The Physics of Superheroes: Spectacular Second Edition (21 page)

To understand what the consequences are when the size of the opening is only a few times bigger than the wavelength of light, consider water waves on the surface of a large lake. A channel is formed between two docks that ride low on the surface of the water. When the separation of the docks is very large, say half a mile apart, compared with the spacing between peaks of the water waves, the waves pass through this region with no noticeable perturbation. Right near the dock, as the waves break, there is a change in the wave front, but in the middle between the docks the waves are hardly affected by the docks. This is the situation for Henry Pym at his normal height, when his pupil is ten thousand times larger than the wavelength of light. For the miniaturized Ant-Man, it is as if the two docks narrow to a bottleneck, so that the separation of the docks is only a few times more than the separation between adjacent wave peaks. The waves still move through the constriction, but as they scatter off the edges of each dock they set up a complicated interference pattern on the other side of the obstruction. This effect is termed “diffraction” and is most noticeable when the dimensions of the object scattering a wave are comparable to the wavelength. If you were hoping to gain information about the cause of the water ripples by examining the wave fronts, you would have obtained a clean, sharp image when the docks were thousands of feet apart and a distorted and confusing picture when the docks were only separated by a few feet.

The effect for Ant-Man is that the image he observes through his shrunken pupil will be blurry and out of focus. This is why an insect’s eye, and in particular its lens, is radically different from the lens in a human’s or larger animal’s eye. Insects use compound lenses that adjust for the diffraction effects. Even so, it would be hard for a fly to read a newspaper, even if he did care about current events. An insect’s eye is very good at detecting changes in light sources (such as the moving shadow created by the rolled-up newspaper of doom), but poor at discerning the contrast between sharp edges. Consequently they rely on other senses, such as smell and touch (hair filaments detect subtle variations in air currents) to navigate their way through the wide world. Unfortunately for Ant Man, the one sense that is least affected by miniaturization, smell, is the one that is the least sensitive in humans.

LIKE A FLASH OF LIGHTNING—
SPECIAL RELATIVITY

IN AN EARLIER CHAPTER I MENTIONED the sonic boom that the Flash creates whenever he runs faster than the speed of sound. Why is there a “boom” when an object moves at or faster than the speed of sound? And how can this help us understand Einstein’s Special Theory of Relativity?

First, let’s consider the boom, and then get to Einstein. Imagine yourself standing out in the countryside, and the Flash is running toward you at the speed of sound—that is, at one fifth of a mile per second. If he starts ten miles away from you, he’ll reach you in fifty seconds. When he is ten miles away, he says, “Flash” and when he is only five miles in front of you, he says, “Rules.” What do you hear? If the Flash was running slower than the speed of sound, then the “Flash” he spoke would reach the five mile mark before he did, and then he would utter “Rules” while the “Flash” was about to reach your ears. You would clearly hear “Flash Rules,” followed a short while later by the sound of the Scarlet Speedster running past you.

If the Flash were instead running faster than the speed of sound, then he would arrive at the five-mile point before the sound he emitted at the ten-mile mark. He would then say “Rules” and continue on toward you. Since the “Rules” has less distance to travel, it would reach you before the “Flash,” so you would hear the words in the reverse order that they were spoken—that is, to you it would sound like he’d said, “Rules Flash.” (Actually it would be more like “Selur Hsalf”) This backward speech would not reach you until after he had passed you. Running faster than the speed of sound, he can cover the distance from five miles away to you in less time than the sound waves.

