The Physics of Superheroes: Spectacular Second Edition (42 page)

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 several 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).

They posed the following situation: Consider a box, in which is placed a cat and a sealed bottle of poison gas, along with another, smaller box that contains one single radioactive isotope. The radioactive element has a half life of one hour, which means, according to quantum mechanics, that after one hour, there is a fifty-fifty chance that it will have decayed. A by-product of this nuclear decay is the emission of an alpha particle (otherwise known as a helium nucleus), and the bottle of poison is arranged such that it will break open if struck by this particle. So, after one hour, there is a 50-percent chance that the cat is dead, having succumbed to the poison vapors released when the bottle was struck by the alpha particle, and a 50-percent chance that the bottle remains undisturbed, leaving the cat alive and well. According to Schrödinger’s equation, prior to the one-hour time limit, the cat can be meaningfully described only as “the superposition (or average) of a dead cat and a live cat.” Once the hour has passed and the lid is opened and one looks inside, the “average cat’s wave function” collapses into one describing either a 100-percent-live or 100-percent-dead cat, but there is no way to know which will be observed before the lid is opened. If the walls of the box are transparent, you can never be sure that the light from the outside has not disturbed the decay process (recall that observing quantum systems can sometimes alter them). This interpretation has been found wanting by many physicists (despite the fact that recent experiments on entangled quantum states of light, as described in
JLA # 19,
the latest version of the Justice League of America, suggest that this is exactly what does occur), and a great deal of thought and argument has gone into attempting to resolve the intellectual unpleasantness associated with Schrödinger’s Cat. One provocative solution to this problem, described below, enables the Flash and Superman to travel to alternate Earths.

In 1957, the physicist Hugh Everett III argued that when the cat is sealed in the box, two nearly identical parallel universes exist: one in which at the end of the hour the cat is alive and another in which it is dead. What we do when we open up the box does not involve collapsing wave functions, nor is the cat 50-percent dead and 50-percent alive before we take a look. Rather, all we do at the end of the hour is determine which of the two universes we live in—one where the cat lives or one where the cat dies. In fact, for every quantum process for which there are at least two possible results, there are that many universes, corresponding to the different possible outcomes. The two Earths reflecting the two possible outcomes of a particular quantum event will each evolve in different ways, depending on the myriad additional quantum events that occur following this initial branching point. If the bifurcation of the Earths occurred recently, then a particular Earth may be similar to our own world. If the separation occurred a long time ago, then during the intervening time, there would be many opportunities for subsequent quantum events to have outcomes different from what was observed in our world. The history of this second Earth may be very much like ours, then, but there is also the possibility of dramatic differences.
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Hence, quantum theory provides a physical justification for both the “What If?” tales in the Marvel universe and the alternate Earths in DC comics. On one Earth, Jay Garrick inhaled “hard water vapor” in a chemistry lab accident, gaining the gift of superspeed with which he fought for justice as the Flash with his teammates in the Justice Society of America. On another Earth, police scientist Barry Allen was doused with an array of chemicals while simultaneously being struck by lightning, leaving him with the gift of superspeed, with which he fought for justice as the Flash with his teammates in the Justice League of America. On another Earth a super-speedster committed crimes as the evil Johnny Quick with his teammates in the Crime Syndicate of America. There are in principle an infinite number of Earths, corresponding to all possible outcomes of all possible quantum effects, though a basic tenet of this theory is that ordinarily there can be no communication between these multiple alternate Earths. Ordinarily. Apparently, for someone able to vibrate at superspeed like the Flash, travel between these many worlds could occur as often as readers kept buying such stories.

To physicists, Hugh Everett III’s proposal led to a very different crisis of infinite Earths. The many-worlds solution to the Schrödinger’s Cat problem represented to most physicists an example of the cure being worse than the disease. Nevertheless, there is nothing logically or physically inconsistent with this theory, and no one has been able to prove that it is incorrect.

Physicists who considered it intellectually unsatisfying to say that a complete theory of nature can predict only probabilities were not heartened by the notion that the theory actually described an infinite number of alternate universes. The “ many-worlds” model has been considered the crazy aunt of quantum theory since its publication, and has been locked in the metaphoric attic until very recently. It was never taught to me, for example, when I studied quantum mechanics in college and again in more detail in graduate school. I discovered the “many-worlds” model completely by accident when, as a graduate student, I came across a copy of Bryce DeWitt and Neill Graham’s 1973 book
The Many-Worlds Interpretation of Quantum Mechanics,
left abandoned in a graduate student’s office. In a successful attempt to procrastinate doing my homework, I picked up this strange book, began reading it, and thereupon learned that somewhere there was another James Kakalios who was actually finishing his assignment on time (not that this knowledge did me any good).

Though few physicists give the “many-worlds” model the time of day, there is one class of theoretical physicists, some of whom are supporters of this idea: string theorists.

