An Excerpt From
The Science of Harry Potter
Broomsticks, Time Travel
"The Bludgers are up!" yells the commentator. In the airborne stadium with golden goalposts, two teams of seven players zoom around on broomsticks, swooping and weaving as they dodge their opponents' missiles-Bludgers-while trying to score with the red Quaffle. The game of Quidditch enthralls the broomstick-riding Harry, who tries to catch the Golden Snitch and win the game for Gryffindor House.
The wizarding world's favorite form of transport, the broomstick, is one of its worst-kept secrets, for every Muggle knows that witches and wizards use them to get about. Even now, scientists and engineers are trying to figure out how they do so. The most prized of racing broomsticks, the Nimbus 2000 and the Firebolt, probably use extremely advanced technology to defy the tug of Earth's gravity, a technology that has massive commercial and scientific implications. Researchers from NASA would sell their grandmothers to obtain Harry's broomstick, not to mention Hover Charms, Mr. Weasley's enchanted turquoise Ford Anglia, the flying motorbike that Hagrid borrowed from Sirius Black, or the candles that hover in the Great Hall of Hogwarts, all of which suggest that witches and wizards must know how to turn gravity on and off at will.
Exotic materials that can produce antigravity could also pave the way to wormholes, hypothetical shortcuts between two widely separated points in space-time. You could, for example, step into one end of a wormhole and emerge from the other a million miles away, 10,000 years in the past. There are several episodes in the Harry Potter books where wizards travel through a shortcut to Platform Nine and 3/4, or to visit the Diagon Alley wizard shopping arcade. Maybe they made these quick trips by wriggling through wormholes.
Enchanted travel opportunities do not end there. Harry used Floo powder to flit about. Other objects and people can appear out of thin air, whether the Knight bus, the food that fills plates at mealtimes, or a wizard clutching an old boot. Such remarkable materializations could be due to exotic technology, perhaps similar to that used in Star Trek to beam members of the Enterprise down to the surface of alien planets. Today, the possibility of such extraordinary feats taking place can be glimpsed when properties of atoms have been shuffled around the laboratory by practitioners of a leading-edge field called quantum teleportation.
The Quest to Fly with Broomsticks
It is a dream that is as old as humanity: to step out into thin air and fly like a bird, to cast off the bonds of gravity, to soar free, zooming through the clouds with the wind rustling past our outstretched and rapidly flapping arms.
Why, then, can't we fly? The short answer is that we are not birds. The longer one is that the human body is unable to deliver the right combination of thrust and lift. The longest answer I intend to give is that we lack feathers to help generate lift and propulsion, efficient lung design, large enough hearts, hollow bones to reduce our weight, and adequate muscle power to generate a sufficient flap.
While we cannot fly unaided, a broomstick is not as preposterous a form of transport as it sounds. Even NASA has pronounced on broomstick propulsion: A considered overview of the various technologies on offer has been put together by Mark Millis, who has the impressive title of project manager for the Breakthrough Propulsion Physics Project at the NASA Glen Research Center in Cleveland, Ohio.
Millis began with the oldest technology, a balloon-assisted broomstick. This does not seem like a particularly promising contender for Harry's wooden steed. First, a blimplike construction would seem unlikely to achieve the Firebolt's quoted performance of zero to 150 mph in ten seconds. (That's fast, although a fraction of the performance of a 6,000-horsepower dragster, which can cover a quarter-mile from a standing start in less than five seconds to reach 320-plus mph.) Millis also points out that balloon-based vehicles would make easy targets for Bludgers.
How about an airplane-style broom? Intriguingly, this suggestion is more magical than it may at first seem. A century after the Wright brothers made their first flight, Jef Raskin, a former professor at the University of California at San Diego and the inventor of the Macintosh computer, says that the usual popular textbook explanations for what keeps aircraft aloft are wrong.
Aircraft fly because air travels faster over the top surface of each wing than underneath. A theory by Dutch-born Daniel Bernoulli established that this speed difference produces a drop in air pressure over the top of the wing, which generates lift. (You can demonstrate this effect at home by blowing between two dollar bills.) But there is a problem, says Raskin. "The naive explanation attributes the lift to the difference in length between the curved top of a wing and the flat bottom of the wing. If this were true, planes could not fly upside down, for then the curve would be on the bottom and the flat on the top." But planes can fly upside down, and not only do some wings have the same curve on top and bottom, but even flat-winged paper airplanes can take to the skies.
