons and quarks and gluons," Arkani-Hamed said. "But before the Standard Model was known to work, there were people exploring lots of other theoretical possibilities that might be consistent with our world. Even if they didn't pan out, collecting ideas that have a chance of working may help lead to developments like the Standard Model."
“Wrong” ideas can advance science in other ways, too. "We should keep in mind that Newtonian mechanics was ultimately found to be incorrect, but it nonetheless was a momentous force in driving science forward," Guth said. "Today there are many developments in physics that are recognized by the community as being important, even though we cannot prove that they are correct."
As to how the prize-winners might spend their gains, other than paying taxes and mortgages, they often said they were still in shock over the award. "I continue to remind my students that they should not go into physics for the money," Guth said.
Editor's picks for further reading
Fundamental Physics Prize
The official web site of the Fundamental Physics Prize Foundation.
Nature: Theoretical physicists win massive awards
Geoff Brumfield talks with winners—and critics—of the new prize.
New York Times: 9 Scientists Receive a New Physics Prize
Kenneth Chang reports on the announcement of the Fundamental Physics Prize winners.
Where will you be in 10100 years?
Yes, I know, we'll all be long gone by then. But if you could somehow stick around around to experience the universe ten thousand trillion trillion trillion trillion trillion trillion trillion trillion years from now, what would it be like?
Answering that question is a professional hobby for astronomers Fred Adams and Gregory Laughlin. They divide the life of the universe into five distinct stages, beginning with, well, the beginning—the Big Bang and the short period of explosive expansion that followed, all the way through to the formation of the very first stars about one million years later. That’s followed by the second stage, which Adams and Laughlin dub the “stelliferous era”—the era during which stars generate most of the universe’s energy. We are creatures of the stelliferous era; this is the universe we recognize as home.
But while the stars are hitting their stride during the stelliferous era, dark energy—the mysterious energy that is causing the expansion of the universe to accelerate—is well on its way to cosmic domination. If the acceleration continues at its present rate, in another hundred billion years or so, most of the visible universe will pass beyond our cosmic horizon. Future denizens of the Milky Way will turn their telescopes to the sky and see just one galaxy: their own.
As Lawrence Krauss and Robert Scherrer pointed out in a 2007 paper, these future astronomers will see no evidence of cosmic expansion or the Big Bang. They will probably conclude that their universe is static; that it is as it has always been and always will be. Ironically, the very force that sculpted their universe—dark energy—will have erased its own fingerprints.
This idea troubled Harvard astronomer Avi Loeb, who imagined a future in which astronomers would look back on today’s cosmology textbooks (which would then be 100 billion years old) with the same combination of reverence and skepticism with which we view biblical origin stories today. “You will have all these textbooks, but their claims will be unverifiable,” says Loeb.
Loeb went looking for a way in which future astronomers could tease out the history of their universe. He found the answer in hypervelocity stars, stars traveling so fast that they escape the gravity of their home galaxy. Using their advanced telescopes to monitor these stars, says Loeb, future astronomers just might be able to probe the universe beyond their galactic boundaries.
But even those galactic boundaries will be erased in the course of time. Astronomers estimate that the longest-lived stars will begin to burn out some ten trillion years from now, throwing our universe into an era of cosmic twilight. Here, the universe is lit only by the feeble embers of white dwarfs and neutrons stars, stellar corpses that will give off energy as they “hoover up” dark matter particles, says Adams. Though galaxies and galaxy clusters have managed to hold themselves together until now, a slow and steady stream of stars—the very same hypervelocity stars Loeb saw as cosmic ambassadors—will absent themselves from their galaxies until, over a period of about 1020 years, galaxies will “evaporate” entirely, Adams and Laughlin calculate. The finely-woven tapestry of the universe will come undone.
A computer simulation of the cosmic web of dark matter and ordinary matter. Image credit: NASA, ESA, and E. Hallman (University of Colorado, Boulder)
Given sufficient time, even the protons and neutrons that make up the stuff of universe will fall to pieces. How long will it take? That is still a mystery, though a combination of experiment and theory suggests that it will happen some time between 1033 and 1045 years after the Big Bang.
At that point, all that’s left of the stars and galaxies that once illuminated our universe will be a smattering of black holes. But even the reign of the black holes won’t last forever. As Stephen Hawking showed theoretically, black holes slowly leak out their contents via a process we now call Hawking radiation. Given enough time—as long at 10100 years—even the biggest black holes will evaporate away.
Only now will we enter what Adams and Laughlin dub the “dark” era. The dark era isn’t just very, very dark; it is also very, very boring. Next to nothing actually happens in the dark era. Thanks to the accelerating expansion of the universe, even humdrum particle collisions will become rarities.
Will the lonely monotony of the dark era ever end? Maybe. The same energy that has been driving the accelerating expansion of the universe could suddenly change character, a phenomenon theorists call vacuum energy decay. It happened once before—when the era of inflation ground to a halt soon after the Big Bang—and theorists believe that it should happen again.
“You could imagine a new start” for the universe, says Adams, in which matter gets a second chance to coalesce into stars, planets, even people. Or, the vacuum energy could decay before the universe ever makes it to the dark era. “If that happens,” says Loeb, “we’re back to a situation where once again we can see all those galaxies that we lost.”
Of course, these scenarios are a strong cocktail of science and speculation—and the further we look into the future, the more speculation is poured into the mix. So why study a universe that even our most distant descendants will never live to see?
The numerical models scientists use to project into the distant future can yield new insights into stellar life cycles—like how small, long-lived stars evolve into red giants—that we can’t observe progressing over the course of one (or many) lifetimes, says Adams. It also gives us a way “to gauge the cosmic importance of various aspects of the standard model,” says Loeb, by watching how they play out over time.
“It is part of our worldview to want to know what will happen,” adds Loeb. Yet I don’t think I’m alone in enjoying the fact that the next plot twist is, ultimately, a mystery.
Editors picks for further reading
Astrobites: Avi Loeb and Freeman Dyson on the future of the universe
Can the universe be saved from the "dark era"? Astronomy blogger Nathan Sanders shares a conversation between Freeman Dyson and Avi Loeb on the prospect of "cosmic engineering."
FQXi: Predicting the End
Science writer Govert Schilling talks with Fred Adams and Greg Laughlin about how they became the authors of the future-biography of our universe.
The Five Ages of the Universe: Inside the Physics of Eternity
Fred Adams and Greg Laughlin had the bad fortune to publish this book just around the time that dark energy was discovered; their predictions therefore don't account for dark energy. Most of their conclusions about the distant future remain valid, though.
