The Physics of Superheroes: Spectacular Second Edition

by Kakalios, James

  This is an intrinsically quantum mechanical phenomenon, in that classically there is no possible way to ever find yourself in the second court. This quantum process is called “tunneling,” which is a misnomer, as you do not create a tunnel as you go through the wall. There is no hole left behind, nor have you gone under the wall or over it. If you were to now run at the wall in the other direction, it would be as formidable a barrier as when you were in the first open-air court, and you would now have the same very small probability of returning to the first court. But “tunneling” is the term that physicists use to describe this phenomenon. The solutions of Schrödinger’s equation that predict tunneling phenomena find that the faster you run at the wall, the larger the probability you will wind up on the other side, though you are not moving so quickly that you leap over the wall. This is no doubt how the Flash, both the Golden and Silver Age versions, is able to use his great speed to pass through solid objects, as shown in fig. 36. He is able to increase his kinetic energy to the point where the probability, from the Schrödinger equation, of passing through the wall becomes nearly 100 percent.

  Fig. 36. Scene from Flash # 123, where Jay Garrick, the Golden Age Flash, demonstrates the quantum mechanical process known as “tunneling.” The matter-wave of an object has a small but nonzero chance of passing through a solid barrier. The faster the object approaches the barrier, the greater the transmission probability. As Jay correctly notes, the barrier is unaffected by the tunneling process.

  Consider two metals separated by a vacuum. An electron in the metal on the left is like a person in the first open-air handball court. Instead of a concrete wall, a thin vacuum separates this electron from the second metal, which can be considered another open-air court. Solving the Schrödinger equation for this situation, one finds that the electron in one metal has a small but nonzero probability of finding itself in the second metal. The electron does not arc across the vacuum gap and does not have enough kinetic energy to escape from the metal on its own. (This is a good thing. Otherwise, all objects would be continually leaking electrons all over the place, and static cling would be one the most gripping problems of the day.) Rather, the electron’s matter-wave extends into the separation space, decreasing in magnitude with distance in the gap. A similar phenomenon occurs with light waves moving from a denser to a less-dense medium. Under conditions for which the light wave should be totally reflected at the interface, there is still a small diffraction of light into the less-dense medium. The diffracted wave’s magnitude decreases the further into the less-dense medium it progresses. Since the square of the electron’s wavefunction represents the probability of finding the particle at a point in space and time, a finite magnitude for the “ matter-wave” indicates that there is a nonzero probability that the electron will be found in the second metal. If the gap is not too large (compared with the electron’s matter wavelength, which in practice means roughly less than one nanometer), then the matter-wave will still have an appreciable magnitude in the second metal. Let us be clear, the electron on one side of the barrier moves toward the obstruction, and most times simply reflects off the wall. If a million electrons strike the barrier then, depending on its height and width, 990,000 electrons might be reflected and 10,000 would wind up on the other side.

  When the separation between the two metals is too large, then the chance of tunneling for even the most energetic electrons becomes very, very small. A person’s momentum is large, so our matter-wavelengths are very small—much less than a trillion trillionths of the width of an atom and much smaller than the width of the concrete wall separating us from the second open-air handball court. Nevertheless, if you were to run toward the concrete wall, there is a very tiny probability that your matter-wave will arrive on the other side of the wall. The greater your kinetic energy, the larger will be your chance of tunneling. Those who doubt that this is indeed possible are invited to begin throwing themselves at concrete walls right now, and to persevere in their attempts no matter how discouraging the initial results.

  Electrons in a solid rattle around at a rate of more than a thousand trillion times per second. Consequently, in one second they have a thousand trillion opportunities to tunnel through a barrier. Send enough electrons against a barrier, and if the height of the wall is not too high nor the thickness of the separation too large, an appreciable fraction will indeed tunnel to the other side. Not only has the phenomenon of quantum-m echanical tunneling been verified for electrons but it is the central principle behind a unique type of device called a “scanning tunneling microscope” that enables one to directly image atoms. As shown in fig. 37, when a metal tip is brought very close to, but not touching, a metal surface, it can intercept the electron clouds surrounding each atom on the surface. When the electrons tunnel from an atom to the metal tip, an electrical current is recorded in a meter connected to the tip. Whether or not tunneling occurs is very sensitive to the separation between the atoms on the surface and the scanning metal tip. A change in distance of just the width of an atom can change the probability of tunneling by a factor of more than a thousand. By moving the tip slowly over the surface and carefully measuring the current at each location, the position of each atom on the surface can be mapped out.

