The writer of the “Flash of Two Worlds” story was Gardner Fox, who had also written many of the Golden Age Flash comics. He proposed a mechanism to explain how the Silver Age Flash could read comic books featuring the Golden Age Flash on this second Earth, while simultaneously providing insight into his work habits. As Barry hypothesized, “A writer named Gardner Fox wrote about your adventures—which he claimed came to him in dreams! Obviously when Fox was asleep, his mind was ‘tuned in’ on your vibratory Earth! That explains how he ‘dreamed up’ the Flash!”70 This crossover meeting between the Silver Age and Golden Age Flash was a hit with comic-book fans, and the Silver Age Flash would more and more frequently cross the vibrational barrier to Earth-2. (The world on which the Golden Age Flash resided, though it appeared first chronologically, was labeled Earth-2, while the world of the Silver Age was designated Earth-1. Our world, Fearless Reader, in which all superheroes exist solely as fictional characters in comic books, is called Earth-Prime.) Eventually, the Silver Age Justice League of America of the 1960s, consisting of the Flash, Green Lantern, the Atom, Batman, Superman, Wonder Woman, and other superheroes, met and had an adventure with Earth-2’s Justice Society of America from the 1940s, whose membership contained the Flash, Green Lantern, the Atom, Batman, Superman, Wonder Woman, and others. So popular was this meeting of the two superteams, that it quickly became an annual tradition. But the Justice League and Justice Society could visit each other’s Earth only so many times before the novelty wore off. Soon the Justice League branched out and visited other Earths, such as Earth-3, where the evil analog of the Justice League of America had formed the Crime Syndicate of America (presumably to distinguish themselves from their European criminal counterpart). Captain Marvel—that is, Billy Batson, who could become a superhero by shouting “Shazam!”—and the rest of his supporting cast inhabited Earth-S, and were in due time paid a crossover visit by the Justice League of America.71 Earth-X, Earth-4, and others soon followed, and eventually the phrase “multiverse” became appropriate to describe the seemingly endless number of alternate universes that abounded.
The issues of the Justice League of America that describe the meeting of the Silver and Golden Age heroes always carried titles such as “Crisis on Earth-2” or “Crisis on Earth-X.” The story lines eventually became so convoluted, with so much alternate history to keep straight, that in 1985, DC Comics attempted to normalize the multiverse. The yearlong miniseries describing this simplification process was called “Crisis on Infinite Earths.” With a vast housecleaning of continuity under way, the writers and editors at DC Comics used this opportunity to weed out poor sellers from many of the less-popular worlds and bring all the heroes from the better-selling titles together on one Earth (coincidentally, the Earth -1 of the Silver Age heroes). Consequently, the “Crisis on Infinite Earths” miniseries is noteworthy to comic-book fans for the deaths of the Barry Allen Flash and Supergirl (both of whom died heroic deaths struggling against the evil tyrant who threatened to destroy the Silver Age Earth-1) and the removal of Superboy from Superman’s history. Unlike most comic-book fatalities, both Barry Allen and Supergirl have remained dead for the most part (though they have both returned to continuity between the writing of the first and second editions of this book), while crime-fighting adventures have begun to creep back into Clark Kent’s teen years once again.
As ridiculous as all of the above may sound, the concept of an infinite number of parallel worlds may be one of the strangest examples of comic books getting their physics right!72 Just four years prior to the publication of Showcase # 4, the notion of an infinite number of parallel, divergent universes was seriously proposed as an interpretation of the equations of quantum mechanics. To reiterate: Some scientists believe that the concept of parallel universes is a serious, viable construct in theoretical physics. Current theories indicate that if such alternate Earths exist, they would be more like those described in the Marvel comics universe, where slight changes in a character’s history (such as those presented by the Watcher in stories such as “What if Gwen Stacy Had Lived?”) lead to diverging worlds that can never be visited by our reality, regardless of one’s vibrational frequency.
