It was revealed in the pages of JLA that J’onn J’onzz is mistaken when he considers himself the last survivor of the Martian race, when the Earth is attacked by a small army of evil Martians, each one possessing J’onn’s superpowers. The Justice League lures the evil Martians to the moon, where the lack of an atmosphere convinces the Martians that they have no reason to fear a fire weakening them. However, while J’onn J’onzz uses his mental telepathy to distract these villains, Superman, Wonder Woman, and Green Lantern employ an enormous cable to drag the moon into the Earth’s troposphere. An array of magic-based superheroes use their mystical powers to prevent both the moon and the Earth from suffering geological catastrophes from their intense gravitational attraction. Our satellite now possesses a combustible atmosphere, and the evil Martians quickly surrender and submit to banishment to another dimension (the Phantom Zone, in fact) rather than being incinerated. Even if you grant all of the above as one major-l eague miracle exception, there is still a serious physics problem with this story line.
Newton’s second law, F = ma, tells us that if a net force is applied to a mass, no matter how large, there will be a corresponding acceleration. By the late 1990s DC Comics had established that Superman was capable of lifting eight billion pounds. Let’s assume that, given the enormous stakes, both Wonder Woman and Green Lantern exerted themselves to provide an equivalent force as they pulled on the moon. So the total force that these three heroes can supply is twenty-four billion pounds. Since the magic-based heroes are nullifying the effects of gravity, we’ll assume that as the moon comes closer to the Earth there is no assist from Earth’s gravitational field (this will keep the calculation at a simple level). The moon has a mass of nearly seventy billion trillion kilograms. Newton’s law therefore indicates that the moon will indeed accelerate owing to this force, but the rate of change of motion will be very, very small. The acceleration of the moon will be 5 trillionths feet/sec2 (the acceleration due to gravity on the surface of the Earth is 32 feet/sec2), and so it will take a very long time to displace the moon a significant distance. At this acceleration, the time needed for the moon to travel roughly 240,000 miles from its normal orbit to within our upper atmosphere is more than 735 years! We can only conclude that J’onn J’onzz performed some outstanding stalling in order to keep the evil Martians from realizing what was going on for more than seven centuries!
WITH THE WINGS OF AN ANGEL, COULD YOU FLY?
Another of the original members of the mutant team the X-Men introduced in 1963 was Warren Worthington III, whose mutant gift comprised two large, feathered wings growing out of his back. None of the other members of this superhero team possessed the power of flight, and aside from Iceman’s ice ramps, the Angel was the only character who could avoid walking or taking the bus when called upon to face off against the Brotherhood of Evil Mutants.85 Other winged superheroes or villains, such as DC Comics’ Hawkman or the Spider-Man villain the Vulture, used “antigravity” devices such as Hawkman’s Nth metal, to overcome gravity. They employed their wings connected to their backs in the case of Hawkman or Hawkgirl or sprouting from his arms for the Vulture, as steering devices to help them maneuver while airborne. In contrast, the X-Men’s Angel used his wings as a means of levitation. It certainly seems reasonable that having wings growing out of your back would enable you to fly, but could it really?
Birds and planes manage to slip the surly bonds of gravity through Newton’s third law—that for every action there is an equal and opposite reaction. A common misconception is that the pressure change induced by a fast-moving object (termed the Bernoulli effect), underlies how airplanes fly. We encountered this pressure differential when we considered the Flash dragging Toughy Boraz behind him in his superspeed wake in Chapter 4. A fast moving object such as the Scarlet Speedster must push the air out of his way as he runs, and consequently leaves a region of air with a lower density behind him. As the air races back to fill this partial vacuum, through the same principle as in our discussion of entropy in Chapter 13, it will push anything in its way, such as the litter swirling behind fast moving traffic or trains. However, if the difference in wind speed above and below the wing is a result of the wing’s contour, then planes should not be able to fly upside down, because the pressure difference generated by the Bernoulli effect would tend to push the plane toward the ground.