The key question remains: How do wings generate lift? Robert Bowles of University College London, a mathematician with expertise in aerodynamics, agrees with Raskin that lift occurs when the flow of air around a wing is turned downward. When flow is deflected in one direction, lift is generated in the opposite direction, according to Newton's third law of motion. However, for a wing, it is crucial to understand that the downward flow depends on air being both deflected by the underside of the wing and bent by the topside.
The latter is trickier to visualize. Because air is slightly viscous it tends to stick to the top of the wing and can generate whirling masses of air called vortices. You can see this effect by adding a dash of milk to black coffee and moving a spoon through it, revealing how movement through such a "sticky" fluid generates a coffee vortex. As vortices are shed by the top surface of a wing, the flow turns downward to generate an upward force on the wing.
With the right equipment, you could detect a force on your spoon as you move it through the coffee, says Bowles. This force-the same as the one that keeps a wing aloft-depends on the angle of attack and the shape of the spoon. Mathematical models show that even flat wings can fly if they have an angle of attack to deflect air downward. As for planes flying upside down, the lift can remain positive even if the angle of attack is negative, because of the shape-a stretched teardrop-of the wing.
Although this "airfoil theory" is now standard in books on mathematical fluid mechanics, some mysteries of flight remain. How to capture the essence of turbulence (when air flow is disorderly), in a computer or clever mathematical formula has in no way been mastered by even the best Muggle scientists. Turbulence is generated to some degree by all forms of flight through air. Next time you board an aircraft, just remember that a little magic helps to keep you aloft.
Wings mark a conventional solution to the broomstick problem, and one that would be a good way to build up frequent-flyer miles, though it may be easy to lose your luggage, remarked Millis, a not entirely serious answer. Save a mention of the Slytherin team whizzing through the air like jump jets, however the many references to swooping and soaring on brooms contain no suggestion of wings, engines, or any such equipment. Harry must sit on exotic technology.
How about a rocket-assisted broom? This is an entirely feasible solution, but a stick thus outfitted could be tricky to steer and, given the long robes that wizards wear, something of a fire hazard. Which brings us to the antigravity and warp-drive brooms, a more promising approach, and a technology in which NASA seems to be very interested. Although it does not use the terms "antigravity" or "warp drive," Millis acknowledges that NASA is investigating related research at the frontier of physics.
The Quest for Antigravity
Conventional attempts to fly have relied on generating another force to counter its tug and, so far, no one has ever found any way of "shielding" matter from its effects. That, of course, has not stopped people from trying to turn off the most familiar force in the Muggles' universe. One can imagine the excitement caused in 1992 when the Russian researcher Evgeny Podkletnov announced to the world in an paper in the obscure journal Physica C that he had shielded an area of space from gravity. The apparatus that accomplished this consisted of a cooled and magnetically suspended ring of superconducting ceramic material disk 145 millimeters in diameter and 6 millimeters thick. Podkletnov applied an alternating electric current to coils surrounding the disk to make it rotate and found that this setup reduced the weight of any object placed over it by up to 2 percent. He observed the antigravity effect with a wide range of materials, ranging from ceramics to wood. The faster the rotations, the greater the reduction in gravity's force.
With Petri Vuorinen of Tampere University, Finland, Podkletnov submitted a second paper in 1996 to Journal of Physics-D. This time, however, the paper's description of additional experiments was picked up by the media and he seems to have been accused of sorcery by his peers. Tampere University-whose Institute of Material Science was at the center of the controversy generated by the announcement-declared that it no longer had links with Podkletnov, and refused to comment on whether the antigravity device functioned or not. Vuorinen denied being involved in the project, the paper was not published, and the work was dismissed as fantasy.
One of the hallmarks of real science is the way that, even if great scientists like Newton and Einstein had never lived, others would have eventually made their discoveries. In the case of antigravity, another scientist, Ning Li, had been independently researching gravity modification at the University of Alabama in Huntsville, and had studied the possibility that superconductors might generate bizarre gravitational effects, as predicted by Einstein's theory of gravity (general relativity). In the mid 1990s she, too, seemed to be getting somewhere-fast-spinning charged atoms in her superconductor were producing a gravitational field-but then she dropped out of sight.
Inspired by Podkletnov's paper in Physica C, a number of scientific institutions decided to take a closer look. Ron Koczor and his colleagues at NASA's Marshall Space Flight Center in Huntsville, Alabama, had taken an earlier interest in Li's work but could not determine how best to test her ideas with experiments. Podkletnov's approach seemed to be a simpler way to do the same thing. But their first attempts to reproduce his gravity-defying experiments proved futile according to a 1997 paper by Koczor's team.