GREAT MINDS REALLY DO THINK ALIKE
So far throughout this book, we have discussed what physicists term “classical mechanics.” To understand the “mechanics” of something means you can predict its statistics (for example, the largest angle at which a ladder may be placed to remain balanced against a wall) and its motion (such as the speed with which the ladder falls when it begins to slip), once the external forces acting on it are identified. The fundamental equation that governs how a macroscopic object will move as the result of an applied force is our old friend Newton’s second law of motion, F = ma. For the motion of large objects such as cars, baseballs, and people, the dominant forces are gravity and electromagnetism. Even when we considered electricity and magnetism, we still made use of F = ma, where the F in the left hand side of this equation was either Coulomb’s force of attraction or repulsion between electric charges or the force of a magnetic field on a moving electrical charge. The aspect of “quantum mechanics” that justifies its separation from “classical mechanics” as a distinct branch of physics is that when one considers electrons and atoms, and their corresponding “ matter-waves,” F=ma suddenly doesn’t cut it anymore.
After a great deal of effort trying to “fix” classical physics for atoms (essentially tweaking Newton’s laws without overturning them completely), physicists reluctantly concluded that a different type of “mechanics” applied inside of atoms. That is, a new equation was needed to describe how atoms would respond to external forces. After roughly twenty-five years of trying one form or another for this equation, nearly simultaneously, Werner Heisenberg and Erwin Schrödinger obtained the correct form for an atom’s equivalent of F = ma.
Have no fear: There is no chance that we will discuss either the Heisenberg or Schrödinger approach in any mathematical detail. In a few pages I’ll give you the Schrödinger equation, but that will only be so that we can gawk at it as if it were some exotic zoo animal. Heisenberg’s treatment of quantum physics involves linear algebra, while Schrödinger’s makes use of a complex partial differential equation (for simplicity, we will focus on Schrödinger for the remainder of this chapter). To fully explain their theories would break the pact we have maintained up till now that nothing more elaborate than high-school algebra would be employed in these pages (the algebra we have used in this book has the same relationship to linear algebra as a housefly does to a house).
Nevertheless, there are two points about mathematics worth making here. The first is that, unlike the case of Isaac Newton discussed in Chapter 1, who had to invent calculus in order to apply his newly discovered laws of motion, both Heisenberg and Schrödinger were able to make use of mathematics that had already been developed at least a century earlier. The mathematical branches of linear algebra and partial differential equations that Heisenberg and Schrödinger employed to describe their physical ideas had been invented by mathematicians in the eighteenth and nineteenth centuries and were well established by the time they were needed in 1925.
Frequently, mathematicians will develop a new branch of mathematics or analysis simply for the pleasure of constructing a set of rules and discovering what conditions and principles then logically follow. Occasionally, physicists later discover that in order to describe the behavior of the natural world under investigation, the same tools that previously existed solely to satisfy mathematicians’ intellectual curiosities turn out to be indispensable. For example, Einstein’s task in developing a General Theory of Relativity in 1915 would have been much more difficult if he hadn’t had Bernhard Riemann’s theory of curved geometry—developed in 1854—to work with. This scenario of physicists making tomorrow’s advances by using yesterday’s mathematical tools has been repeated so often that physicists tend to not think about it too much.
The second point about the
theories of Heisenberg and Schrödinger is that while they employ different branches of mathematics and look very different, careful inspection by Schrödinger in 1926 demonstrated that they are mathematically equivalent. Because they describe the same physical phenomena (atoms, electrons, and light), and are motivated by the same experimental data, it is perhaps not very surprising that they turn out to be the same theory, even though the mathematical languages used to express them are vastly different.
