Rating: ••• (Recommended)
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At least once a year, I try to tackle a science book to humble myself about all the things I don’t know. This year’s book was Brian Green’s The Fabric of the Cosmos that tries to answer the question, “What is Reality?” for general readers. In what is usually a readable style, Green helps explain String Theory, Inflationary Cosmology and the Uncertainty Principle. One thing that brought me great pleasure in reading this book was the realization that my contemporaries who were physics majors awoke each Saturday morning for a required class in the late 1960s and early 1970s, learning about things that have since been proven wrong. I’m glad I had slept in.
Green teaches readers in this version of a Physics for Poets course, and is gentle enough to direct those of us with passive interest to skip some sections of the book that become a bit obtuse (I plowed through despite his warnings and came out unscathed.) Piece by piece, Green explains the state of modern Physics, and describes some of the questions that have been answered, and some of the questions that remain. Here’s an excerpt from the end of Part II, “Time and Experience,” Chapter 7, “Time and the Quantum,” pp. 208-216:
Decoherence and Quantum Reality
When you first encounter the probabilistic aspect of quantum mechanics, a natural reaction is to think that it is no more exotic than the probabilities that arise in coin tosses or roulette wheels. But when you learn about quantum interference, you realize that probability enters quantum mechanics in a far more fundamental way. In everyday examples, various outcomes—heads versus tails, red versus black, one lottery number versus another—are assigned probabilities with the understanding that one or another result will definitely happen and that each result is the end product of an independent, definite history. When a coin is tossed, sometimes the spinning motion is just right for the toss to conic out heads and sometimes it’s just right for the toss to come out tails. The 50-50 probability we assign to each outcome refers not just to the final result—heads or tails— but also to the histories that lead to each outcome. Half of the possible ways you can toss a coin result in heads, and half result in tails. The histories themselves, though, are totally separate, isolated alternatives. There is no sense in which different motions of the coin reinforce each other or cancel each other out. They’re all independent.
But in quantum mechanics, things are different. The alternate paths an electron can follow from the two slits to the detector are not separate, isolated histories. The possible histories commingle to produce the observed outcome. Some paths reinforce each other, while others cancel each other out. Such quantum interference between the various possible histories is responsible for the pattern of light and dark bands on the detector screen. Thus, the telltale difference between the quantum and the classical notions of probability is that the former is subject to interference and the latter is not.
Decoherence is a widespread phenomenon that forms a bridge between the quantum physics of the small and the classical physics of the not-so-small by suppressing quantum interference—that is, by diminishing sharply the core difference between quantum and classical probabilities. The importance of decoherence was realized way back in the early days of quantum theory, but its modern incarnation dates from a seminal paper by the German physicist Dieter Zeh in 1970, and has since been developed by many researchers, including Erich Joos, also from Germany, and Wojciech Zurek, of the Los Alamos National Laboratory in New Mexico.
Here’s the idea. When Schrodinger’s equation is applied in a simple situation such as single, isolated photons passing through a screen with two slits, it gives rise to the famous interference pattern. But there are two very special features of this laboratory example that are not characteristic of real-world happenings. First, the things we encounter in day-to-day life are larger and more complicated than a single photon. Second, the things we encounter in day-to-day life are not isolated: they interact with us and with the environment. The book now in your hands is subject to human contact and, more generally, is continually struck by photons and air molecules. Moreover, since the book itself is made of many molecules and atoms, these constantly jittering constituents are continually bouncing off each other as well. The same is true for pointers on measuring devices, for cats, for human brains, and for just about everything you encounter in daily life. On astrophysical scales, the earth, the moon, asteroids, and the other planets are continually bombarded by photons from the sun. Even a grain of dust floating in the darkness of outer space is subject to continual hits from low-energy microwave photons that have been streaming through space since a short time after the big bang. And so, to understand what quantum mechanics says about real-world happenings—as opposed to pristine laboratory experiments—we should apply Schrodinger’s equation to these more complex, messier situations.
