Of course not. Except perhaps on The X-Files, no one has ever seen a superposition. Cats are either alive or dead, never both. There is a fundamental difference between a cat and an atomic-size object. But what is it?
One answer has been the fodder for science fiction, because it suggests that our universe is infinitely (literally!) more complex than we perceive it to be. What better inspiration for fiction could one have? This answer, which goes under the name of the “many worlds” interpretation of quantum mechanics, suggests that the fundamental difference between a cat and a particle is that we can see the cat. Treating ourselves and our consciousness as quantum-mechanical objects, we can imagine that we, too, are entangled with the cat and the poison apparatus and the box. Before we observe (or “measure”) the state of the cat, there are two coupled configurations that make up the wavefunction describing the apparatus, the cat, and us—no decay, live cat, a nice surprise for us when we open the box; or particle decay, dead cat, a sad sight for us when we open the box. When we observe the cat, we are collapsing the wavefunction to one of these two possibilities. Each time our consciousness acts, we follow one track out of what may be an infinite number of possible “branches” of the quantum wavefunction of the universe. We perceive a single universe, but that’s because we are condemned to live in the universe of our perception. Our quantum partner lives in the universe of the alternative perception, where, if our cat lives, the alternative cat dies—and vice versa. A physicist friend of mine likes to say not altogether in jest that he finds solace in this view, because whenever he makes a mistake or misses a great discovery, there’s some branch of the wavefunction in which his quantum partner hasn’t.
If this conviction isn’t sufficient solace, you might want, every now and then, to jump into one of these parallel universes, where things might be going better for you. This, of course, is the situation Worf encounters in the Next Generation episode “Parallels,” in which he finds himself alternately married to Deanna and single. As far as I can tell, it is also the context of a television series called Sliders, in which an intrepid group of adventurers gets to jump around from universe to universe; in these episodes, the characters are the same, but certain essential details are unnervingly different from week to week.
It is also, amusingly enough, a solution proposed by at least one professional physicist (and a lot of amateur ones) to the grandmother paradox, that plague of backward time travel. If you go back in time, but into a parallel quantum universe, then there is no problem with killing your grandmother, since your grandmother remains alive in the universe in which you originated and to which you will presumably return. (In this case, one might be tempted to ask, What is the point of bothering to go back in time to kill your grandmother, since there will always be some universe in which she is hit by a truck?)
The idea of many parallel universes is interesting, but the idea of jumping around between them probably doesn’t hold up. The central tenet of quantum mechanics is that once the wavefunction has collapsed and one choice out of several has been made, there is no going back. Even in the “many worlds” picture, once you perceive reality you are stuck with that reality. This idea is directly related to a powerful constraint in physics called the Conservation of Probability, a principle that states something very simple: The sum of the probabilities for all different possible outcomes of some measurement must be 1—that is, something must happen. Moreover, only a single result can be obtained for any measurement. Generally, any model that allows you to jump between branches of the wavefunction will violate this principle.
One of the reasons I don’t pursue notions of parallel universes and possible travel between them is that I think they’re ill-conceived, in the sense that Sidney Coleman suggested: They seem to be trying to explain quantum mechanics in classical terms, by making it consistent with our perceptions—rather than vice versa. What seems to me to be a more reasonable approach, in which an attempt is made to understand the classical world as an approximation of the underlying quantum world, purely in the context of the quantum theory itself, has taken some time to develop.
Some of the important insights have been arrived at only recently, 60 years or so after Schrodinger posed his paradox. Moreover, only the general framework of this picture has been worked out; it goes by the name of “decoherence” (not to be confused with what the reader may be feeling at this point). The basic idea is simple: The macroscopic world doesn’t behave like the quantum universe; therefore, classical objects—the objects at macroscopic scales—don’t involve superpositions of mutually exclusive possibilities.
How can this be, if macroscopic objects are made up of quantum objects? Well, it’s a matter of large numbers and also of the constant interactions between all the constituents of these macroscopic objects. Let’s reconsider the simple two-particle system with total spin equal to zero. The wavefunction is made up of two mutually exclusive possibilities: A up, B down plus A down, B up. But this entanglement persists only as long as nothing else interacts with the system. If particle B collides with particle C, in a process in which the spin of particles B and C can be exchanged (for example), then the correlation of particle A with particle B is reduced. If B has a million such collisions, with a million other particles, the original correlation with A will quickly be washed out. The system, and hence the wavefunction describing the system, will then evolve as if A and B are now independent. In modern parlance, A and B will decohere. One can envision a coherent superposition of A and B reappearing momentarily because of a later interaction, but if there are lots of particles around, and lots of interactions, this possibility becomes increasingly remote.