Schrödinger and Heisenberg, completely independent of each other, developed different descriptions of the quantum world in the same year. The notion that some ideas become “ripe” for discovery at certain moments in history is found time and again and is not confined to theoretical physics. Of course, simple mimicry accounts for much of the similarity in television programs or Hollywood movies, just as the breakthrough of Superman in Action Comics led to a rapid proliferation of superhero comic books by many other publishers, including National Comics, hoping to bottle lightning again. There are, however, well-documented cases of movie studios or television networks simultaneously and independently deciding that it is time for the reintroduction of a particular genre, such as the pirate movie or the urban doctor drama. This synchronicity also occurs in comic books, as in the example of the X-Men and the Doom Patrol. In March 1964, DC Comics published My Greatest Adventures # 80, featuring the debut of a team of misfit superheroes (Robotman, Negative Man, and the obligatory female teammate, Elasti-Girl) whose freakish powers caused them to be shunned by normal society. They were led by a wheelchair-bound genius named the Chief, who convinced them to band together to help the very society that rejected them, frequently fighting their opposites in the Brotherhood of Evil Mutants. Three months later, comic fans could buy X-Men # 1, published by Marvel Comics, where they would meet a team of mutants (Cyclops, Beast, Angel, Iceman, and the obligatory female teammate, Marvel Girl) whose freakish powers caused them to be shunned by normal society. These superpowered teens were led by the wheelchair-bound mutant telepath Professor X, who recruited and trained them to help the very society that rejected them, frequently fighting their opposites in the Brotherhood of Evil Mutants.
Despite some profound differences (Professor X is bald and clean-shaven, while the Chief has red hair and a beard), the striking similarities in concept have led many comic-book fans to wonder whether the X-Men were modeled after the Doom Patrol. However, interviews with the writers of both comics and the research of comic-book historians indicate that it is more likely that the near simultaneous appearance is a coincidence. The long lead time needed to conceive, write, draw, ink, and letter a comic book prior to its printing and newsstand distribution suggests that the X-Men were well into production by the time the Doom Patrol first appeared.
Another publishing synchronicity is the case of the moss-covered muck monsters Swamp Thing at DC (written by Len Wein) and Man-Thing at Marvel (co-written by Gerry Conway), which appeared within one month of each other in 1971. Both Wein and Conway insist that their creations were not influenced by the other, and the fact that they were roommates at the time is purely coincidental.
If the behavior of objects on the atomic scale is governed by the matter-waves that accompany their motion, then what atomic physics needed was a matter-wave equation that described how these waves evolve in space and time. In 1925, Schrödinger (fig. 31) essentially guessed the right mathematical expression.
With the Schrödinger equation, scientists had a framework with which they could understand the interactions of atoms with light. This was Schrödinger’s motivation for developing his matter-wave equation. A generation later, armed with the insights about the nature of matter made possible by the Schrödinger equation, a new class of scientists developed the transistor and, separately, the laser, as well as nuclear fission (as in atomic bombs) and nuclear fusion (in hydrogen bombs). The paths to both the transistor and the laser were difficult ones, and it was only with the guidance of quantum theory that these devices were successfully developed. A generation later still, the CD player, personal computer, cell phone, and DVD player—to name only a few— would be created. None of these are possible without the transistor or the laser, neither of which are possible without the Schrödinger equation. It is small wonder that until fairly recently, Schrödinger’s portrait was on the 1,000 Schilling note in his native Austria, for he can truly be considered one of the architects of the lifestyle that we in the twenty-first century take for granted.
Fig. 31. Erwin Schrödinger, theoretical physicist, Nobel Laureate, and ladies’ man, thinking of the Schrödinger equation—the foundation of quantum mechanics and our modern technological lifestyle.
A moment ago, I said that Schrödinger “guessed” the form of the matter-wave equation. Perhaps “guessed” is too strong a word. Erwin Schrödinger used considerable physics intuition to develop a new equation to describe the behavior of atoms. Mere mortals may never know how exactly someone such as Newton or Schrödinger does what they do. The insight that leads to a new theory of nature is perhaps more powerful than that of artistic creation, for a new physical theory must not only be original, but also mathematically coherent and accord with experimental observations. The most elegant theory in the world is useless if it is contradicted by experiments.
While we may not know how Schrödinger did what he did, we do know where and when he did it. Historians of science inform us that Schrödinger developed his famous expression in 1925, while staying at a Swiss Alpine chalet that he borrowed from a friend during a long Christmas holiday. Furthermore, while we know that his wife was not staying at this chalet, we also know that he was not alone. Unfortunately, we do not know which of Schrödinger’s many girlfriends was with him at the time.