In essence, this is what Zeh emphasized, and his work, together with that of many others who have followed, has revealed something quite wonderful. Although photons and air molecules are too small to have any significant effect on the motion of a big object like this book or a cat, they are able to do something else. They continually “nudge” the big object’s wavefunction, or, in physics-speak, they disturb its coherence: they blur its orderly sequence of crest followed by trough followed by crest. This is critical, because a wavefunction’s orderliness is central to generating interference effects (see Figure 4.2). And so, much as adding tagging devices to the double-slit experiment blurs the resulting wavefunction and thereby washes out interference effects, the constant bombardment of objects by constituents of their environment also washes out the possibility of intereference phenomena. In turn, once quantum interference is no longer possible, the probabilities inherent to quantum mechanics are, for all practical purposes, just like the probabilities inherent to coin tosses and roulette wheels. Once environmental decoherence blurs a wavefunction, the exotic nature of quantum probabilities melts into the more familiar probabilities of day-to-day hife.’~ This suggests a resolution of the quantum measurement puzzle, one that, if realized, would be just about the best thing we could hope for. I’ll describe it first in the most optimistic light, and then stress what still needs to be done.
If a wavefunction for an isolated electron shows that it has, say, a 50 percent chance of being here and a 50 percent chance of being there, we must interpret these probabilities using the full-fledged weirdness of quantum mechanics. Since both of the alternatives can reveal themselves by commingling and generating an interference pattern, we must think of them as equally real. In loose language, there’s a sense in which the electron is at both locations. What happens now if we measure the electron’s
position with a nonisolated, everyday-sized laboratory instrument? Well, corresponding to the electron’s ambiguous whereabouts, the pointer on the instrument has a 50 percent chance of pointing to this value and a 50 percent chance of pointing to that value. But because of decoherence, the pointer will not be in a ghostly mixture of pointing at both values; because of decoherence, we can interpret these probabilities in the usual, classical, everyday sense. Just as a coin has a 50 percent chance of landing heads and a 50 percent chance of landing tails, but lands either heads or tails, the pointer has a 50 percent chance of pointing to this value and a 50 percent chance of pointing to that value, but it will definitely point to one or the other.
Similar reasoning applies for all other complex, nonisolated objects. If a quantum calculation reveals that a cat, sitting in a closed box, has a 50 percent chance of being dead and a 50 percent chance of being alive— because there is a 50 percent chance that an electron will hit a booby-trap mechanism that subjects the cat to poison gas and a 50 percent chance that the electron misses the booby trap—decoherence suggests that the cat will not be in some absurd mixed state of being both dead and alive. Although decades of heated debate have been devoted to issues like What does it mean for a cat to be both dead and alive? How does the act of opening the box and observing the cat force it to choose a definite status, dead or alive?, decoherence suggests that long before you open the box, the environment has already completed billions of observations that, in almost no time at all, turned all mysterious quantum probabilities into their less mysterious classical counterparts. Long before you look at it, the environment has compelled the cat to take on one, single, definite condition. Decoherence forces much of the weirdness of quantum physics to “leak” from large objects since, bit by bit, the quantum weirdness is carried away by the innumerable impinging particles from the environment.
It’s hard to imagine a more satisfying solution to the quantum measurement problem. By being more realistic and abandoning the simplifying assumption that ignores the environment—a simplification that was crucial to making progress during the early development of the field—we would find that quantum mechanics has a built-in solution. Human consciousness, human experimenters, and human observations would no longer play a special role since they (we!) would simply be elements of the environment, like air molecules and photons, which can interact with a given physical system. There would also no longer be a stage one / stage two split between the evolution of the objects and the experimenter who measures them. Everything—observed and observer—would be on an equal footing. Everything—observed and observer—would be subject to precisely the same quantum mechanical law as is set down in Schrödinger’s equation. The act of measurement would no longer be special; it would merely be one specific example of contact with the environment.