When a team of astronomers in 1992 released the first full-sky map of the cosmic microwave background—also known as the afterglow of the big bang—George Smoot, one of the group’s leaders and later a Nobel laureate, said, “If you’re religious, this is like looking at God.”
Mystical undertones stir passions and risk muddying our understanding of science. But whatever one’s views, it is an intriguing coincidence that a possible key to reading Smoot’s words comes to us from none other than Dante Alighieri’s “Paradiso,” written in the early years of the 14th century. The cosmic microwave background, or CMB, shows us a slice of the universe as it looked more than 13.7 billion years ago, and the structure of that universe bears a striking resemblance to that of Dante’s heaven—at least according to some commentators. It is as if the poet had presaged some of the most striking developments of modern mathematics and cosmology six centuries before they emerged.
“Paradiso,” the third and final part of the “Divine Comedy,” narrates an allegorical journey in which Dante ascends from Earth, visits heaven, and eventually gets to behold the creator himself. First, Dante crosses a series of concentric spheres, all centered at Earth, which hold the planets, Sun, moon, and the stars. The next sphere he reaches is one that encloses the entire physical universe. As he crosses it, he steps into the spiritual realm.
The otherworld however also has a geometric structure, and it is completely symmetrical to that of the physical world, with nine concentric spheres, which are inhabited by angels and the souls of the most virtuous dead. But instead of growing ever larger, these spheres grow ever smaller. And at the center, Dante says, sits God, occupying a single point and emanating a blinding light.
Thus Dante’s entire universe—both physical and spiritual—consists of two sets of concentric spheres, one centered at Earth, the other at God. If you were to point a laser vertically up toward the sky from any point on Earth, you’d be pointing it straight at that single point where Dante places God.
In a sense, then, the successive spheres of the spiritual world enclose all of the physical spheres, Dante seems to imply, even though they get smaller and smaller as you move farther away from Earth and closer to God. Such a geometry seems impossible, and the passage has mystified commentators for centuries. In fact, these bizarrely nested spheres are both mathematically and physically possible. To discover why, we have to turn to mathematics that wouldn’t be discovered until centuries after Dante’s death.
In the geometry of our everyday experience, also known as Euclidean geometry, if we draw a sphere around us, the larger the sphere’s radius, the larger its circumference; more precisely, doubling the radius of a sphere doubles its circumference. But this is an empirical fact and not a logical necessity: there is such a thing as non-Euclidean geometry, in which it is perfectly allowable for a sphere to have a circumference that is not proportional to its radius.
Moreover, non-Euclidean geometry is not just a bizarre, abstract invention of mathematicians. In fact, Einstein showed in his theory of general relativity that the geometry of the universe itself is fundamentally non-Euclidean. This is what allows space to twist and bend like a cosmic contortionist.
The discrepancy between the real world and Euclidean geometry is tiny in ordinary situations—a satellite’s orbit around Earth, for example, may be a few inches shorter compared to what you would expect from Euclidean geometry—but becomes substantial in extreme situations such as around black holes.
Dante’s universe, then, can be interpreted as an extreme case of non-Euclidean geometry, one in which concentric spheres don’t just grow at a different pace than their diameters, but at some point they actually stop growing altogether and start shrinking instead. That’s crazy, you say. And yet, modern cosmology tells us that that’s the structure of the cosmos we actually see in our telescopes.
We can think of the observable universe as being made of concentric spheres, just like Dante’s universe. Because light travels at a finite speed, we see distant galaxies as they were in the past, at the time when they emitted the light that we now receive from them. By definition, light covers one light-year of distance every year. Thus, for example, we can picture all galaxies that we see as they were one billion years ago as residing on a sphere centered at our position and of radius one billion light-years. (These spheres are of course not solid objects, and they not absolute but relative to the observer, contrary to those in Dante’s 14th-century cosmology.)
Now, the universe we see all sprang up from a very small region of space, and has been expanding ever since. Cosmologists have placed the beginning of time at about 13.7 billion years ago. That means that our game of drawing concentric spheres cannot be pushed to an arbitrary distance. But it also has another consequence. As the radius of the spheres pushes close to that magic number of 13.7 billion and change, we are looking at smaller and smaller regions of space, despite the fact that those regions still span our entire field of view, in all directions of the sky.
In fact, when astronomers map the CMB, they are mapping a sphere that surrounds us and that is very close to that initial moment—at roughly 400,000 years after the big bang—and thus has a “radius” of around 13.7 billion light-years. But its circumference is a lot smaller than what you would expect from Euclidean geometry—more than a thousand times smaller. Spheres that are even closer to the big bang are even smaller, until our field of view converges to that single point we call the big bang. Theoretically, we could cast a laser in any direction and still aim at that single point.
One very bizarre consequence of the non-Euclidean nature of the observable universe is that distant objects appear larger than their true size. For the first 10 billion light years or so, galaxies look smaller if they are farther away, but beyond that distance they instead start taking up a larger and larger field of view in the sky, as if space itself acted like a magnifying lens. In practice, the effect is exceedingly difficult to actually observe in our telescopes, because at those distances galaxies look extremely faint. But in recent years astronomers have begun several projects to detect the magnification effect in their observations, not by looking at the apparent size of galaxies but at their spacing. To do so, they map hundreds of thousands of galaxies over a range of distances spanning many billions of light-years. “You look at where the galaxies formed, not at how big they are,” explains astronomer Tamara Davis of the University of Queensland, who participates in one such mapping effort called WiggleZ.
Of course, Dante lived five centuries before any mathematicians ever dreamed of notions of curved geometries. We may never know if his strange spheres were a mathematical premonition or esoteric symbolism or simply a colorful literary device.
Editor's picks for further reading
Non-Euclidean Geometry Online: a Guide to Resources
Mircea Pitici's brief introduction to non-Euclidean geometry.
The Poetry of the Universe
Mathematician Robert Osserman's volume of "math for poets."
The World of Dante
Explore Dante's writing with interactive maps, images, music, and more.
You’ve just started reading this post. The decision is done. Seconds have ticked by and you’ve chosen to use them clicking on this article, rather than pursuing hang gliding, water skiing, mountain climbing, chocolate sampling, or countless other options. Sure you could do those things later, but what was “now” is already gone. If only you had a wormhole time machine and could go back in time to undo your choice! But how to make a wormhole time machine? Read on if you’d like some suggestions from the world of theoretical physics.
Step in to my time machine. Credit: NASA/Les Bossinas (Cortez III Service Corp.), via Wikimedia Commons
Flash back to the late 1980s—with your imagination, not a time machine just yet. The extraordinary astronomer and science communicator Carl Sagan, fresh off his award-winning PBS series Cosmos, decided to write a science fiction novel about interstellar travel, "Contact." Needing a way for his protagonist to travel quickly to another planet, he asked his friend Caltech astrophysicist Kip Thorne for advice.
