The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

  These experiments are a magnificent affront to our conventional notions of space and time. Something that takes place long after and far away from something else nevertheless is vital to our description of that something else. By any classical—commonsense—reckoning, that's, well, crazy. Of course, that's the point: classical reckoning is the wrong kind of reckoning to use in a quantum universe. We have learned from the Einstein-Podolsky-Rosen discussion that quantum physics is not local in space. If you have fully absorbed that lesson—a tough one to accept in its own right—these experiments, which involve a kind of entanglement across space and through time, may not seem thoroughly outlandish. But by the standards of daily experience, they certainly are.

  Quantum Mechanics and Experience

  For a few days after I first learned about these experiments, I remember feeling elated. I felt I'd been given a glimpse into a veiled side of reality. Common experience—mundane, ordinary, day-to-day activities—suddenly seemed part of a classical charade, hiding the true nature of our quantum world. The world of the everyday suddenly seemed nothing but an inverted magic act, lulling its audience into believing in the usual, familiar conceptions of space and time, while the astonishing truth of quantum reality lay carefully guarded by nature's sleights of hand.

  In recent years, physicists have expended much effort in trying to explain nature's ruse—to figure out precisely how the fundamental laws of quantum physics morph into the classical laws that are so successful at explaining common experience—in essence, to figure out how the atomic and subatomic shed their magical weirdness when they combine to form macroscopic objects. Research continues, but much has already been learned. Let's look at some aspects of particular relevance to the question of time's arrow, but now from the standpoint of quantum mechanics.

  Classical mechanics is based on equations that Newton discovered in the late 1600s. Electromagnetism is based on equations Maxwell discovered in the late 1800s. Special relativity is based on equations Einstein discovered in 1905, and general relativity is based on equations he discovered in 1915. What all these equations have in common, and what is central to the dilemma of time's arrow (as explained in the last chapter), is their completely symmetric treatment of past and future. Nowhere in any of these equations is there anything that distinguishes "forward" time from "backward" time. Past and future are on an equal footing.

  Quantum mechanics is based on an equation that Erwin Schrödinger discovered in 1926. 6 You don't need to know anything about this equation beyond the fact that it takes as input the shape of a quantum mechanical probability wave at one moment of time, such as that in Figure 4.5, and allows one to determine what the probability wave looks like at any other time, earlier or later. If the probability wave is associated with a particle, such as an electron, you can use it to predict the probability that, at any specified time, an experiment will find the electron at any specified location. Like the classical laws of Newton, Maxwell, and Einstein, the quantum law of Schrödinger embraces an egalitarian treatment of time-future and time-past. A "movie" showing a probability wave starting like this and ending like that could be run in reverse—showing a probability wave starting like that and ending like this— and there would be no way to say that one evolution was right and the other wrong. Both would be equally valid solutions of Schrödinger's equation. Both would represent equally sensible ways in which things could evolve. 7

  Of course, the "movie" now referred to is quite different from the ones used in analyzing the motion of a tennis ball or a splattering egg in the last chapter. Probability waves are not things we can see directly; there are no cameras that can capture probability waves on film. Instead, we can describe probability waves using mathematical equations and, in our mind's eye, we can imagine the simplest of them having shapes such as those in Figures 4.5 and 4.6. But the only access we have to the probability waves themselves is indirect, through the process of measurement.

  That is, as outlined in Chapter 4 and seen repeatedly in the experiments above, the standard formulation of quantum mechanics describes the unfolding of phenomena using two quite distinct stages. In stage one, the probability wave—or, in the more precise language of the field, the wavefunction— of an object such as an electron evolves according to the equation discovered by Schrödinger. This equation ensures that the shape of the wavefunction changes smoothly and gradually, much as a water wave changes shape as it travels from one side of a lake toward the other. 18 In the standard description of the second stage, we make contact with observable reality by measuring the electron's position, and when we do so, the shape of its wavefunction sharply and abruptly changes. The electron's wavefunction is unlike more familiar examples like water waves and sound waves: when we measure the electron's position, its wavefunction spikes or, as illustrated in Figure 4.7, it collapses, dropping to the value 0 everywhere the particle is not found and surging to 100 percent probability at the single location where the particle is found by the measurement.