At the time of writing, Koczor was awaiting delivery of a replica of Podkletnov's apparatus, which NASA had commissioned with $600,000 from the company Superconductive Components of Columbus, Ohio. Aware of the skeptics, of which there are very many, Koczor stresses that it is important to keep an open mind until he has a chance to test the device. (He adds: "Please don't call it an antigravity machine. You don't know the level of heartburn and pain that would cause me.")
Other commercial organizations have stated that, though they doubt the effect is real, the implications of this research are too huge to ignore. If a souped-up version of this apparatus could be fitted on a spacecraft, rocket propulsion would be history: a nudge is all that would be required for lift-off. The same, of course, would go for a broomstick: one prod, and your toes would soon be skimming the ground.
MAGNETS, THE LEVITRON AND LEVITATING FROGS
One striking example of gravity defiance is found in an enchanting toy called the Levitron, which consists of a magnet, in the form of a spinning top, that can hover an inch or three above a repelling magnetic base. At first sight, the Levitron seems truly magical. We have known that such a device should not function since 1842, when Samuel Earnshaw of St. John's College, Cambridge, published a paper that showed that levitation should be impossible using stationary magnets. The American inventor Roy Harrigan was assured as much by Muggle wizards, who warned him that he was wasting his time by trying to defy Earnshaw's theorem. Fortunately he ignored them and, like a true magician, pulled the Levitron out of his hat two decades ago, and the toy was then developed by Bill Hones of the company Fascination Inc. As if to underline its magical ability, the toy's patents referred to how its stability depended on the way it spins like a top but missed one important scientific point. Although this explanation actually violates Earnshaw's theorem, the Levitron's ability to hover patently does not.
A convincing scientific account of how it works had to wait until a 1996 study by Sir Michael Berry. Working at the University of Bristol, Berry is one of the wizards of quantum mechanics, the most revolutionary scientific theory of the past century, which was developed by European physicists who realized that the previous theories of physics did not hold true for subatomic particles, such as electrons.
The "antigravity" force that repels the top from the base of the Levitron is magnetism. Think of the base magnet with its north pole pointing up, and the top as a magnet with its north pole pointing down. As anyone who has played around with magnets knows, there is repulsion between two north poles, which balances the downward tug of gravity and makes the Levitron float.
However, in order for the toy to function, the top has to spin; otherwise, the magnetic force would flip it over. Then its south pole would point downward, and the force from the base would be attractive-that is, in the same direction as gravity-and the top would fall. The tricky part for Berry was explaining how a slight horizontal or vertical movement of the Levitron produces a force pushing the top back toward the point about which it gently bobs and weaves. It is precisely because it wobbles (technically speaking, the top "precesses") that it does not violate Earnshaw's theorem. In recent decades, one of the building blocks of atoms, the neutrons, has been trapped using a similar effect, so the theory has implications far beyond magnetic toys. However, there are no references in Harry Potter to spinning broomsticks, so there must be another way to overcome Earnshaw.
Enter the curious case of the levitating frogs, which, once again, blurs the distinctions between science and magic. The feat was carried out by Andrey Geim while at the Nijmegen High Field Magnet Laboratory in Holland, working with Peter Main and Humberto Carmona. The team suspended a frog in midair without use of mirrors, strings, sleight of hand or any other trickery. They defeated the force of gravity with a balancing force of magnetism rather than attempting to turn gravity off at its source. "This is, in fact, as close as we can-probably ever-approach the science-fiction antigravity machine," they say.
The floating frog is impressive proof of a fact that most of us do not realize: it's not just metals that respond to magnetic fields. The team has repeated this uplifting feat with grasshoppers, fish, mice and plants. In fact, it is possible to levitate magnetically every living creature due to an omnipresent form of magnetism called diamagnetism.
This kind of levitation is not ruled out by Earnshaw's theorem unlike other types of magnetism: paramagnetism and ferromagnetism. Diamagnetism is a quantum phenomenon that cannot be explained by the classical physics of Earnshaw, and it turns out that everything from wood, grapes and water to pizza, frogs and even humans can be lofted by a magnet, providing it is strong enough.