Thorne is an expert in general relativity, Einstein’s masterful theory of gravity. The equations of general relativity serve as a recipe for how nature kneads the dough of spacetime (space and time combined) into various shapes—from as flat as a pancake to as curvy as a croissant. These shapes determine how other things move. Just as an ant at a picnic would take a more winding route around an apple than across a napkin, objects in the universe (planets, comets, and so forth) veer along curved paths in warped regions. What distorts these sectors of spacetime is the amount and distribution of mass and energy. For example, the gravitational well of the solar system is carved out by the mass of the Sun.
In extreme cases, a glop of mass concentrated in a small enough region will tear the fabric of spacetime, causing what is called a singularity—a point of infinite density where spacetime seems to reach a dead end. Such is the case with what is called the Schwarzschild solution of Einstein’s equations of general relativity, used to describe the ultra-dense, collapsed stellar cores known as black holes. However, as Einstein and his assistant Nathan Rosen showed in 1935, one can mathematically extend the Schwarzschild solution across an “Einstein-Rosen bridge” and link it to another region of spacetime. In the 1960s, the creative Princeton physicist John Wheeler, who was Thorne’s PhD advisor, dubbed these connections “wormholes,” imagining a worm taking a shortcut by crossing an apple’s interior. (Wheeler also coined the term “black hole.”)
When Sagan contacted Thorne he was envisioning something like a Schwarzschild wormhole connecting two otherwise distant parts of space—an interstellar Chunnel, so to speak. But Thorne realized that a Schwarzschild wormhole wouldn’t do. For one thing, it was unstable to matter, meaning that the gravitational effect of even the slightest drop of mass would cause it to collapse. Therefore it would close off if a spaceship tried to enter—that is, if the space voyagers could make it that far. If the wormhole entrance lay in the bowels of a black hole, the travelers would encounter deadly radiation, bone-crushing gravitational forces, and enough stomach-churning acceleration to make even the Dangerous Sports Club give it a miss.
Thorne asked his then-student Michael Morris to help him come up with an alternative. They crafted a novel solution of Einstein’s equations of general relativity that would represent a wormhole that could be traversable by human voyagers, such as the fictional heroine of "Contact." The solution was custom-designed to eliminate the nasty aspects of navigating into a black hole and allow for a relatively quick, comfortable ride. After passing into the wormhole’s “mouth” (as its entrance was called) and journeying through its “throat” (as its passageway was called), a voyager would find herself emerging from another mouth somewhere in another part of space. Instead of traveling hundreds of years or more to reach another star, if all went well, she’d swiftly arrive in its vicinity.
Morris and Thorne realized that their scheme was extremely hypothetical—requiring a virtually inconceivable engineering feat. For one thing, the amount of mass needed to create the wormhole was comparable to that of a galaxy. Moreover, a new type of negative mass material, called “exotic matter,” would be necessary to prop open the wormhole’s throat and prevent it from collapsing. No known substance has negative mass.
Offering some cause for optimism, physicist Matt Visser of Victoria University of Wellington soon found a way to minimize the amount of exotic matter required. As he and others have pointed out, exotic matter has features in common with the energy of the quantum vacuum, the bedrock state of particle physics, which has a repulsive pressure. Perhaps a future civilization could mine enough of this energy to suffice for wormhole construction. A hypothetical energy called “phantom energy,” a type of dark energy with a considerable amount of negative pressure, used to explain the acceleration of the universe’s expansion, also holds promise as a potential way to stabilize wormholes.
Shortly after Morris and Thorne published their first paper they collaborated with Ulvi Yurtsever, another of Thorne’s PhD students at Caltech, on another remarkable article showing how a wormhole could be used as a time machine. The key would be to speed up one of the mouths of the wormhole to close to the speed of light while leaving the other one fixed. According to the phenomenon of time dilation, an aspect of Einstein’s special theory of relativity, time in the vicinity of a near-light-speed object will slow down significantly relative to a stationary observer. Therefore, while the fixed mouth ages 100 years, the high-speed mouth, if it is fast enough, might experience only one year. If the calendar reads 2112 for the former, it would read 2013 for the latter. Now suppose a space traveler sails into the fixed mouth in 2112. If passage through the throat is quick enough, she would emerge through the moving mouth in 2013.
If you are still thinking about all the things you could have done if you hadn’t clicked on this post, you now know the answer. Assuming you have an advanced spaceship and a CPS device (Cosmic Positioning System), simply find a wormhole, journey through it, go back to the time before you started reading this, and convince yourself to go surfing instead. You are cautioned however that your actions would create a paradox1, because if you never read the article you wouldn’t know how to go back in time (or at least wouldn’t have the need). Proceed to the past at your own risk!
1 To avoid paradoxes such as meeting yourself in the past and convincing yourself never to pursue time travel, or going back in time and accidently eliminating your ancestors, some physicists have asserted that backward time travel is impossible. Stephen Hawking, for example, postulated the Chronology Protection Conjecture to shield the past from tampering. Others such as Igor Novikov of Moscow State University and the Lebedev Physics Institute in Russia have argued, in what he called the Self-Consistency Principle, that past-directed temporal voyages are fine as long as the altered past is consistent with the present—that is, it was really supposed to happen. For example, if you go back in time and convince Carl Sagan that wormholes wouldn’t fit into his novel, maybe that’s just the incentive he needed to contact Kip Thorne and check if they would, leading to what actually happened. Finally, there are some who speculate that backward time travel could lead to a bifurcation of time into parallel realities.
In any case, the work of Thorne, Morris, Yurtsever, Novikov, Hawking, Visser and others has propelled the discussion of time travel and wormholes from fanciful science fiction into serious, peer-reviewed—albeit highly speculative—science. Who knows, perhaps someday our civilization will be advanced enough to test such far-reaching hypotheses and create or find actual wormholes. Only time will tell—and if wormholes exist, we have all the time in the world.
Editor's Picks for Further Reading
Daily Mail: Stephen Hawking: How to Build a Time Machine
Stephen Hawking on wormholes and the paradoxes of time travel.
Space Time Travel: Flight Through a Wormhole
Explore computer-generated images of a hypothetical trip through a wormhole.
Wikipedia: Wormholes in Fiction
From "A Wrinkle in Time" to "Fringe," discover how writers of books, television, and movies have used wormholes in their storytelling.