In the years following the development of the Schrödinger equation, scientists have developed techniques to describe how the electron’s matter-wave interacts with quantum versions of electric and magnetic fields (a process called “Quantum Electro-Dynamics” or QED) and how the matter-waves of quarks inside a nucleus behave (a process termed “Quantum Chromo- Dynamics” or QCD). A remaining goal of theoretical physics is to understand how to unite the physics of large-scale massive objects, governed by gravitational physics, with the quantum world. There is a perfectly good theory for gravity, namely Einstein’s General Theory of Relativity. There is an excellent theory to describe the quantum nature of electrons (QED). Combining these theories into one coherent whole has proven beyond the abilities of any scientist up until now. The closest that theorists have come to a quantum theory of gravity is something called “string theory.”

A gross oversimplification of string theory is that it suggests that matter is itself a wave, or rather a vibration of an elemental string, and that these “strings” are the basic building blocks of everything in the universe. In its current state, many physicists are skeptical about string theory. Their first objection is that, in order for the equations to balance, string theory works only in eleven dimensions (ten spatial and one time). This is somewhat awkward because, as near as we can tell, we live only in three spatial dimensions, and no one has ever encountered additional dimensions.
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To address this discrepancy string theorists have suggested that there really are eleven dimensions, but seven of these spatial dimensions curl up into little balls, with a diameter less than a billionth trillion trillionths of a centimeter, a length scale labeled the Planck length, though some versions posit the existence of very large dimensions. Another drawback of string theory is tied to this extradimensional notion: Probing length scales so small requires correspondingly higher energies than current and next-generation particle accelerators can achieve. Without the verification provided by experimentation, the only criterion to determine whether the equations are on the right track is mathematical elegance. This may be dangerous; while it is true that the equations of classical mechanics (electricity and magnetism) and quantum mechanics do indeed have a certain mathematical beauty, there is no a priori reason to believe that nature really cares whether we find the equations pretty or not. Nevertheless, string theory is presently the only likely candidate for a quantum theory of gravity, and only further study will determine its success.

Physicists investigating quantum gravity have invoked the many-worlds interpretation in order to resolve logical inconsistencies in their calculations involving time travel. Recently, some scientists have claimed that time travel is not physically impossible, though it is highly unlikely to ever actually be accomplished. The problem with time travel into the past is set forth in the famous “grandfather paradox.” Essentially, if one could indeed travel back in time, it would be possible to murder your grandfather when he was a young man, before your own father was conceived. In this way you would prevent your own birth, but the only way you could have prevented it is if you had first been born. In order to find a way around this conundrum, modern theoretical physicists have dusted off Hugh Everett III’s many-worlds interpretation. If there are indeed an infinite number of alternate parallel universes, then (the theorists argue) when you travel backward in time, the severe distortions in space-time necessary to make this journey would also simultaneously send you to a universe parallel to your own. You are therefore free to kill as many grand-parents as ammunition allows, without fear of altering your own existence, because your own grandfather is safe in the past in your own universe, undisturbed by the havoc you are wreaking in alternate past worlds.

These modern theoretical notions were actually anticipated in the 1961 adventure “Superman’s Greatest Feats” in
Superman # 146.
In this story, Superman agrees to travel into the past as a favor for Lori Lemaris, a mermaid from the sunken city of Atlantis with whom he had a “special relationship” (while she was a girl and was his friend, Lori was not Superman’s girlfriend). Lori beseeches Superman to prevent the sinking of Atlantis, which occurred millions of years ago. Superman argues that all of his previous attempts (presented in earlier issues of Action Comics and
Superman
) to change history have failed, but Lori’s pleading (and what appear to be bedroom eyes) convinces Superman to give it a try. Given that it takes great effort and a velocity larger than 1,100 feet per second to break the sound barrier (the effort, as discussed in Chapter 4, is due in part to the work one must do to push the air out of his way), it was proposed in DC comics that with an even-greater effort and a much faster velocity, one could pass through the “time barrier.” (Both the Flash and Superman, each capable of these necessary speeds, could travel back and forth through time as their story lines required.) Superman thus zooms to at least 8,000,000 B.C.E. and reaches nearly the exact moment when the advanced civilization of Atlantis, which resides on a small island off the shore of what appears to be a coastal resort, is about to succumb to “giant waves caused by a colossal undersea earthquake.” Superman races to another island a safe distance from the undersea quake, which is the home to
another
advanced civilization. Why we have never heard about this other ancient civilization is not addressed. Superman borrows some “strange metal” from buildings about to be torn down on this other island and fashions an enormous crane with which he lifts the entire island of Atlantis, depositing it onto a third, secure deserted island, where it is spared by the earthquake. (Let’s not even get into what this “strange metal” could possibly be composed of that would give it a tensile strength sufficient to lift an island.)