In any case, we can always rely on Newton’s third law, which tells us that forces always come in pairs. To provide an upward force on the airplane wing equal to or greater than the weight of the plane, an equivalent downward force from the wing must be applied to the air moving past it. The down draft of air in the region underneath the wing results in an upward lift that carries the plane into the wild blue yonder. When Superman leaps, he pushes down on the ground so that an equal and opposite force pushes back on him, starting him up and away. Similarly, birds flap their wings, pushing a quantity of air downward. The downward force of the wing on the air is matched by an upward force by the air on the wing. The greater the wingspan, the larger the volume of air displaced, and the greater the corresponding upward force. This is why it is impossible for Prince Namor the Sub-Mariner to fly using his tiny ankle wings. These petite wings are too small to provide sufficient lift to counter Namor’s weight.
If Warren Worthington III weighs 150 pounds (equivalent to a mass of 68 kilograms), then his wings must provide a downward force on the air of at least 150 pounds, such that the air’s reaction on his wings balances his weight and keeps him above the ground. Of course, if he wants to accelerate, then his wings have to provide a force greater than 150 pounds in order for there to be an excess force (upward lift minus downward weight due to gravity) to provide a net acceleration. If his wings provide an upward force of 200 pounds while gravity exerts a downward force of 150 pounds, then Warren experiences a net vertical force of 50 pounds. Force equals mass times acceleration, so this upward force of 50 pounds creates vertical acceleration of 11 feet/sec2. With this acceleration, the Angel will go from 0 to 60 mph in a little more than eight seconds, neglecting the considerable air resistance that he would have to overcome. Once he stops flapping his wings, the only force acting on him is gravity pulling him back to Earth. Of course he can glide once airborne, but he must continue to apply a downward force on the air to truly fly and not coast.
Two hundred pounds is a considerable force for his wings to apply, but it is not unreasonable that a person could bench press 133 percent of his body weight. Birds such as the California condor or the wandering albatross weigh roughly thirty or twenty pounds, respectively, and yet are able to generate sufficient force to fly. But Warren Worthington III is not built like a bird. Birds do not have wings growing out of their backs—their arms have evolved into wings. They have two additional modifications that assist their arm-wings: (1) They have a keeled sternum bone—that is, birds have a hinge built into the flat bone in the center of their chests that is comparable to your rib cage. This hinge acts as an anchor point for their other adaptation, namely (2) birds have two extremely large chest muscles, the supercorocoiderus and the pec toralis, used for beating their wings. Birds have so much breast meat because they need these muscles, their pectorals, to be large, as they provide the majority of the force to the wings in flight. Recall from chapters 8 and 25 that the strength of bone or muscle increases with its cross-sectional area. Consequently, the Angel must have enormous pectorals if he is to be able to use his wings to get off the ground. With a wingspan of 16 feet and a weight of 150 pounds, Warren has a weight-to-wingspan ratio of nine pounds per foot, in contrast to a ratio of three pounds per foot for a California condor. Warren’s arms do not participate in supplying a force to his wings, and he must provide an upward lift using only his chest and back muscles, making him a muscle-bound—and fairly ineffective superhero.
There are other adaptations for flight that Warren could possess that would require additional miracle exceptions. To reduce their body weight, birds have lightweight bones, wi
th a very porous structure that yet remains remarkably strong. Birds also have very efficient respiratory systems, so that every single oxygen molecule residing in their lungs is replaced within two deep breaths. In contrast, with every breath we take, we exchange only 10 percent of the air molecules residing within our lungs. Birds need to be able to rapidly refresh their air supply, as their breast muscles are working so hard to maintain them aloft. Warren’s breathing could be similarly efficient. But for all this, unless he is to be drawn with enormous pectoral muscles—more fitting for some of the female superhero characters from the 1990s—the wings on his back are more ornamental than functional.
ENTER . . . THE VISION!