Are physicists victims of their own success? They have strived to find the fundamental laws of matter, and in recent years they’ve done it. The so-called standard model of physics provides us with a thorough census of the subatomic particles that combine to make everything we see, and its equations define a complete mathematical explanation of how they behave. The golden age, it seems, has come and gone.
Or has it?
A millennium from today, historians will look back at the twentieth century primarily as the age of a rich flowering of science. Within a few decades molecular biology unveiled the body and soul of the genetic code, cosmology reconstructed the history of the universe, and geophysics disclosed a home planet more dynamic than ever previously imagined. Yet the biggest revolution of all, from which all those others drew, was ironically the smallest: the conquest of microphysics.
Three icons of twentieth century science. Clockwise: The double helix structure of DNA, revealed by analysis of its x-ray diffraction pattern (credit: Richard Wheeler via Wikimedia); anisotropies in the microwave background radiation, providing a picture of the very early universe (credit: WMAP Science Team, NASA); motion of the continents, proved and then mapped by analysis of magnetic field reversals at mid-ocean ridges. In each case, the enabling sensitive instruments and technologies depend upon profound understanding of the properties of matter, based on microphysics (credit: EMAG2)
History does not come with time-stamps affixed, but two epochal experiments roughly bracket the High Golden Age of microphysics. In 1912, Ernest Rutherford decoded atoms experimentally, revealing that each has a tiny nucleus containing all its positive charge and almost all its mass. That nucleus is surrounded by electrons, which are bound to it by electric forces. Just a year later, Niels Bohr introduced strange new ideas about the laws of motion in the microworld. His breakthrough matured into quantum mechanics.
Quantum mechanics broke the code of the microworld, but it took decades to master its text. Finally, in the “November Revolution” of 1974, two separate experimental groups announced the discovery of a striking set of new particles, the charmonium system. Their discoveries provided a brilliant confirmation of, and a fertile proving ground for, the collection of theoretical ideas we now call the Standard Model. The charm quarks (and their antiquarks) that make the charmonium particles rounded out the theory of the weak interaction, and the forces that bind them were just right for the theory of the strong interaction. Those theories tamed nuclear physics, and together with electromagnetism and gravity they complete the description of matter.
The Standard Model provides, we believe (after very thorough, rigorous, quantitative testing!), a complete mathematical explanation of how subatomic particles combine to make atoms, atoms to make molecules, and molecules to make materials, and how all this stuff interacts with light and radiation. Its equations are comprehensive yet economical, symmetrical but spiced with interesting detail, austere yet strangely beautiful. The Standard Model provides a complete, secure foundation for astrophysics, materials science, chemistry, and physical biology. Good stuff!
The Standard Model marks the ultimate triumph of reductionism. As Isaac Newton put it, we analyze matter by finding complete and simple laws governing the behavior of its elementary components, and then use those laws to synthesize the properties of macroscopic objects.
Triumph on that scale has a dark side: It’s a tough act to follow. By the late 1980s, articles and books with titles like “The End of Physics” began to appear. At the same time, “Theory of Everything” hyperbole erupted.
Neither reaction, however unseemly, was entirely baseless. The achievements of this golden age did mark the end of a certain special—and especially wonderful—kind of physics. After plumbing the bottom of ordinary matter (that is, physical material that’s reasonably accessible and usefully stable), where do you go? As physicists deciphered the atom, they revolutionized chemistry and enabled microelectronics; as they deciphered the nucleus, they revolutionized not only astrophysics and physical cosmology, but also bomb technology and medicine. There is no realistic prospect that the sort of frontier physics explored at the Large Hadron Collider, as esoteric and expensive as it is marvelous, will yield practical fruit. (This is not to say that the indirect value of this work, which serves as “the moral equivalent of war” for many talented, enthusiastic, creative young seekers, will not repay the money invested in it. It will, handsomely.) Its application in the natural world is likely to be restricted to the extremely early universe, and (maybe) a few super-extreme astrophysical situations, like Hawking’s black hole explosions.
But lamenting the passing of a golden age, or professing to reanimate it, are exercises in nostalgia. A healthier attitude, and an attitude that is truer to the unselfconscious exploratory spirit of the golden age itself, is to engage with its legacy of unanswered challenges and new opportunities. What a legacy it is, and what opportunities there are!
For the Standard Model, despite its practical success in describing ordinary matter, leaves many loose ends and unanswered questions. One of its ingredients, the Higgs particle, has not yet been observed directly. That embarrassment may soon be remedied, but other flaws run deeper. Its equations remain lopsided in peculiar ways. They beg to be embedded in a larger, still more symmetric theory. There are, in fact, excellent ideas for advancing toward such unification. Those ideas suggest new lines of experimental investigation, notably the search for proton decay and for supersymmetric particles. The other interactions, and indeed quantum mechanics itself, have not yet been organically united with gravity. String theory might help with those problems, but it’s clear that crucial ideas still await discovery.
We’d also like to understand why the laws of microphysics appear so nearly unchanged if we run time backwards. The only known explanation predicts the existence of a remarkable new class of particles called axions. These wraithlike cousins of photons, more elusive even than neutrinos, plausibly provide the astronomical dark matter. And if axions don’t—what does?
These and other unanswered challenges amply refute the notion that physicists are, in any meaningful sense, close to having a “Theory of Everything” (or that we’ve reached “The End of Physics”).
Yet the biggest challenges, I think, are of a different kind. The art of using our comprehension of microphysics is an open-ended invitation to creativity. Music-making doesn’t end when you’ve learned how your instrument works—it begins.
Can we engineer quantum computers, and through them fashion truly alien forms of intelligence? Can we tune in to the messages the universe itself broadcasts in gravity waves, in neutrinos, and in axions? Can we understand the human mind, molecule by molecule, and systematically improve it? To ask these questions is to discover, in the ripeness of one golden age, the seeds of new ones.
Can science fiction influence the course of real science?
By “science fiction,” I don’t mean fantasy—vampires, werewolves, elf princesses, that kind of thing. Science fiction may seem fantastical, but even its most fantastic elements are driven by real science.
The obvious predictions of science fiction are all around us, from iPads to cell phones and various other electronic wonders that we treat as disposable. My 2-year-old son entertains himself with toys that are more technologically sophisticated than the first computer I ever owned. The next phase in casually transforming us all into cyborgs may be fully-immersive augmented reality, at least if Google has anything to say about it.
Science fiction isn’t just a sneak preview of future gadgets, though. For scientists, it is an inspiration machine. The theoretical physicist and TV personality Michio Kaku recalls watching "Flash Gordon" in his youth and realizing that the real hero of the series wasn’t the handsome, athletic Flash: it was the brilliant scientist Dr. Zarkov. As Kaku recounts in his book "Physics of the Future," “[Dr. Zarkov] invented the rocket ship, the invisibility shield, the power source for the city in the sky, etc. Without the scientist, there is no future.”