All everyday materials are made of atoms, two hundred thousand million million of which would fit on the period at the end of this sentence. And all kinds of magnetism rest ultimately on the behavior of electrons in atoms. Traditionally, atoms have been described as miniature solar systems, in which negatively charged electrons fly around the positively charged atomic nucleus like tiny spinning planets. (Today, we think of electrons as a negatively charged mist, rather than as discrete particles.)
Because electrons are electrically charged, their motion can generate magnetic fields. In this way, they turn into magnets that can themselves be affected by magnetic fields. When a magnetic field of sufficient intensity distorts the electron orbits in the frog's atoms, they generate a tiny net electric current, which, like an electromagnet, generates an opposing magnetic field. Like opposing magnets, the repulsive force pushes the fields apart.
"There is a sense in which the Levitron and the frog are the same, since diamagnetism is microscopically the result of tiny rotating magnets-little versions of the Levitron's spinning top," says Michael Berry, who has worked with Andrey Geim, now in the University of Manchester, to extend his theory to show how levitating amphibians also defy Earnshaw.
When the little frog underwent this form of levitation it looked comfortable inside the magnet and, afterward, happily rejoined its fellow frogs in the laboratory's biology department. Geim's research team has been exposed to high fields, as has one of his American colleagues who spent several hours inside a magnet (reclining, not levitating), and none of them has suffered any ill effects. Geim has even levitated a hamster, called Tisha, who went on to live to a healthy old age of three. (Remarkably, they coauthored a levitation paper in the journal Physica B by A. K. Geim and H.A.M.S. ter Tisha.) Because there are no signs that these strong static fields have any health effects, Harry could easily be carried aloft this way. All it requires is a big enough magnet. The frog was lifted two meters up a cylinder by a magnetic field 100,000 times stronger than Earth's natural magnetic field and between 10 and 100 times stronger than refrigerator magnets.
The natural pose when riding a broomstick-leaning forward, so the body is more horizontal than vertical-is in fact the best posture for magnetic levitation. The catch is that you would not really need a broomstick at all to exploit diamagnetism, and you would have to be inside a vast magnet several meters across that could generate many times the field currently used by the magnetic resonance imaging scanners that are commonly used in medicine.
"I would enthusiastically volunteer to be the first levitatee," says Michael Berry. "To be levitated in this way could be an interesting experience...more like the weightlessness experienced by astronauts in space. But there is a difference: the diamagnetism of the body is not quite uniform-tissues, bone, blood and so on have different magnetic properties-so we would feel slight pullings and pushes over the body. If the magnetic force on flesh is greater than that on bone, it would be as though we were held up by our flesh, with our bones hanging down-a bizarre reversal of the usual situation, and possibly the basis for an (expensive) type of face-lift."
Intriguingly, one of the Potter books contains a fleeting reference to how there is too much magic in the air around Hogwarts for electronics to work-a tantalizing hint that the school is bathed in an electromagnetic field powerful enough not only to disrupt sensitive microchips but also to lift a person into the sky. However, so strong a field would also exert an extraordinary tug on anything ferromagnetic, such as iron, cobalt and nickel, making its presence obvious and something of a nuisance to the inhabitants. Kennilworthy Whisp also points out that no spell yet devised allows wizards to fly unaided in human form. We may have to look elsewhere to find the secret of the Firebolt.
In other fields of physics, antigravity is beginning to be taken seriously. Strangely enough, Einstein himself formulated the idea, but then abandoned it. Today, however, there are hints that his first instincts were correct. There is growing evidence from our studies of the heavens to suggest that mysterious "dark energy" may be shoving huge collections of stars-galaxies-away from one another, which sounds as ominous as anything out of the pages of the Harry Potter books.
Einstein's 1915 theory of gravity came about after he realized that a person falling from a sufficient height would not feel his own weight, not until he hit the ground, that is. The force of acceleration matches that of gravity so precisely that the faller's sensation of weight is canceled out. Thus gravity and acceleration are equivalent. Einstein recognized that his 1905 special theory of relativity had to be generalized so that it could describe varying accelerations found in real-life situations, when gravitational fields are not uniform.
General relativity replaced the previous way of describing gravity devised by Sir Isaac Newton. Einstein did not view gravity as a force, as did Sir Isaac, but the curvature of a four-dimensional mixture of space and time called space-time. While special relativity deals only with flat space-time, general relativity deals with space-time that has been warped by gravity. For example, space-time is warped into a shape like the inside of a bell around Earth so that falling objects are toppling into the bell and orbiting satellites and spacemen are rolling around within it.