  Stage one—the evolution of wavefunctions according to Schrödinger's equation—is mathematically rigorous, totally unambiguous, and fully accepted by the physics community. Stage two—the collapse of a wavefunction upon measurement—is, to the contrary, something that during the last eight decades has, at best, kept physicists mildly bemused, and at worst, posed problems, puzzles, and potential paradoxes that have devoured careers. The difficulty, as mentioned at the end of Chapter 4, is that according to Schrödinger's equation, wavefunctions do not collapse. Wavefunction collapse is an add-on. It was introduced after Schrödinger discovered his equation, in an attempt to account for what experimenters actually see. Whereas a raw, uncollapsed wavefunction embodies the strange idea that a particle is here and there, experimenters never see this. They always find a particle definitely at one location or another; they never see it partially here and partially there; the needle on their measuring devices never hovers in some ghostly mixture of pointing at this value and also at that value.

  The same goes, of course, for our own casual observations of the world around us. We never observe a chair to be both here and there; we never observe the moon to be in one part of the night sky as well as another; we never see a cat that is both dead and alive. The notion of wavefunction collapse aligns with our experience by postulating that the act of measurement induces the wavefunction to relinquish quantum limbo and usher one of the many potentialities (particle here, or particle there) into reality.

  The Quantum Measurement Puzzle

  But how does an experimenter's making a measurement cause a wavefunction to collapse? In fact, does wavefunction collapse really happen, and if it does, what really goes on at the microscopic level? Do any and all measurements cause collapse? When does the collapse happen and how long does it take? Since, according to the Schrödinger equation, wavefunctions do not collapse, what equation takes over in the second stage of quantum evolution, and how does the new equation dethrone Schrödinger's, usurping its usual ironclad power over quantum processes? And, of importance to our current concern with time's arrow, while Schrödinger's equation, the equation that governs the first stage, makes no distinction between forward and backward in time, does the equation for stage two introduce a fundamental asymmetry between time before and time after a measurement is carried out? That is, does quantum mechanics, including its interface with the world of the everyday via measurements and observations, introduce an arrow of time into the basic laws of physics? After all, we discussed earlier how the quantum treatment of the past differs from that of classical physics, and by past we meant before a particular observation or measurement had taken place. So do measurements, as embodied by stage-two wavefunction collapse, establish an asymmetry between past and future, between before and after a measurement is made?

  These questions have stubbornly resisted complete solution and they remain controversial. Yet, through the decades, the predictive power of quantum theory has hardly been compromised. The stage one / stage two for
mulation of quantum theory, even though stage two has remained mysterious, predicts probabilities for measuring one outcome or another. And these predictions have been confirmed by repeating a given experiment over and over again and examining the frequency with which one or another outcome is found. The fantastic experimental success of this approach has far outweighed the discomfort of not having a precise articulation of what actually happens in stage two.

  But the discomfort has always been there. And it is not simply that some details of wavefunction collapse have not quite been worked out. The quantum measurement problem, as it is called, is an issue that speaks to the limits and the universality of quantum mechanics. It's simple to see this. The stage one / stage two approach introduces a split between what's being observed (an electron, or a proton, or an atom, for example) and the experimenter who does the observing. Before the experimenter gets into the picture, wavefunctions happily and gently evolve according to Schrödinger's equation. But then, when the experimenter meddles with things to perform a measurement, the rules of the game suddenly change. Schrödinger's equation is cast aside and stage-two collapse takes over. Yet, since there is no difference between the atoms, protons, and electrons that make up the experimenter and the equipment he or she uses, and the atoms, protons, and electrons that he or she studies, why in the world is there a split in how quantum mechanics treats them? If quantum mechanics is a universal theory that applies without limitations to everything, the observed and the observer should be treated in exactly the same way.

  Niels Bohr disagreed. He claimed that experimenters and their equipment are different from elementary particles. Even though they are made from the same particles, they are "big" collections of elementary particles and hence governed by the laws of classical physics. Somewhere between the tiny world of individual atoms and subatomic particles and the familiar world of people and their equipment, the rules change because the sizes change. The motivation for asserting this division is clear: a tiny particle, according to quantum mechanics, can be located in a fuzzy mixture of here and there, yet we don't see such behavior in the big, everyday world. But exactly where is the border? And, of vital importance, how do the two sets of rules interface when the big world of the everyday confronts the minuscule world of the atomic, as in the case of a measurement? Bohr forcefully declared these questions to be out of bounds, by which he meant, truth be told, that they were beyond the bounds of what he or anyone else could answer. And since even without addressing them the theory makes astonishingly accurate predictions, for a long time such issues were far down on the list of critical questions that physicists were driven to settle.

  But to understand quantum mechanics completely, to determine fully what it says about reality, and to establish what role it might play in setting a direction to time's arrow, we must come to grips with the quantum measurement problem.