Dr. Wernher von Braun (center), then Chief of the Guided Missile Development Division at Redstone Arsenal, Alabama, discusses a "bottle suit" model with Dr. Heinz Haber (left), an expert on aviation medicine, and Willy Ley, a science writer on rocketry and space exploration. Source: NASA, via the Wikimedia Commons
To Stephen Hawking
, science fiction offers a kind of exercise for the imagination. As he wrote in the forward to Lawrence Krauss
’ 1995 classic "The Physics of Star Trek":
“Science fiction [...] is not only good fun but it also serves a serious purpose, that of expanding the human imagination. We may not yet be able to boldly go where no man (or woman) has gone before, but at least we can do it in the mind.[…] There is a two-way trade between science fiction and science. Science fiction suggests ideas that scientists incorporate into their theories, but sometimes science turns up notions that are stranger than any science fiction.”
Yet even some of those strange notions, like Einstein’s theory of general relativity, were anticipated by science fiction. As Krauss pointed out in "Hiding in the Mirror," the very first page of H.G. Wells’ "The Time Machine," published in 1895, included an explanation from the unnamed time traveler about how objects require existence in time as well as space. To modern ears, his description sounds a lot like Einstein’s vision of space and time.
Yet at the same time that Wells was presaging Einstein, some physicists believed that science was turning the final pages in the book of nature. In 1900, the scientist Lord Kelvin famously declared that physics was nearly complete—that we only needed to solve two minor lingering problems to know all there was to know about the universe. As it turned out, resolving those two problems did not usher in the end of physics—it led directly to the theory of relativity and quantum theory, as well as all of the scientific discoveries and technology that’s come about from them: television, nuclear energy, computers, transistors, cell phones...you get the idea. So while physicists thought that we were nearing the end of a journey, science fiction writers, with their fantastical stories of time travel and robots, showed that we were just at the beginning. And the science fiction writers were right.
In the aftermath of this quantum revolution, science fiction doubled down. This was the era of pulp adventures like the "Flash Gordon" serials that inspired Michio Kaku. Science fiction authors like Isaac Asimov, Robert Heinlein, and Arthur Clarke were the vanguard of a generation of science fiction authors who also had strong scientific backgrounds.
And it wasn’t just science fiction authors writing about the future. Theoretical physicist S. James Gates, Jr. recounts how his father brought home four non-fiction books in the late 1950s, all written by the science writer Willy Ley. With titles like "Space Pilots," "Man-Made Satellites," "Space Stations," and "Space Travel," these books brought scientific credibility to dreams of mankind’s star-faring future and inspired Gates to pursue the sciences. (Lest we think the only benefits of science fiction are intellectual, in a recent interview for the radio program "On Being", Gates also relates how Isaac Asimov’s "Lucky Starr" books helped him cope with his mother’s death.) Today Gates serves as director for the Center for String and Particle Theory at University of Maryland.
This isn’t to say that science fiction gets everything right, of course. For one thing, the golden age of sci-fi was full of laser pistols and flying cars that never quite made it into the mainstream. (At least, not yet.) In "The Amazing Story of Quantum Physics," physicist James Kakalios explains that this pulp-era futurism went awry by over-estimating the amount of energy we’d have access to. Turns out it takes a lot of energy to build a laser pistol or a flying car!
But the deepest error in science fiction—and the one that most rankles physicists like Gates—is how easy it often makes scientific accomplishment look. “I know from a life in science that nothing could be farther from the truth. The effort to advance science is one of the most monumental struggles I have witnessed in my life. Progress is usually painfully slow.”
David Brin, a physicist who now has a successful career as a science fiction author, agrees:
“The most annoying thing is when sci-fi or fantasy stories get the process of science all wrong. When, for plot reasons and just to get the heroes in jeopardy, they show science and scientists behaving in ways that are paranoid, incurious, conniving, unscrupulous, and addicted to secrecy....But science is about doing things in the open. And that's when horrible mistakes get pointed out, in advance.”
Science fiction has its fair share of mad scientists slinking about in gloomy dystopias. But more often, it is an optimistic genre. When science fiction author Robert J. Sawyer was recently asked about his top five science fiction predictions, for instance, his top pick was that there was a future. During the Cold War decades, it was science fiction that offered a hopeful vision of the future. Gates actually attributes much of the success of science fiction to the zeitgeist of this post-World War II era. “The challenge of Sputnik only turbo-charged these conditions and the kind of science fiction produced in this climate was almost guaranteed to have caught my attention.”
The finest science fiction is inspired by the same thing that has inspired the greatest science discoveries throughout the ages: optimism for the future. As I read today’s science fiction, I worry that many modern authors do not seek to inspire the way they once did. Brin points out that “images of a can-do, problem-solving humanity seem to be offered less and less,” despite his own best efforts to buck this trend.
Like Gates, I was strongly influenced by Isaac Asimov, who first inspired my interest in science, fiction, and the future. Which authors have inspired you with their hopeful visions of the future?
Editor's picks for further reading
Bulletin of the Atomic Scientists: The Science Fiction Effect
In this essay, Laura Kahn explores the connection between science fiction and science fact.
Inside NOVA: Cinema Science: Time Travel
In this blog post, explore the real science behind time travel as seen in science fiction films.
Smithsonian’s Surprising Science: NASA Picks Best and Worst Sci-Fi Movies
Find out which films get the science right—and which ones get it very, very wrong.
Technology Review: The Best Hard Science Fiction Books of All Time
If you thought that physicists couldn’t take a joke, a web site called arXiv begs to differ.
Arxiv is a preprint server, meaning that it’s where you can get an advance look at papers that haven’t yet been published in scientific journals. Of course, not every paper that appears on the arXiv is bound for The Astrophysical Journal. And every year, just around April Fools' Day, a crop of unusual papers tends to appear on the site.
After all, April Fools' Day brings out the geeky best in us all. So let’s celebrate the week of pranks and pratfalls with some highlights from this year’s April Fools' day haul:
Non-detection of the Tooth Fairy at Optical Wavelengths: "A wisdom tooth, freshly removed from the author’s lower left jaw, was placed under a pillow, upon which the author subsequently laid her head and fell asleep. The telescope was programmed to obtain an eight-hour time series of a six-meter-radius circle centered on the author’s sleeping bag. For a distance of 17 meters, the limiting absolute magnitude M is 99.7."