While the details of the operations of decoherence on macroscopic aggregations of many particles have not yet been fully worked out, the idea of decoherence seems eminently sensible. Not as much fun, perhaps, as having many parallel universes (with the number of independent universes increasing each time someone has a perception!), but infinitely simpler. And decoherence suggests that quantum mechanics solves its own problems—that is, the classical limit is just the limit at which there are no coherent superpositions of mutually exclusive states for systems composed of large numbers of particles. The individual quantum states of the many individual particles making up the classical macroscopic system quickly decohere, and the wavefunction of the system evolves into a sum of many different states, but the states that describe mutually exclusive macroscopic configurations (for example, live plus dead cat) have random plus and minus signs and end up canceling out the sum. Moreover, decoherence resolves the question that began this discourse: Am I correlated in some quantum superposition with the cosmos—so that when the Moon is in the seventh house and Jupiter aligns with Mars, Peace will guide the planets and Love will rule the stars? No , I’m not. Decoherence assures that there are likely to be no coherent macroscopic superpositions of my state and Jupiter’s in the wavefunction of the universe.
Alas, this conclusion suggests that the fascinating phenomena of quantum mechanics are forever exiled to the world of the very small, and will remain directly irrelevant to our experience. But this need not be the case, and I believe therein lies our future…
Without a doubt, the most exciting experimental frontier of physics—at least, from a technological viewpoint—lies in the growing exploitation of quantum phenomena for macroscopic applications. There are two ways in which quantum phenomena can sneak into the observable realm. The first involves a situation where a macroscopic aggregation of many particles can exist together in a single quantum state. Normally, a macroscopic configuration corresponds to many many different microscopic states, and it is precisely this fact that causes interesting coherent configurations of all the particles to be washed out on large scales. However, if there is only a single configuration of all the particles which corresponds to an observable macrostate, then there is nothing to wash out.
The most recent prominent example of such a macroscopic manifestation of quantum phe
nomena is known as Bose-Einstein condensation, after the two physicists who proposed it. First, I should explain that there are two kinds of known particles in nature—those that have a value of spin of 1/2 some unit of angular momentum and those that have an integer value. The laws of quantum mechanics imply that the particles with integer spin like to occupy the same state, if possible. Mathematically, this is expressed as follows: If I have an integer-spin particle in a certain quantum state, the probability that a second nearby identical particle with integer spin will occupy the same state is increased even if there is no other attraction between the two particles. Correspondingly, the total energy of the configuration with the two particles in the same state will be less than if they were in different states. But recall from chapter 14 that the energy difference (quantum leaps) between individual quantum states for a single particle is infinitesimally small; therefore the ambient energy available at room temperature for normal particles is sufficient to allow them to populate many different quantum states with ease.
However, if one cools a system of such particles to very low temperatures, perhaps a few millionths of a degree above absolute zero, it is predicted that the quantum-mechanical tendencies of the particles will at some certain point become manifest, and the whole configuration will collapse into a single quantum state called a Bose-Einstein condensate. This new state of matter will behave very differently from normal macroscopic matter, because it will be in a pure quantum state, and not in a superposition of many different quantum states. One could then operate with this macroscopic configuration in many different ways as if it were one huge, macroscopic particle. The technological potential of this condensate configuration, as well as its potential as a research tool for exploring the properties of matter, is great.
Creating a true Bose-Einstein condensate was the grail of experimental atomic physics for years, and in 1995 two groups managed to confine several thousand atoms into a Bose-Einstein phase for a minute or more. Research in this area is still too preliminary to have resulted in any practical technological devices. However, research in another, closely related area has already reaped benefits.
In 1911, the Dutch experimental physicist H. Kammerlingh Onnes cooled liquid mercury down to -270°C and discovered something amazing. The resistance to electric current suddenly vanished entirely, and the material became what is now known as a superconductor. A current introduced in a loop of superconducting wire persisted for days, even weeks, after the battery that started it flowing was removed.
Superconductors have come a long way since Onnes, and they have already had an impact on our technology. Anytime one wants to generate currents without resistance, thus avoiding the buildup of heat as well as the associated expenses of power generation, superconductors come in handy. They can be used in supercomputers, for instance, where heat generated by the current flow between the billions of tightly packed storage units would be prohibitive, and they are used in high-energy accelerators, where huge current flows are needed and the heat and electrical bills would be otherwise unacceptably high. Superconductors are a form of Bose-Einstein condensate, but can exist at higher temperatures than a pure Bose-Einstein state, because of extra interactions between the particles. A normal conducting material exhibits resistance because the electrical current is carried by individual electrons, which periodically bump into imperfections and impurities in the material and thereby lose energy. But if all the electrons are coupled together into a single quantum state, this state simultaneously occupies the whole wire, and the resultant current involves the simultaneous motion of the entire configuration, which is thus unaffected by the wire’s small-scale impurities.
Closer to the spirit of science fiction is the other realm where observable quantum phenomena are taking place. Experimenters now have tools of sufficient sensitivity to manipulate single atoms in what are called atomic traps. Moreover, they can also manipulate electromagnetic radiation so that single quanta of radiation can be trapped in an optical fiber, or a cavity. “With single particles thus isolated, the interactions that normally cause decoherence to take place do not. For the first time, the fundamental quantum properties of individual atoms interacting with radiation can be directly studied. Moreover, all the famous quantum-mechanical thought experiments involving entanglement, including the classic Einstein-Podolsky-Rosen proposal, can be studied. To date, these experiments have confirmed the predictions of quantum mechanics, as opposed to those theories in which the probabilistic nature of measurement is just an approximation to some underlying classical theory. From my point of view, the ability to do “quantum engineering” for use in circuit applications, switching, and of course quantum computers promises the greatest long-term benefits of this research. When we can miniaturize switches and motors down to the atomic level—down to where our classical expectations dissolve—a whole new world of technology, much closer to the Star Trek universe of the twenty-third century than to the Microsoft universe of the twentieth century, beckons us in ways we cannot yet even imagine.