At this point, the reader may wish to reexamine Schrödinger’s portrait in fig. 31. We may have a new answer to the question, “Why is this man smiling?” Certainly Erwin does not strike one as a traditional ladies’ man. If one ever wondered whether there might be some mathematical expression that would make one attractive to the opposite sex, the Schrödinger equation might be a good starting point. Even the brief overview of quantum physics presented in this chapter will no doubt enhance your romantic desirability. This is in addition, of course, to the irresistible sex appeal that accompanies an encyclopedic knowledge of superhero comic books!
SCHRÖDINGER’S CAT OF TWO WORLDS
Schrödinger’s equation is the F = ma for electrons and atoms. Newton’s second law, when the external forces F are specified, describes the acceleration a, and from this the velocity and position of an object can be determined. Similarly, Schrödinger’s equation, given the potential energy of the electron through the term V, enables the calculation of the probability per volume ψ2 of finding the electron at a certain point in space and time. Once I know the probability of where the electron will be, I can calculate the average location or momentum of the electron. Given that the average values are the only quantities that have any reliability, this is actually all that should be asked of a theory.
The emphasis on average quantities in quantum physics is different from our consideration of averages in the earlier discussion of thermodynamics (Chapter 13). There we spoke of the average energy per atom in an object—characterized by its temperature—simply because it was convenient. In principle, if we had enough time and computer memory, or were superfast like the Flash or Superman, we could keep track of the position and momentum of every air molecule in a room, for example. We could thereby calculate the instantaneous force on the walls per unit area, which would convey the same information as a determination of the pressure. In quantum systems, on the other hand, the wavelike properties of matter set a limit on our ability to carry out measurements, and the average is as good as we’ll ever get.
What is it about the wavelike nature of matter that makes it so difficult to accurately measure the precise location of an electron in an atom? Think of a clamped violin string with a fundamental vibration frequency and se
veral higher harmonic tones. Assume that the string is vibrating at a given frequency, but one that we cannot hear. If the vibrations were so fast that we could not see the string vibrate back and forth, how would we verify that the string is indeed vibrating? One way would be to touch the string and feel the vibrations with our fingers. If our fingertips were sensitive enough (like Daredevil’s), we could even determine the exact frequency at which the string had been vibrating.
I say “had been vibrating,” because once we have touched the string, it will no longer be oscillating at the same frequency as before. It will either have stopped shaking altogether or will be vibrating at some different frequency. Perhaps we can determine the vibration frequency by bringing our fingers near to, but not in direct contact with, the string. In this way we can sense the vibrations in the air caused by the oscillating violin string. In order to improve the sensitivity of this measurement, we need to bring our fingertips very close to the string. But then the air vibrations will bounce from our fingers and ricochet to the string, providing a feedback that can alter its vibratory pattern. The farther away we hold our fingertips, the weaker the feedback, but then our determination of the vibratory frequency will be less accurate.
The matter-wave oscillations of an electron within an atom are just as sensitive to disturbances. Measurements of the location of an electron will perturb the matter-wave of the electron. Much has been written about the role of the “observer” in quantum physics, but it’s no more profound than when you try to look at something smaller than the probe you are using to view it—you will disturb what you are trying to see.
Quantum theory can provide very precise determinations of the average time one must wait before half of a large quantity of nuclear isotopes has undergone radioactive decay (defined as the “half life”) but is not useful for predicting when a single atom will decay. The problem with single events is best illustrated by the following challenge: I take a quarter from my pocket and am allowed to flip it once, and only once. What is the probability that it will come up heads? Most likely your gut instinct is to answer 50 percent, but you’d suspect a trick. And you’d be right—it is a trick question. To those who say the chance of getting heads is fifty-fifty, I say: Prove it. And you can’t, not based upon a single toss, as long as we live in world containing two-headed quarters. If you toss the coin a thousand times (or toss one thousand coins once) you would find that for a fair coin, it would land heads-side up very close to 50 percent of the time. But probability is a poor guide for single, isolated events. Yet probability is all that the Schrödinger equation offers. This did not sit well with many older physicists who were accustomed to the clockwork precision of Newtonian mechanics, and they proposed a conceptual experiment that would open a Pandora’s box (a box that contained a cat).
The Physics of Superheroes: Spectacular Second Edition Page 29