On the influence of the Illuminati in astronomical adaptive optics: "It is clear that the Illuminati are alive and well in modern times (Brown 2000). For instance, it is well known that pop stars Britney Spears and Lady Gaga have been aided in their astronomical rise to the top by the Illuminati (YouTube 2012). The secret to success in ground-based diffraction-limited astronomical imaging is less well known."
Gods as Topological Invariants: "We show that the number of gods in a universe must equal the Euler characteristics of its underlying manifold. By incorporating the classical cosmological argument for creation, this result builds a bridge between theology and physics and makes theism a testable hypothesis. Theological implications are profound since the theorem gives us new insights in the topological structure of heavens and hells. Recent astronomical observations can not reject theism, but data are slightly in favor of atheism."
And one from last year:
Schrödinger's Cat is not Alone: "Cat interferometry will inevitably lead to the 'Many Cats' interpretation of Quantum Mechanics, allowing to shed new light on old mysteries and paradoxes. For example, according to this interpretation, conservative estimates show that decision making of a single domestic cat will create about 550 billion whole universes every day, with as many replicas of itself."
Of course, arXiv isn't the only place to find physics pranks. The Museum of Hoaxes maintains a colorful list of the top scientific April Fools' Day pranks, including:
The bigon: On April 1, 1996 Discover magazine announced the discovery of a new subatomic particle, the bigon. According to scientist responsible for the breakthrough, Discover reported, "Bigons could be responsible for ball lightning, migraines, the unexplained failures of equipment and soufflés, the spontaneous human combustion."
The lost day: In 2004, Nature got in on the fun with a report the trade winds had blown an entire day—specifically, April 1—off the calendar.
Have you been a part of a great science prank? Tell us about it—or tell us about the prank you only wish you could pull off.
Imagine describing our universe to an alien from an alternate dimension. Where would you start?
You might reasonably begin by explaining that we live in three dimensions of space and one dimension of time. Space and time are so fundamental to our understanding of the universe that they are woven into nearly every equation in physics. They are the words in which we speak the language of nature—so tried, tested, and true that we don’t even know how to talk about the cosmos without engaging space and time in the conversation.
But what if it turns out that space and time are not the fundamental infrastructure of our cosmos—what if they are themselves products of some deeper physics?
This idea is called emergence. We see it in nature, as when fish school or birds flock. If you were only to study an individual fish or bird, you would never predict how they would come together as a group. Yet each one “knows” simple rules that, when combined, create a wide range of agile and elegant behaviors. Could it be that physicists have been studying flocks all along, not realizing that it’s the birds that are truly fundamental?
“There aren’t many things in quantum gravity that everyone agrees on,” says Eleanor Knox, a philosopher at King’s College London who specializes in the philosophy of physics. “Yet the one thing many people seemed to agree on in quantum gravity was that we were going to have to cope with space and time not being fundamental.”
It sounds radical, but physics has a long and proud history of spearheading exactly this kind of coup. “Historically, whenever we thought something was fundamental, it turns out that it is not,” says Nathan Seiberg, a theoretical physicist at the Institute for Advanced Study. Kepler, for instance, believed that the Platonic solids were the fundamental constituents of the universe. Today we know better. In the 17th century, scientists thought that cold was a substance that could flow from one place to another, chilling your doorstep or tip of your nose. Now we understand that heat and cold are just another way of talking about the statistical properties of a collection of molecules. Of course, that doesn’t mean that it feels any less real when you burn your tongue on your hot cocoa.
So why are physicists picking on space? Relativity delivered the first strike. “In relativity, space and time are not rigid. They are dynamic,” says Seiberg. Building all of physics on such a malleable infrastructure is akin to constructing your house on a foundation of Jello.
More alarmingly to theorists, our ability to measure features in space is intrinsically limited. A ruler can’t measure distances smaller than the width of its painted markings; the resolution of a microscope is constrained by the wavelength of the light in which it makes images; even scanning tunneling microscopes are limited by the physical size of their probe tips.
Can’t we just build a better microscope? “It’s not because we don’t have the budget to build a powerful enough machine,” explains Seiberg. If we somehow tried to make an infinitely small measuring device, that device would become so dense that it would warp the fabric of space. The conclusion: “Space itself is ambiguous,” says Seiberg. Strike two.
Space also took a hit from an unlikely foe: the hologram. We think of holograms as the dazzling, silvery images on postcards and credit cards: two-dimensional objects that project three-dimensional pictures. More generally, though, a hologram is anything—even an equation—that encodes an extra dimension’s worth of information. It turns out that you can write equations that describe our universe perfectly well using different combinations of spatial dimensions, creating mathematical holograms that are indistinguishable from reality. Like a book that can be translated into many disparate languages without losing a syllable of meaning, our universe seems to tell a story that is independent of the words in which we have always chosen to express it.
Finally, physicists have known for some time that their descriptions of space start to break down when they’re applied to the strange-but-true environments inside black holes and close to the time of big bang. In such cases, the familiar equations start popping out infinities—nonsense answers that suggest that the equations are missing some essential machinery. “Something else should kick in,” says Seiberg.
But what is that something else? “I don’t think I have an answer to that,” says Seiberg. Knox also leaves the door open to as-yet-unknown possibilities: “Whatever it is that’s fundamental, it’s not the stuff we have a handle on right now.” Morever, Seiberg adds that though theorists have assembled a strong case that space is emergent, time presents a more difficult problem. “In order to understand emergent time, we need a complete revolution in the way we think about physics.”
Letting go of space and time without ready replacements may seem like a surefire way to plunge into the abyss of abstraction. But it may be only by loosening our grip that we can come to grasp what is truly fundamental.
Editor's picks for further reading
Discover Magazine: Newsflash: Space and Time May Not Exist
If time isn't fundamental, what is it?
FQXi: Breaking the Universe's Speed Limit
John Donoghue investigates the possibility that the speed of light is not a constant.
FQXi: Melting Spacetime
Joanna Karczemarek investigates how space and time could emerge from deeper physics.
Are we living in someone else’s fantasy?
The Chinese philosopher Zhuangzi posed this question more than two thousand years ago when he recalled waking from a dream unsure whether he was a man who dreamed he was a butterfly or a butterfly dreaming that he was a man. Today, with the advent of computers that can simulate cells, cities, and even solar systems, philosophers and scientists are asking this ancient question in a new way: Are we living in a computer simulation?
This question is more than just the premise of "The Matrix." It's a conjecture that lives at the intersection of humanity and technology—and though it might seem like philosophy, it spurs ambitious new questions about what computers are capable of and about the nature of reality itself. As theorists begin to think of our universe as nothing more than a vast collection of information, can we ever truly know whether our reality is as “real” as we think it is?