When Roy Thomas took over the writing duties of the Marvel comic book The Avengers in the mid 1960s, he would frequently reintroduce Golden Age characters with a new Silver Age twist, just as DC Comics had done when they initiated the Silver Age. One of the more popular characters created by Thomas and artist John Buscema is the Vision. Originally a supernatural costumed crime-fighter in the 1940s, the new Vision introduced in Avengers # 57 is an android86 created by Ultron, another android. Ultron is one of the Avengers’ most dangerous foes, and the Vision was initially intended to infiltrate the superteam in order to destroy them from within. Rebelling against his programming, the Vision saved the lives of the Avengers and went on to become a valued member of the team.
In addition to laser vision, the power of flight, and the mind of a computer, the Vision possessed the superpower of total independent control of his body’s density. He could make his body, or any part thereof, as hard as diamond or so insubstantial that he could pass through solid objects. Kitty Pryde of the X-Men walks through walls using her mutant ability to vary her quantum-mechanical tunneling probability, but the Vision should stick to using the door when he wants to enter a room.
The density of any object is defined as the mass per volume, and can be altered either by changing the mass or varying the volume. The volume is governed by the average spacing between atoms. Any solid typically has its atoms packed fairly closely, so the atoms can be considered to be touching (they have to be this close in order to form chemical bonds, which are what hold the atoms together in a solid after all). Very roughly, all solids have the same density, within a factor of ten or so.
Even if the Vision could control his density at will and could maintain the structural integrity of his body, he could not pass through walls. A gas, such as the air in your room, is comparatively dilute, with the average spacing between atoms being roughly ten times larger than the size of an atom. Yet the fact that the air in your room is less dense than the walls does not mean that the air can pass through the solid walls. Good thing, too, otherwise the air in an airplane would leak out through the fuselage and make air travel an even more unpleasant experience. We must therefore conclude that Ultron made a second error when he constructed the density-altering Vision (the first was believing that such a noble android would betray the mighty Avengers).
CAN THE ATOM USE THE TELEPHONE TO REACH OUT AND TOUCH SOMEONE?
The DC superhero the Atom has appeared throughout this book, and his ability to reduce his size and mass independently have provided excellent illustrations of a wide range of physical phenomena. Of course, occasionally his shrinking would take him to ridiculous extremes, such as whenever he visited other worlds that contained civilizations, cities, and advanced technology all residing within an atom. Given that there are nearly a trillion trillion atoms in a cubic centimeter of a typical solid, it’s amazing that the Atom ever managed to find these nanoworlds, unless they are a routine feature of every element in the periodic table. The implausibility of the Atom’s powers was slyly acknowledged in 1989, in a scene in his second regular series, The Power of the Atom # 12. In this story, the Atom shrinks both himself and a colleague in order to escape a supervillain’s death trap, and they wind up decreasing to subatomic lengths in order to pass through the empty spaces in the floor’s atoms. Pausing in their miniaturization, they discuss the events of the past few issues while sitting on an electron. The Atom’s friend suddenly notes that they are smaller than oxygen molecules and wonders, “How are we even breathing?” To which the Atom honestly replies, “I’m not sure.”
Superman can fly, the Flash can run really fast, Hawkman has his wings and antigravity belt, Storm rides on thermally generated air currents, but how do you get around when you’re very, very tiny? Ant Man uses flying carpenter ants as his personal taxi service, the Wasp has wings that grow out of her back when she shrinks, but the Atom has Bell Telephone. In his Silver Age debut issue, Showcase # 34, the Atom employs a unique mode of transportation. In this story he needs to confront a small-time crook named Carl Ballard who is clear across town. Presumably, after looking up Ballard in the phone book, the Atom dials his number while setting up a metronome near the receiver, which creates a “tick-tock” sound. Shrinking himself smaller and smaller, the Mighty Mite jumps into one of the holes on the speaker of his telephone, and in the next panel we see him flying out of the receiver of Carl Ballard’s phone.
The “explanation” for this trick is revealed on a text page in the back of the comic.87 By dialing Ballard’s phone number, the Atom causes an electrical impulse to travel from his phone to the central telephone exchange, which then forwards the signal to Ballard’s phone. When the circuit is completed once Ballard answers the ringing phone, the signal—i n this case the ticking metronome—is transmitted from the Atom’s phone to Ballard’s. At this point the Atom jumps into his speaker, shrinking down to the size of an electron, and rides these electrical impulses from his phone to Ballard’s.