  Just such an image can be seen in fig. 38, which shows the location of carbon atoms on the surface of a crystal of graphite (more commonly known as “pencil lead”). The gray scale is not real (carbon atoms aren’t really black or white, or any color for that matter), but is used to represent the magnitude of the current recorded in the tip at any position, which in turn reflects the electron density at each spot. Fig. 38 shows us that the carbon atoms in graphite form hexagons much like the six-sided plates that make up a snowflake. The fact that the carbon atoms form a hexagonal lattice implies that a crystal of graphite consists of sheets of carbon atoms, as in fig. 38, lying atop one another. Building a three-dimensional crystal out of such two-dimensional sheets, the solid essentially stacks each sheet atop the other like the thin layers in a puff pastry. The planes in solid graphite are so loosely held together that you can easily peel them apart with just your hand, simply by scraping a pencil point along a sheet of paper. The fact that this form of solid carbon makes a better writing implement than if all carbon atoms had four equally strong bonds (otherwise known as “diamond”) can be inferred directly from this atomic image. We’ll have more to say about the nature of carbon bonds in Chapter 25.

  Fig. 37. Cartoon showing the basic mechanism of a scanning tunneling microscope. A fine metal tip is brought very close to a conducting surface. By very close, I mean within a few atoms’ widths. When the tip passes over an atom on the surface, the electron probability clouds of the atom may lead to quantum-mechanical tunneling into the tip. When the tip is right above an atom, the tunneling probability is high, and the current in the tip is large. In this way the atoms of the surface can be scanned and imaged.

  In the next chapter we will discuss the physics of transistors and diodes, and I’ll give away the punch line now and tell you that these semiconductor devices are essentially valves that regulate and amplify the flow of current. One way this current can be controlled is through the tunneling process. Normally, when two conductors are set close to each other, separated by a thin insulating barrier, no current can flow from one conductor to the other. By applying a voltage across this sandwich structure, the effective height of the wall separating the electrons of one region from the other can be varied. As noted, the tunneling probability is a very sensitive function of this barrier height. In this way, the tunneling effect is used to modulate the flow of electrons across the device. These “tunneling diodes” are integral components of cell phones, as well as many other solid-state devices. Quantum- mechanical tunneling is therefore not an esoteric theoretical novelty, or useful solely in atomic microscopes. Many of the products we associate with our current lifestyle would not be possible without tunneling being a reliable phenomenon.

  Fig. 38. Scanni
ng tunneling microscope image of the surface atoms of graphite, the form of carbon used in pencil lead. Each white spot indicates a region of space where the tunneling current was high for that tip location (see fig. 37). The hexagonal lattice of carbon atoms is readily apparent. The grayscale is used to indicate the intensity of the tunneling current. The y-axis extends for 1nm while the x-axis is 0.5nm long. Courtesy of Dr. Laura Adams and Prof. Allen Goldman at the University of Minnesota.

  When we apply the laws of quantum physics to large objects like Kitty Pryde of the X-Men (fig. 35), we find that tunneling is still possible, but very unlikely. How unlikely? Assuming Kitty’s mass is 50 kilograms (such that her weight is 110 pounds—one of her code names was Sprite, after all), then even if she could run at a wall as fast as she could a million times a second, it would take longer than the age of the universe before she could expect to quantum- mechanically tunnel through to the other side. Clearly the one-time miracle exception comes into play in a big way here. With our improved understanding of physics, we can now more accurately describe Kitty Pryde’s mutant power as being able to alter her macroscopic quantum wave function, increasing her tunneling probability to near 100 percent at will. Quite useful when one has locked the keys inside the car.