The philosopher Nick Bostrom, director of the Future of Humanity Institute at the University of Oxford, posed the latest iteration of this ancient question in a 2003 paper. His "simulation argument" begins with the observation that modern computers have improved at an exponential rate since their invention. If computing power continues to grow at this pace, advanced civilizations will one day be able to build titanic, densely-packed supercomputers capable of doing everything from beating the stock market to predicting the weather months or years in advance. “Post-human” programmers might even use these machines to simulate entire civilizations, vast electronic worlds that would put today’s computer games to shame.
What would it take to create this kind of simulation?
When it comes to simulating a person, scientists estimate it might take 1017 operations per second—that's one followed by 17 zeroes—to simulate a human brain, based on the number of neurons in the brain and rate of which those neurons “talk” to each other. Assuming that simulating the sensory events a person experiences—every taste, sound, smell, touch and sight that is coded in our neurons—takes about 100 million bits per second, and that approximately 100 billion humans have lived on Earth to date, Bostrom estimates it might take 1036 calculations in total to create a simulation of the whole of human history that is indistinguishable from reality.
That’s just to simulate the parts of the universe that humans can sense. What about the microscopic structure of the Earth's interior or the subtle features of distant stars? These little details could be safely omitted until a simulated person needed to observe them. In addition, to save computing power, maybe not every person in a simulation would be fully simulated. Perhaps some of the characters in the simulation would be "zombies or 'shadow-people'—humans simulated at a level sufficient for the fully simulated people to not notice anything suspicious," Bostrom writes in his paper.
So how close are we to achieving this dream (or nightmare)? Today’s most powerful supercomputers are capable of operating at roughly 10 petaflops per second—that is, 1016 calculations per second. A planet-sized computer based on current electronics might carry out 1042 operations per second. Bostrom also notes that quantum physicist Seth Lloyd of MIT has calculated that a 1-kilogram "ultimate laptop" that operates at the known limits of physics might be capable of 5 × 1050 operations per second. So, the planet-sized computer might be able to simulate all of human history in a millionth of a second; the ultimate laptop, a hundredth of a billionth of a second.
Given that fully simulating every person who has ever lived might only take a tiny fraction of an advanced civilization's resources, Bostrom reasons that the number of computer-generated minds buzzing away inside simulations could vastly outnumber the total sum of real minds that have ever lived. If that is true, the odds are that we are simulated, not real. It may even be possible that our simulators are themselves simulated, and their simulators are simulated, and so on. "Reality may thus contain many levels," Bostrom says.
This does not prove that we live in a simulation, Bostrom emphasizes. There are a number of caveats that could stop this bizarre future before it starts. One glum possibility is that civilizations might very well go extinct or collapse—say, by annihilating themselves in a nuclear war—before they can develop supercomputers of such immense power. Another thought is that civilizations simply have no desire to commit the vast resources needed to create supercomputers. Or perhaps advanced civilizations might not indulge in such simulations—maybe they would be ethically opposed to simulating minds and their suffering, or they might prefer to entertain themselves with machines that directly stimulate their brain's pleasure centers. "Personally, I assign less than 50 percent probability to the simulation hypothesis—rather something like in the 20 percent region, perhaps, maybe," Bostrom writes, although he describes this as a gut feeling rather than part of his logical argument.
Unless the simulators decide to make themselves known, there may be no way to prove or disprove the simulation argument. Some have suggested looking for "glitches" in the simulation, but such glitches would be more plausibly explained as hallucinations, visual illusions, fraud or self-deception. Even if errors did pop up, a smart simulator could simply wipe any memory of the anomaly from our simulated brains.
If we are living in a computer simulation, how should we live our lives? "The simulation hypothesis currently does not seem to have any radical implications for how one should live," Bostrom said. Still, "it helps to shed light on, among other things, the prospects of our species."
Also, thinking of the universe as a computer may actually be a helpful approach in science. "You can start thinking about what kind of computer it is, what kind of operations can it do, what kinds of problems can it solve," said theoretical computer scientist Scott Aaronson at MIT. "That's an extraordinarily fruitful way of thinking about the universe that has led to the whole field of quantum computers—devices based on the quantum physics that explains how the fundamental building blocks of the universe behave."
We may never know whether we are living in someone else's fantasy; whether we’re the man or the butterfly. But if we do one day develop supercomputers capable of simulating minds and universes, perhaps our creations will be able to answer the question for us.
There is a moment in a dream when you realize that things don’t add up: You know that geese don’t speak English, and yet there you are chatting away with one about the price of gasoline. You’re sure that you never went to flight school, so why are you piloting this Cessna over Dubuque?
Then you wake up.
But sometimes, you don’t. Sometimes, as you confront two seemingly unassailable, clashing truths, you realize that you’re not dreaming at all—you’ve just encountered a paradox, and it’s a wake-up of an entirely different kind.
For centuries, paradoxes have helped physicists and philosophers challenge and deepen their understanding of how our world works. Paradoxes reveal assumptions and prejudices we never knew we had and open hidden hatches into new physics.
“There’s no getting around it: The universe is really strange, and paradoxes hit you with that,” says Anthony Aguirre, a physicist at the University of California, Santa Cruz.
For Aguirre, that’s a good thing: “That feeling of mystery is really what’s exciting in physics. You know there is something fun, interesting, and potentially important to be gained by going down that road.”
“Sometimes I consider that my knowledge is broken up into tectonic plates of understanding on the Earth of my total knowledge--a small part of the total universe of possible understanding,” says physicist Robert Nemiroff, who gives a special lecture on paradoxes to his students at Michigan Technological University. “Sometimes, I learn something that demands that two plates collide--both plates cannot be used to understand this new thought. This new thought can frequently be coined as a paradox. If resolved, these plates can lock into a larger plate of greater understanding, if I am lucky.”
“Paradoxes heighten what’s at stake conceptually,” says MIT science historian David Kaiser, who adds that physicists like Niels Bohr, John Wheeler, and Albert Einstein all deployed paradoxes strategically to underline mathematical contradictions that others deemed inconsequential. “Paradoxes are one way of grappling with what the equations really say.”
Here are the stories of three paradoxes from far-flung times and places in the history of physics and math. Though they have all been resolved, they remind us just how weird the universe really is. It is a dream from which we will never wake up. But who would want to?
How is it that anyone or anything ever moves from point A to point B? This simple question is the crux of a paradox first posed by the ancient Greek philosopher Zeno, and it has made generations of math students question the nature of reality every time they walk across a room.