The writer of this text page, DC Comics editor Julie Schwartz, correctly describes how a telephone transfers sound into electrical impulses. A thin diaphragm vibrates when sound waves strike it, which in turn compress or dilate carbon granules that are adjacent to the membrane. The electrical conduction through the carbon grains is very sensitive to how tightly they press against one another. As you speak, the interconnections between the grains alternately contract or expand, and the electrical signal down the wire is appropriately modified. At the other end of the telephone connection, the electrical signal causes other carbon grains to undergo equivalent vibrations that are transferred to another diaphragm. The diaphragm’s vibrations create pressure waves in the air that are then detected by the ear of the person receiving the call. All of this Julie Schwartz got right. Where he goofed is in assuming that the Atom could hitch a ride on the electrical impulses propagated down the wire.
When you speak, complex sound waves can convey all sorts of information. The sound waves can be detected by another membrane (such as an eardrum), causing it to vibrate in accordance with the amplitude, wavelength, and even phase information encoded in the message you spoke. But it is the wave that carries that information—not the air you expelled from your mouth. By speaking, you set up alternating regions of less-dense and more-dense air (equivalently you can think about the density variations as pressure modulations—a reasonable approximation at a constant temperature) that move away from the speaker. It is not the air coming from your mouth that reaches the listener; otherwise you would never have to worry about noisy neighbors in the apartment next door.
Similarly, the information encoded in electrical impulses in a telephone wire is transmitted by means of density waves of electrons, rather than having the electrons move down the wire. What happens is that a region of electrons of higher-than-normal density is unstable (as the negatively charged electrons repel each other) and expands into the adjacent regions, causing a buildup of electron density in the next spatial location, which in turn causes a bulge farther down the line, and so on. The speed of this transmission is determined by the electrostatic repulsion that pushes the electrons away from each other. That is, if I shake one electron, how long will it take a second electron some distance away to respond to the first electron’s motion? Pretty quickly, as it turns out, as the electr
ical interaction between two charges in the wire is communicated at roughly one third of the speed of light. Depending on the distance, there will be a barely perceptible time lag between moving the first charge and it being noticed by the second charge. The speed of light is so fast—186,000 miles per second—that this time lag will be less than a billionth of a second over a distance of 12 inches. If the Atom were riding on one electron carrying the electrical impulse signal along the telephone wire, he would have to jump to the next bunch of electrons with the speed of light in order to “ride the wave” all the way to the receiver.
It’s a good thing that the information in a telephone wire is in fact transmitted at the speed of light, as the average speed that an electron moves along a wire in response to an external electric field is less than a millimeter per second, nearly a trillion times slower. If you had to wait for the electrons to physically travel along the telephone wires before your message could be sent, it would be quicker to just walk to the house of the person you’re calling and speak to her face-to-face.
EVERY PHYSICIST’S SECRET SUPERPOWER
When not fighting crime as the Atom, Ray Palmer’s civilian identity is equally heroic, for he is a physics professor at Ivy University. As mentioned in Chapter 13, it was the late-night discovery of a strange meteorite that led to the research breakthrough that enabled Palmer to develop a second career as a costumed crime fighter. As shown in fig. 43, Palmer discovers that the meteor is in fact a chunk of white-dwarf-star matter that will enable him to miniaturize himself and independently control his mass. Ray strains to lift and carry the meteorite, which is roughly twelve inches in diameter, over to his car. We are privy to Prof. Palmer’s thoughts as he struggles with the great weight. “So heavy—I can hardly lift it! Puff! I don’t know the odds against one white dwarf hitting another out in space—Puff—but it could happen—and when it did, this piece drifted until it landed in this field.” (By the way, as also shown in fig. 43, in the mid 1960s, physics professors typically drove Cadillac convertibles.)
The Physics of Superheroes: Spectacular Second Edition Page 38