If he were running at exactly the speed of sound, then when he yelled “Flash” at the ten-mile point it would reach the five mile mark at the exact same instant as the Tornado Titan himself did. When he then says “Rules,” it takes off from the five mile point toward you at the same moment that the “Flash” does, so that they both reach your eardrums at the same moment, twenty-five seconds later. You don’t hear “Flash Rules” or “Rules Flash” or even “Suler Hsalf” but the two words superimposed at the same instant. Sound is a pressure wave, so the waves from the two words add up and create a larger vibration than if heard separately. The Flash would not even have to be talking or making noise as he advanced toward you—the disturbance created as he pushed the air out of his way would form a pressure wave that you would hear as a thunderous roar (or a “sonic boom”) at the exact instant the Sultan of Speed cruised by. If the Flash ran faster than the speed of sound, this disturbance would still be created. In this case he would race past you in relative silence, and then later on the sonic boom, traveling at the speed of sound, would eventually reach you, with explosive consequences. (The “Rules Flash” he spoke in the previous paragraph would be lost in the sonic crash.) The “crack” of a gunshot, or of Catwoman’s whip, are mini sonic booms created by the bullet or the tip of the whip moving faster than the speed of sound in air.

The danger posed by the indiscriminate creation of sonic shock waves by the Flash is recognized by current comic-book writers. In
DC: The New Frontier
, a 2004 revisiting of DC Comics’ Silver Age heroes, set in the late 1950s when they historically made their first appearances, the writer Darwyn Cooke describes a scene where the Flash races from Central City (hazily located in the American Midwest) to Las Vegas, Nevada. In caption boxes that describe the Flash’s thoughts as he runs cross-country, he tells us, “I wait until I’m clear of the city limits before I hit the sound barrier. That’s one I figured out the hard way a few times. Flying glass and pedestrians don’t mix.” Indeed they don’t, as graphically demonstrated in
Flash # 202 (Vol. 2).
In this story, our hero has lost his memory and, in civilian clothes, does not realize that he possesses superspeed. Acting instinctually when mugged by a street gang, his high-velocity movements blow out every window on the block and cause massive structural damage to the surrounding buildings.
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Regardless of the order in which you hear what the Flash says, whether it’s “Flash Rules” or “Rules Flash,” if you have keen eyesight and can read lips you can be sure of the order in which the Flash actually said these words. This agreement is due to the fact that the light reflecting from the Flash travels much faster than sound (186,000 miles in one second, compared with one fifth of a mile per second). This is how we are able to determine the distance a thunderstorm is from us by comparing the timing between the lightning and the sound of thunder.
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But what if the Flash were running close to the speed of light? All sorts of strange things happen concerning length, time, and mass for objects moving near light speed, as described by Albert Einstein in 1905 in his Special Theory of Relativity (it’s called “special” because it ignores gravity, which is accounted for in the “General” Theory of Relativity, developed in 1915). This is neither the time nor place to go into a full discussion of relativity. A fair treatment of the topic would overwhelm the present book. But I do want to mention a basic point about traveling near the speed of light that won’t take too long, and that we’ll build on when we consider the connection between electricity and magnetism in Chapter 19.

The Special Theory of Relativity can be boiled down to two statements that appear simple, but contain a wealth of physical insight. They are (1) nothing can travel faster than the speed of light (sorry, Superman and Flash), which is the same speed for everyone, no matter how fast they are moving, and (2) the laws of physics are the same for everyone, regardless of whether you are moving or not. The first point is the really weird one. If the Flash is running as fast as a speeding bullet, to us the bullet is traveling at 1,000 miles per hour, while to the Flash, running in the same direction at the same speed, the bullet appears stationary (which is why he is able to, “with a sweeping motion,” pluck it from the air so easily). But the speed of light is 186,000 miles per second to both you, standing still, and to the Flash, regardless of how fast he runs. Even if he is racing at half the speed of light—at 93,000 miles per second—the speed of light relative to him is not 93,000 miles per second, but still 186,000 miles per second, the same as for you standing on the street corner. How can this be?