Einstein's theory suggested the universe was dynamic: It would either expand, then collapse under the relentless pull of gravity, or it would continue to expand forever. However, like many scientists of his time, he assumed the universe was not contracting or expanding, but unchanging. To make his theory predict a static universe he added a fudge factor, something he called the "cosmological constant," representing antigravity, though he had no idea if it was real. Einstein said later that his introduction of a cosmological constant was the biggest blunder of his career. He had missed the chance to predict what the American astronomer Edwin Hubble discovered in 1929: the universe is expanding. However, recent experiments suggest that Einstein's original "repulsive suggestion" of antigravity was on the right track and that the expansion of the universe recently began speeding up, as if something were pushing it: the antigravitational force of dark energy seems to be loosening gravity's grip. Dark energy gets stronger as the universe expands. That means our cosmos may fly apart faster as time goes by, ending with a whimper, not a bang.
The source of this repulsive gravity is unknown. It may be something entirely new, and these first observations may mark the start of efforts to grapple with a puzzle as mysterious as the pitch-black monolith that stars in Stanley Kuplbrick's masterpiece 2001: A Space Odyssey.
Over huge distances this force becomes something to reckon with, and is strong enough to dent the effects of gravity. However, there is skepticism that it will be possible to harness this force to lift a broomstick. "The only more or less accepted fact about antigravity (and there is not universal agreement) is the evidence for the acceleration of the expansion of the universe, which points to a 'cosmological constant' or 'energy field' (normally called quintessence) which produces antigravity," says Miguel Alcubierre of the Universidad Nacional Autonoma de México. "The effects, however, are extremely small."
Wriggling Through Wormholes
If we could find materials that have enormous non-gravitational tension or pull, another form of transport might become possible. (Although a rubber band shows this kind of behavior, as do electric fields, their pulls are just not strong enough.) In that case we might be able to create wormholes, which are the cosmic equivalent of their counterpart in an apple. But rather than providing a route between core and peel, cosmic wormholes provide shortcuts between two distinct points in space-time, separated by five miles or five million, five years or five million years. These could explain some of Harry's more spectacular journeys such as the one he took through Tom Riddle's diary. The description of his falling into one page, June thirteenth, sounds very much as though he was passing through a wormhole portal. Wormholes may likewise snake to the sorcery shops of Diagon Alley or from King's Cross Station to Platform Nine and 3/4.
To understand wormholes, we must turn to Einstein's theory of gravity as warped space-time. Then we have to look at what happens as a result of the extreme space-time distortions caused by the biggest gravitational tug of all, that occurring around black holes, where gravity is so intense than even light cannot escape. While working with Nathan Rosen in Princeton in the 1930s Einstein had discovered that the equations of relativity show that a black hole forms a bridge between two places/times (regions of space-time). Such an "Einstein-Rosen bridge"-which we now call a wormhole-could lead to the possibility of movement through vast distances across the universe, or even time travel.
But it seems unlikely that wizards use black holes for transportation. For one thing, a wormhole itself cannot even exist for long enough for light to cross from one part of the universe to the other. In effect, gravity quickly slams this portal shut. This proved to be a headache when the late astronomer Carl Sagan decided to write a science-fiction novel, Contact. Sagan wanted to fix this problem so that his characters could travel from Earth to a point near the star Vega. In 1985 he approached Kip Thorne at Caltech for help, who in turn enlisted the aid of his students.
They tried to work out what kinds of matter and energy would be needed for the feat of interstellar travel. In 1987 they reported that for a wormhole to be held open, its throat would have to be threaded by some form of exotic matter, or some form of field, that would exert negative pressure and have antigravity associated with it.
Thorne recently said that researchers were still studying whether it was possible to get enough exotic matter in the mouth of a wormhole to maintain its gape. But the bottom line, at present at least, is that it looks as though it will be a difficult feat. "I regarded it as fairly negative a few years ago and it has become more negative," declared Thorne. However, he admits that his skepticism that wormholes will ever be established to be feasible for travel is not the final word on the matter.
That is just as well for Harry Potter. His experiences do seem to mirror those described in Contact. Sagan describes traveling through a wormhole as racing down a long dark tunnel. After a pinch of Floo powder was thrown into the burning flames of a fireplace, Harry described how he felt as if he were being sucked down a giant plug hole. As he spun around, blurred fireplaces flashed past him while bacon sandwiches churned within him. Similarly, Sagan referred to the texture of the tunnel walls as they flashed past, from which it was possible to sense the incredible speed, one at which even a collision with a sparrow would produce a devastating explosion.