  A long-standing puzzle in comic books is that if Kitty Pryde can walk through walls, why doesn’t she fall through the floor at the same time? How, when she is “phasing” and immaterial, can she walk? In X-Men # 141, it was argued that while phasing, Kitty actually walks on a surface of air, and is not in actual contact with the floor. While immaterial in her phasing mode, she is therefore unaffected by any trapdoors opening beneath her. Assuming for the moment that she can indeed walk on air—that is, that somehow the air provides enough resistance to the backward force of her feet that it supplies a forward thrust, propelling her forward—the question still arises as to how her partially material foot can follow her body through a wall.

  If the mechanism by which she is able to pass through solid barriers is indeed quantum- mechanical tunneling, then it is perfectly reasonable that she would not slide through the floor. When an electron tunnels from one side of a barrier to the other, it conserves energy in the process. If it has a certain amount of energy on one side of the barrier, it has the same total energy after the tunneling process is complete. In fact, tunneling occurs only when the energy of the object is exactly the same on both sides of the barrier. The ratio of kinetic to potential energy can change when tunneling across a barrier from one allowed region to another. But Kitty has shown that even when not walking through a wall, she can “phase” as bullets or energy blasts pass through her. In this case she is “tunneling” as she stands still and lets the “barrier” move through her.

  Technically, she cannot walk while tunneling, as she may not increase her energy by pushing against any object, whether the object is the solid floor or a cushion of air. But at the same time, she cannot lose any energy either. All she needs to do is walk normally as she approaches a wall, turn on her mutant power of maximizing her tunneling probability, and she will glide through the partition with the same speed as she had when she neared it. For those times when she desires to phase through a floor, such as in Astonishing X-Men # 4, where she actually phases through nearly a hundred feet of solid metal to reach an underground laboratory, she would jump up slightly while in her corporeal mode, and then right before her feet touch the ground, activate her mutant tunneling ability. She would continue her motion with the last kinetic energy she had while solid, and descend with a steady velocity. It’s probably safer for her if she keeps her mutant tunneling power activated until she is near the floor in the lower room, and avoids becoming material near the ceiling, where she would have to deal with her now-large gravitational potential energy.

  24

  SOCK IT TO SHELLHEAD—SOLID-STATE PHYSICS

  IF ANY SUPERHERO DEMONSTRATES the value of a physics education, and in particular the study of semiconductors, which is part of solid-state physics, it is Iron Man, who wore a high-tech suit of armor to fight for justice. The heart of Iron Man’s amazing offensive and defensive capabilities was a modern (in 1963) technological marvel: the transistor.

  The transistor truly is a revolutionary device, as its ability to amplify and modulate voltages has had a profound impact on all of our lives. Initially, the transistor was used solely to duplicate the functions of vacuum tubes, so that radios and television sets could become lighter and more efficient. As scientists and engineers learned how to make transistors smaller and smaller, their use for mathematical calculations led to the development of electronic computers. The solid-state transistor is the fountainhead of nearly every electronic device in use today. At this point, we have enough physics under our belt to understand how this remarkable device works. Before delving into semiconductor physics, let’s review the events that led to Shellhead’s76 comic-book debut.

  The Cold War loomed large in the monthly adventures of Silver Age comic books of the late 1950s and early 1960s. In DC comics, fighter pilots with the “right stuff” figured prominently in several offerings. When an alien Green Lantern crash-landed on Earth and was at death’s door in Showcase # 22, he instructed his power ring to seek out someone brave, honest, and fearless to whom he could bequeath the ring and power lantern. The ring selected an American test pilot, Hal Jordan. (In DC’s Showcase # 6, another fighter pilot, Ace Morgan, led the Challengers of the Unknown, while the test pilot Larry Trainor was transformed into Negative Man during a flying mishap, as relayed in My Greatest Adventures # 80.) The Marvel Age of comics began in 1961 (the same year that both Russian and American astronauts first traveled to space), when four adventurers—a scientist, his girlfriend, her teenage brother, and a former fighter pilot—took an unauthorized rocket flight through a cosmic radiation belt in order to beat the Communists “to the stars.” The cosmic rays they absorbed would turn this quartet into the Fantastic Four.