When the Flash runs toward you, from the Flash’s point of view it is as if he is stationary but you are racing toward him. The Special Theory of Relativity states that for both you and the Flash, you must agree that the speed of light is 186,000 miles per second. In order for this to be true, Einstein argued that from your point of view, the Flash will appear thinner (that is, his length in the direction he is running will appear compressed) and time will seem to pass slower for him than for you. From the Flash’s point of view, a yardstick he holds would still be one yard long, and his watch keeps time just as it always has, but to him it is you who are moving rather than him, and he will make similar determinations about you (your length will be shortened and time will move slower for you, as it appears to the Flash). This is because in order to measure the length of a yardstick that the running Flash is holding, for example, you have to consider the front and back ends of the stick, and record the times when they pass a given point. For two people moving relative to each other (say, a running Flash and a stationary observer) it becomes impossible for them to agree as to whether or not two things happen at the same time when the events are separated in space and time. The shortening of lengths as a function of velocity will play a key role in helping us understand how an electrical current generates a magnetic field in Chapter 18.

The concept that two observers can disagree as to the ordering of events was certainly not invented by Einstein, nor is it unique to the Special Theory of Relativity. As pointed out by Lev Landau and G. B. Romer in their excellent short book,
What is Relativity?
, even when both observers are stationary they can disagree depending on where they’re situated relative to an object (Go to the house on the left. Which house? Which left? My left or your left?) Just such an ambiguity played a central role in the climax of “The Race to the End of the Universe,” in the December 1967 issue of
Flash # 175.
Space aliens force Superman and the Flash to run a race across the Milky Way galaxy, ostensibly as a competition on which they intend to gamble. However, the aliens are actually disguised supervillain foes of the Flash, and their true intent is to destroy the Scarlet Speedster and the Man of Steel. At the end of the race, the Justice League of America watches on monitors, yet no clear winner is declared. Those members of the Justice League watching the finish line from monitors placed on the left-hand side of the line claimed Superman had won the race, while those watching monitors on the right-hand side of the finish line are sure that the Flash is the victor. While this comic provided a graphic illustration of one of the fundamental principles of the Special Theory of Relativity, namely that differing observers could disagree about the simultaneity of events when objects are moving at high velocities, at least one reader in 1967 found the lack of a clear winner at the conclusion of this story to be a titanic rip-off.

Information cannot travel faster than light, so there will always be a discrepancy as to the order in which events occur. In order to balance out so that the one thing everyone agrees on is the value of the speed of light, it will appear that lengths are shortened in motion and that time passes more slowly. Comic books frequently get this wrong when dealing with characters who can travel at the speed of light (such as Negative Man of the Doom Patrol and Captain Marvel—not the “Shazam” guy, or the late 1960s-early 1970s officer of the Kree military, but an African-American heroine in the Avengers in the late 1980s who could transform her body into coherent photons of light). The other characters in the story should not be able to see these heroes, as there’s no way for light to be scattered from them if they are moving as fast as light. At best, they might appear as a spark of lightning from a great distance away, but would be invisible when nearby. The highest velocity the universe allows is the speed of light. As the Flash runs faster and faster, one would think that he should be able to pass this limit, but this can’t happen (in the real, physical universe—not the comic-book universe where it happens all the time). To explain this phenomenon from the point of view of a stationary observer, it must be that the faster he goes, the harder it becomes for him to further accelerate. From Newton’s second law (force is equal to mass times acceleration), we know that if the force that his running shoes apply stays constant but there is no corresponding acceleration, it must be because his mass has increased. So in addition to time seeming to be slower and lengths appearing to shrink, the mass of the running Flash will seem (to us stationary slow-pokes) to increase the faster he runs. This is occasionally referred to in the comic books. In
Flash # 132,
the Monarch of Motion is attempting to run at light-speed, but finds that he is in fact “slowing down. I’m going slower and slower, despite all my efforts . . .” As shown in fig. 17, the “grim truth dawns on the harried speedster,” namely that he can’t run any faster because he is getting heavier. Of course, those of us with an understanding of Einstein’s Special Theory of Relativity understand perfectly well what is happening to the Flash—an alien is shooting him with a “gravity increasing ray,” as shown in fig. 18! But taken out of context, fig. 17 provides an excellent illustration of Einstein’s Special Theory of Relativity.