Here’s one rendition of the paradox: Say you want to walk down the hallway from your bedroom to your bathroom. First, you have to cover half the distance between the rooms. Next, you’ll need to cross half the remaining distance. As you continue down the hall, you will always have half the previous distance left to cross. Though you will move ever closer to the threshold of the bathroom door, you will never actually reach it.
Obviously, we don’t spend our entire lives stranded in hallways. Why not? The answer is at the heart of calculus: It turns out that infinitely long sequences of numbers can actually have finite sums. This means that even though we must cross an infinite number of progressively smaller “chunks” of space on our way to the bathroom, the time it takes to do so is finite. That’s why we eventually get there.
Yet Zeno’s paradox also reflects one of the biggest questions in physics today: Is space—or spacetime—continuous, or is it broken up into discrete chunks? In Zeno’s world, space was continuous: It could be subdivided into smaller pieces on and on into infinity. Yet we know this isn’t how matter works. If you split a cookie in half over and over again (as many guilty sweet-tooths have no doubt tried at home) you will eventually be left with the indivisible components (electrons and quarks) of one atom. Eat them or don’t, but you cannot divide them in half.
This is also the moral of the story of quantum mechanics: The energy contained in all the particles that make up the universe is quantized. Why should spacetime be any different? In fact, some of the leading theories of quantum gravity predict that, on the tiniest scales, spacetime should break down into discrete chunks. Like a pointillist painting, spacetime may look perfectly smooth from afar, but up close it dissolves into pixels. There are currently experiments in the works to test this prediction.
Why is the sky dark at night? Before you say that it’s because the sun has set, consider that it took the greatest minds in science more than three hundred years to resolve this paradox. Everyone from Einstein to Edgar Allan Poe was swept up by this apparently simple puzzle.
The history of Olbers’ paradox goes back at least as far as Johannes Kepler, who posed it in 1610. If the universe is infinite, argued Kepler, containing an infinite number of stars distributed evenly across the sky, then every point on the night sky should be illuminated by starlight. The brightness of any individual star, as seen from Earth, fades in proportion to the square of its distance from Earth, but the number of stars at a given distance from Earth increases in proportion to the square of the distance from Earth, so it is a wash. The night sky, therefore, should be just as bright as the daylight sky. To Kepler, this meant that the universe must not be infinite after all.
In 1823, Heinrich Olbers drew up a different solution to the paradox that now bears his name. Olbers argued that as the light from each star makes its way toward Earth, it runs into interstellar dust and gas that absorb some its energy. Stars that are sufficiently far enough away from Earth would therefore be “cut off” from us.
The problem with Olbers’ logic is that dust and gas must spit back out the energy that they have absorbed, leaving us with the same problem we started with.
This is where Poe enters the picture. In his prose poem “Eureka,” published in 1848, he inserted time into the equation: What if light from distant stars just hasn’t had enough time to reach us yet? Poe wrote:
...yet so far removed from us are some of the "nebulae" that even light, speeding with this velocity, could not and does not reach us, from those mysterious regions, in less than 3 millions of years.
He may have had the details wrong, but the idea was right: Because stars have not been shining forever, and because it takes time for light to travel from here to there, there is a certain horizon from beyond which light has not yet reached us. Today, we know that the universe had a beginning (the Big Bang) and that the universe is expanding, causing light from distant stars to get stretched out (“redshifted”) beyond the visible part of the spectrum and into the infrared and radio bands, compounding the dark-sky effect.
“Olbers’ paradox is based on such a mind-numbingly simple observation,” says Aguirre. “What impresses me is the sheer amount of time that went by as people came up with one complicated and wrong solution after the next.”
The Twin Paradox
When Einstein proposed that time and space were elastic, it was weird enough. But the twin paradox challenges our understanding of Einstein’s rules even further. Imagine two twins, one a space traveler and the other an avowed homebody. The traveler sets out on a mission to a distant planet in a newfangled rocket that zips along at close to the speed of light. It’s a round-trip journey, so when she gets back, she is eager for a reunion with her twin. She wants to share the amazing stories of her voyage, of course, but she’s also looking forward to gloating about one favorable side effect of life in the cosmic fast lane: Because time passes more slowly for objects traveling close to the speed of light, the traveling twin anticipates that though she has hardly aged a bit, her stay-at-home sister will be sporting many years’ worth of new wrinkles. (Both twins are a bit vain.)
The stay-at-home sister is just as excited to see her twin. She knows her special relativity, too, and reasons that from her point of view, she was traveling close to light speed aboard spaceship Earth, while her sister sat complacently aboard her stationary vessel. Therefore, she will be the young-looking one, and will have fun counting up all her sister’s gray hairs.
And here is the paradox: Einstein tells us that no observer is “more correct” than any other, but the sisters can’t both be younger than each other. Still, Einstein wasn’t wrong. The solution to the paradox is that the sisters’ journeys were not actually identical. The traveling twin did not keep up a constant velocity throughout her entire trip. She accelerated to get up to speed, and then she changed directions—another kind of acceleration—before decelerating to get back into orbit around Earth. So the traveler, not her stay-at-home sister, gets the anti-aging benefits of time dilation.
Paradox solved? In one sense, yes. But in another sense, says Aguirre, the twin paradox reveals a deeper conundrum within the laws of relativity. The crux of the resolution, he says, is that even while velocity is relative, acceleration is absolute. “Where does this absolute non-accelerated reference frame come from? Einstein tried to do away with it in general relativity, but even a century later the question is largely open.”
Will today’s paradoxes be tomorrow’s truisms? Paradoxes arise when equations clash with our intuition about reality, says Kaiser. But intuition can change. “Newtonian mechanics did not look or sound ‘intuitive’ in the 17th century,” Kaiser points out. Today, we take it for granted that Newton’s conceptions of speed, gravity, and mass are in harmony with human intuition, but perhaps intuition itself has been reshaped by Newton’s view of the world. Will the apparent paradoxes of quantum theory and relativity one day feel just as natural as Newton’s laws? Is it possible to “grow out” of a paradox?
“Even once you know the golden thread that unravels the seeming contradiction, paradoxes are still appealing,” says Kaiser, who thinks of them as a kind of mental bodybuilding. “Paradoxes are like a much more satisfying version of Sudoku or a crossword puzzle.” The best part: “In the process we might really learn something about how the universe works.”
Editor's picks for further reading
arXiv: Paradox in Physics, the Consistency of Inconsistency
In this article, Dragoljub A. Cucic classifies paradoxes in physics and reviews their utility.
Edge: The Paradox
In this essay, Anthony Aguirre argues that a better understanding of paradoxes would improve our cognitive toolkit.
FQXi: Black Holes: Paradox Regained
Stephen Hawking conceded his bet on the black hole information paradox, but the debate continues.