Is that it? Does decoherence resolve the quantum measurement problem? Is decoherence responsible for wavefunctions’ closing the door on all but one of the potential outcomes to which they can lead? Some think so. Researchers like Robert Griffiths, of Carnegie Mellon; Roland Omnès, of Orsay; the Nobel laureate Murray Gell-Mann, of the Santa Fe Institute; and Jim Hartle, of the University of California at Santa Barbara, have made great progress and claim that they have developed decoherence into a complete framework (called decoherent histories) that solves the measurement problem. Others, like myself, are intrigued but not yet fully convinced. You see, the power of decoherence is that it successfully removes the artificial barrier Bohr erected between large and small physical systems, making everything subject to the same quantum mechanical formulas. This is important progress and I think Bohr would have found it gratifying. Although the unresolved quantum measurement problem never diminished physicists’ ability to reconcile theoretical calculations with experimental data, it did lead Bohr and his colleagues to articulate a quantum mechanical framework with some distinctly awkward features. Many found the framework’s need for fuzzy words about wavefunction collapse or the imprecise notion of “large” systems belonging to the dominion of classical physics, unnerving. To a significant extent, by taking account of decoherence, researchers have rendered these vague ideas u n necessary.
However, a key issue that I skirted in the description above is that even though decoherence suppresses quantum interference and thereby coaxes weird quantum probabilities to be like their familiar classical counterparts, each of the potential outcomes embodied in a wave function still vies for realization. And so we are still left wondering how one outcome “wins” and where the many other possibilities “go” when that actually happens. When a coin is tossed, classical physics gives an answer to the analogous question. It says that if you examine the way the coin is set spinning with adequate precision, you can, in principle, predict whether it will land heads or tails. On closer inspection, then, precisely one outcome is determined by details you initially overlooked. The same cannot be said in quantum physics. Decoherence allows quantum probabilities to be interpreted much like classical ones, but does not provide any finer details that select one of the many possible outcomes to actually happen.
Much in the spirit of Bohr, some physicists believe that searching for such an explanation of how a single, definite outcome arises is misguided. These physicists argue that quantum mechanics, with its updating to include decoherence, is a sharply formulated theory whose predictions account for the behavior of laboratory measuring devices. And according to this view, that is the goal of science. To seek an explanation of what’s really going on, to strive for an understanding of how a particular outcome came to be, to hunt for a level of reality beyond detector readings and computer printouts betrays an unreasonable intellectual greediness.
Many others, including me, have a different perspective. Explaining data is what science is about. But many physicists believe that science is also about embracing the theories data confirms and going further by using them to gain maximal insight into the nature of reality. I strongly suspect that there is much insight to be gained by pushing onward toward a complete solution of the measurement problem.
Thus, although there is wide agreement that environment-induced decoherence is a crucial part of the structure spanning the quantum-to-classical divide, and while many are hopeful that these considerations will one day coalesce into a complete and cogent connection between the two, far from everyone is convinced that the bridge has yet been fully built.
Quantum Mechanics and the Arrow of Time
So where do we stand on
the measurement problem, and what does it mean for the arrow of time? Broadly
speaking, there are two classes of proposals for liiiking
common experience with quantum reality. In the first class (for example, wavefunction as knowledge; Many Worlds; decoherence), Schrodinger’s
equation is the be-all and end-all of the story; the proposals simply provide
different ways of interpreting what the equation means for physical reality.
In the second class (for example, Bohm; Ghirardi-Rimini-Weber),
Schrodinger’s equation must be supplemented with
other equations (in Bohm’s case, an equation that
shows how a wavefunction pushes a particle around)
or it must be modified (in the Ghirardi-Rimini-Weber
case, to incorporate a new, explicit collapse mechanism). Akey
question for determining the impact on time’s arrow is whether these
proposals introduce a fundamental asymmetry between one direction in time and
the other. Remember, Schrodinger’s equation, just
like those of
In the first class of proposals, the Schrodinger framework is not at all modified, so temporal symmetry is maintained. In the second class, temporal symmetry may or may not survive, depending on the details. For example, in Bohm’s approach, the new equation proposed does treat time future and time past on an equal footing and so no asymmetry is introduced. However, the proposal of Ghirardi, Rimini, and Weber introduces a collapse mechanism that does have a temporal arrow—an “uncollapsing” wavefunction, one that goes from a spiked to a spread-out shape, would not conform to the modified equations. Thus, depending on the proposal, quantum mechanics, together with a resolution to the quantum measurement puzzle, may or may not continue to treat each direction in time equally. Let’s consider the implications of each possibility.