As far as provoking our imagination goes (which is what science fiction and, I believe, modern science are all about), these human-scale applications of quantum mechanics pale in comparison to the implications at the two extremes of scale, the smallest distances we can now imagine and the scale of the universe as a whole.
Recall that at its foundations quantum mechanics relies on the discrete nature of the available states of finite systems. This discrete nature implies that not only are the energy levels of particles in atoms, and atoms in solids, discrete, but also that electromagnetic radiation—and all types of radiation, for that matter—comes in discrete packets. In the case of electromagnetism, these packets are called photons, and they are responsible not just for carrying electromagnetic signals but, it turns out, for transmitting the electromagnetic force itself.
Now, both Newton’s law of gravity and Einstein’s general relativity tell us that gravity is similar to electromagnetism, except for the fact that it is much weaker. By analogy, then, there should be particles like photons which transmit the gravitational force in nature. We call such particles gravitons. So far so good. However, remember also that general relativity tells us that gravity is essentially related to the nature and curvature of space and time. It is, in fact, nothing other than a result of the curvature of space-time itself. Our notions of space and time suggest that these are continuous; however, at the scale where the gravitational interaction between elementary particles becomes significant because of their proximity to each other, and if we are to describe this interaction in terms of quantum gravitons, our classical notions of the continuousness of space-time probably must go out the window. Right now, we are flailing around trying to find out what to replace these notions with.
The scale where this becomes significant is unbelievably small: smaller compared to the size of an atom than an atom is to the size of our solar system! Nevertheless, there are two places in nature where particles will get so close together that the quantum nature of gravity becomes important: (1) in the final stages of the collapse of matter into a black hole, and (2) at the beginning of the universe.
Both of these locations, where the density of matter becomes so high that quantum gravitational effects become important, contain what are sometimes called quantum singularities. This term has a certain cachet. It rolls off the tongue nicely, and this is doubtless why it crops up so often on TV and in the movies, from the Star Trek films to Ghostbusters. Perhaps the enticement is the same as any other enticing aspect of the human experience. In a quantum singularity, anything goes! The laws of physics as we know them break down. Quantum effects become so significant that even the nature of space and time are modified. Perhaps, like virtual elementary particles, whole new universes are created at these minuscule scales by quantum processes. Most exciting of all, perhaps our own universe itself began through such a quantum process.
These ideas have captured the imagination of science fiction writers. I re
member reading, when I was a graduate student, a particularly interesting short story (whose name, alas, I have long forgotten) by the science fiction writer Stanislaw Lem in which the observable universe was created as a quantum event. I was sufficiently taken with this at the time that I acknowledged Lem in my PhD thesis, which involved some rather wild (in retrospect) speculations on the nature of gravity in the early universe. But the idea of quantum creation of universes has also captured the imagination of some of the most brilliant theoretical physicists and mathematicians on the planet.
This was brought home to me when I received responses to my query from several physicists about the one thing they would most like to know. The Caltech general relativist and author Kip Thorne wrote that he would “most like to know the laws of quantum gravity, and what they say about (1) how our Universe originated, (2) whether there are other universes, (3) the nature of the singularity in the core of a black hole, (4) whether universes can be created by such singularities, and (5) whether backward time travel is possible.” While this perhaps violated my “one thing you would most like to know” stipulation, I was willing to ignore it, because clearly all five of Kip’s questions—among the most exciting questions at the forefront of physics—are so strongly coupled that to know the answer to one is probably to know the answer to all. Nevertheless, numbers 2 and 4 perhaps stand out in significance. If our own universe is not unique, and if universes can be created willy-nilly by quantum processes, the whole nature of what we mean by science, and by the future, can change.
It was precisely this which two eminent theoretical physicists wrote to me about. They were the Nobel laureate Steven Weinberg, of the University of Texas at Austin, and John Preskill of Caltech, who, coincidentally, was a student of Weinberg’s at Harvard in the 1970s and was on the Harvard faculty while I was there as a fellow. Most recently, Preskill, along with Kip Thorne, gained a measure of celebrity by winning a long-standing wager with Stephen Hawking on the possible existence of what are called “naked” singularities—singularities not shrouded deep inside a black hole. Thorne and Preskill contended that such things might exist, and Hawking has conceded the point. I have known both men as colleagues and teachers since I have been a physicist, and I found it remarkable and at the same time satisfying that these two deeply thoughtful individuals came up with almost the same question. Their question harks back (as Preskill explicitly acknowledged) to Einstein’s response when he was asked what he would most like to know about the universe. He replied, “What I would most like to know is whether God had any choice in creating the universe.”
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