  The “red menace” of Communism continued to rear its head in Marvel superhero comic books fairly often. The Hulk, who appeared a year after the debut of the Fantastic Four, owed his existence to a Commie spy, when physicist Dr. Robert Bruce Banner was exposed to an overdose of gamma radiation from a detonating gamma bomb. His assistant (who was in reality a Communist agent—you would think that a research assistant named Igor Starsky would have been a tip-off when he received his security clearance, but never mind) deliberately did not stop the countdown, hoping to eliminate America’s leading bomb expert, but instead created the Hulk.

  The Soviet presence in early Marvel comics was faced by the Human Torch, Ant Man, Spider-Man, the Mighty Thor, and the Avengers. But none of the mighty Marvel superheroes of the early 1960s were so closely allied with the Cold War as the invincible Iron Man. Tales of Suspense # 39 introduced the brilliant inventor and industrialist Tony Stark to the Marvel universe. Using his mastery of transistorized technology, Stark developed many new weapons for the military as part of his effort to help the United States win the fight against Communism in Indochina. Not content to merely test his new weapons in the lab, Stark accompanies an inspection team into the jungles of Vietnam, so that he could more accurately assess the effectiveness of his inventions. Alas, we soon see why more CEOs do not take such a hands-on approach to quality control. A booby trap kills the military advisers traveling with Stark, and leaves Tony himself with a piece of metal shrapnel lodged in his chest, dangerously close to his heart. To make matters worse, he is captured and brought to the hidden camp of Wong-Chu, “the red guerrilla tyrant.” A doctor at Wong-Chu’s camp determines that the shrapnel is actually migrating and that in a few days it will reach Stark’s heart and kill him.

  Wong-Chu offers Stark a deal: Work in my weapons development lab (this is apparently a pretty well-equipped guerrilla camp) in return for surgery that will save your life. Stark agrees, intending to use his brief remaining days to create some sort of weapon to both save his life and combat his captor. Along with the brillian
t physicist Professor Yinsen, also a captive of Wong-Chu, Stark constructs a metal chest plate that, once fully electrically charged, will prevent the shrapnel from reaching his heart. Realizing that he will need offensive and defensive weapons if he and Yinsen are to escape the guerrilla camp, the chest plate becomes part of an iron suit, which contains an array of transistorized weaponry. The suit is completed moments before the shrapnel can claim Stark’s life, though Prof. Yinsen is killed when he decoys their captors away from Stark as the chest plate finishes charging up. Yinsen’s death is avenged, and the other prisoners in the camp are freed as Iron Man defeats the Communist warlord. (The 2008 film Ironman would faithfully follow this origin storyline, substituting Middle Eastern terrorists for Communists.) Making his way back to the States through the jungles of North Vietnam (a story not fully told until years later in Iron Man # 144), Tony Stark would continue to use his technological suit of armor to defend America against Communist aggression.

  And boy, did Shellhead attract the Communist foes! At times he seemed to have a “red magnetism” field built into his suit of armor. Borne out of the Vietnamese conflict, Iron Man would battle more Communist villains in his first four years than nearly all other Marvel superheroes combined. Iron Man would face the Red Barbarian (Tales of Suspense # 42); the Crimson Dynamo (Tales of Suspense # 46 and 52—a Russian power station built in the form of a suit of armor designed to defeat Iron Man); the Mandarin (Tales of Suspense # 50, 54, 55, 61, 62—a Chinese warlord modeled after the Sax Rohmer pulp fiction villain Fu Manchu, who possessed ten deadly rings of power); and the Titanium Man (Tales of Suspense # 69-71—a Soviet-built stronger version of Iron Man created to defeat our hero in televised conflict, thereby proving to the world the superiority of Communism over capitalism). Throughout all this, Tony Stark maintained the fiction that Iron Man was a separate person, hired by Stark to serve as his body-guard. Given the number of times Communist agents tried to kidnap Stark or steal his research plans, this was not such a far-fetched cover story.