time symmetry persists (as I suspect it will), all of the reasoning and all
of the conclusions of the last chapter can be carried over with little change
to the quantum realm. The core physics that entered our discussion of time’s
arrow was the time-reversal symmetry of classical physics. While the basic
language and framework of quantum physics differ from those of classical
physics—wavefunctions instead of positions and
velocities; Schrodinger’s equation instead of
We would thus come to the same puzzle encountered in Chapter 6. If we take our observations of the world right now as given, as undeniably real, and if entropy should increase both toward the future and toward the past, how do we explain how the world got to be the way it is and how it will subsequently unfold? And the same two possibilities would present themselves: either all that we see popped into existence by a statistical fluke that you would expect to happen every so often in an eternal universe that spends the vast majority of its time being totally disordered, or, for some reason, entropy was astoundingly low just following the big bang and for the last 14 billion years things have been slowly unwinding and will continue to do so toward the future. As in Chapter 6, to avoid the quagmire of not trusting memories, records, and the laws of physics, we focus on the second option—a low-entropy bang—and seek an explanation for how and why things began in such a special state.
If, on the other hand, time symmetry is lost—if the resolution of the measurement problem that is one day accepted reveals a fundamental asymmetric treatment of future versus past within quantum mechanics— it could very well provide the most straightforward explanation of time’s arrow. It might show, for instance, that eggs splatter but don’t unsplatter because, unlike what we found using the laws of classical physics, splattering solves the full quantum equations but unsplattering doesn’t. A reverse-run movie of a splattering egg would then depict motion that couldn’t happen in the real world, which would explain why we’ve never seen it. And that would be that.
Possibly. But even though this would seem to provide a very different explanation of time’s arrow, in reality it may not be as different as it appears. As we emphasized in Chapter 6, for the pages of War and Peace to become increasingly disordered they must begin ordered; for an egg to become disordered through splattering, it must begin as an ordered, pristine egg; for entropy to increase toward the future, entropy must be low in the past so things have the potential to become disordered. However, just because a law treats past and future differently does not ensure that the law dictates a past with lower entropy. The law might still imply higher entropy toward the past (perhaps entropy would increase asymmetrically toward past and future), and it’s even possible that a time-asymmetric law would be unable to say anything about the past at all. The latter is true of the Ghirardi-Rimini-Weber proposal, one of the only substantive timeasymmetric proposals on the market. Once their collapse mechanism does its trick, there is no way to undo it—there is no way to start from the collapsed wavefunction and evolve it back to its previous spread-out form. The detailed form of the wavefunction is lost in the collapse—it turns into a spike—and so it’s impossible to “retrodict” what things were like at any time before the collapse occurred.
Thus, even though a time-asymmetric law would provide a partial explanation for why things unfold in one temporal order but never in the reverse order, it could very well call for the same key supplement required by time-symmetric laws: an explanation for why entropy was low in the distant past. Certainly, this is true of the time-asymmetric modifications to quantum mechanics that have so far been proposed. And so, unless some future discovery reveals two features, both of which I consider unlikely— a time-asymmetric solution to the quantum measurement problem that, additionally, ensures that entropy decreases toward the past—our effort to explain the arrow of time leads us, once again, back to the origin of the universe, the subject of the next part of the book.
As these chapters will make clear, cosmological considerations wend their way through many mysteries at the heart of space, time, and matter. So on the journey toward modern cosmology’s insights into time’s arrow, it’s worth our while not to rush through the landscape, but rather, to take a well-considered stroll through cosmic history.
In addition to Green’s readable prose, and simple explanations and examples, The Fabric of the Cosmos contained 85 illustrations that provide one more way of grasping the material presented. By the end of the book, readers will come away with the acquisition of some of the threads of string theory, and an understanding, no matter how counterintuitive it may seem, of what reality is all about.
Steve Hopkins, August 26, 2004
ã 2004 Hopkins and Company, LLC
The recommendation rating for this book appeared in the September 2004 issue of Executive Times
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