  In the next two sections, we'll describe some of the most prominent and promising attempts to do so. The upshot, should you at any point want to rush ahead to the last section focusing on quantum mechanics and the arrow of time, is that much ingenious work on the quantum measurement problem has yielded significant progress, but a broadly accepted solution still seems just beyond our reach. Many view this as the single most important gap in our formulation of quantum law.

  Reality and the Quantum Measurement Problem

  Over the years, there have been many proposals for solving the quantum measurement problem. Ironically, although they entail differing conceptions of reality—some drastically different—when it comes to predictions for what a researcher will measure in most every experiment, they all agree and each one works like a charm. Each proposal puts on the same show, even though, were you to peek backstage, you'd see that their modi operandi differ substantially.

  When it comes to entertainment, you generally don't want to know what's happening off in the wings; you are perfectly content to focus solely on the production. But when it comes to understanding the universe, there is an insatiable urge to pull back all curtains, open all doors, and expose completely the deep inner workings of reality. Bohr considered this urge baseless and misguided. To him, reality was the performance. Like a Spalding Gray soliloquy, an experimenter's bare-bones measurements are the whole show. There isn't anything else. According to Bohr, there is no backstage. Trying to analyze how, and when, and why a quantum wavefunction relinquishes all but one possibility and produces a single definite number on a measuring device is missing the point. The measured number itself is all that's worthy of attention.

  For decades, this perspective held sway. However, its calmative effect on the mind struggling with quantum theory notwithstanding, one can't help feeling that the fantastic predictive power of quantum mechanics means that it is tapping into a hidden reality that underlies the workings of the universe. One can't help wanting to go further and understand how quantum mechanics interfaces with common experience—how it bridges the gap between wavefunction and observation, and what hidden reality underlies the observations. Over the years, a number of researchers have taken up this challenge; here are some proposals they've developed.

  One approach, with historical roots that go back to Heisenberg, is to abandon the view that wavefunctions are objective features of quantum reality and, instead, view them merely as an embodiment of what we know about reality. Before we perform a measurement, we don't know where the electron is and, this view proposes, our ignorance of its location is reflected by the electron's wavefunction describing it as possibly being at a variety of different positions. At the moment we measure its position, though, our knowledge of its whereabouts suddenly changes: we now know its position, in principle, with total precision. (By the uncertainty principle, if we know its location we will necessarily be completely ignorant of its velocity, but that's not an issue for the current discussion.) This sudden change in our knowledge, according to this perspective, is reflected in a sudden change in the electron's wavefunction: it suddenly collapses and takes on the spiked shape of Figure 4.7, indicating our definite knowledge of the electron's position. In this approach, then, the abrupt collapse of a wavefunction is completely unsurprising: it is nothing more than the abrupt change in knowledge that we all experience when we learn something new.

  A second approach, initiated in 1957 by Wheeler's student Hugh Everett, denies that wavefunctions ever collapse. Instead, each and every potential outcome embodied in a wavefunction sees the light of day; the daylight each sees, however, streams through its own separate universe. In this approach, the Many Worlds interpretation, the concept of "the universe" is enlarged to include innumerable "parallel universes"—innumerable versions of our universe—so that anything that quantum mechanics predicts could happen, even if only with minuscule probability, does happen in at least one of the copies. If a wavefunction says that an electron can be here, there, and way over there, then in one universe a version of you will find it here; in another universe, another copy of you will find it there; and in a third universe, yet another you will find the electron way over there. The sequence of observations that we each make from one second to the next thus reflects the reality taking place in but one part of this gargantuan, infinite network of universes, each one populated by copies of you and me and everyone else who is still alive in a universe in which certain observations have yielded certain outcomes. In one such universe you are now reading these words, in another you've taken a break to surf the Web, in yet another you're anxiously awaiting the curtain to rise for your Broadway debut. It's as though there isn't a single spacetime block as depicted in Figure 5.1, but an infinite number, with each realizing one possible course of events. In the Many Worlds approach, then, no potential outcome remains merely a potential. Wavefunctions don't collapse. Every potential outcome comes out in one of the parallel universes.

  A third proposal, developed in the 1950s by David Bohm—the same physicist we encountered in Chapter 4 when discussing the Einstein-Podolsky-Rosen paradox—takes a compl
etely different approach. 8 Bohm argued that particles such as electrons do possess definite positions and definite velocities, just as in classical physics, and just as Einstein had hoped. But, in keeping with the uncertainty principle, these features are hidden from view; they are examples of the hidden variables mentioned in Chapter 4. You can't determine both simultaneously. For Bohm, such uncertainty represented a limit on what we can know, but implied nothing about the actual attributes of the particles themselves. His approach does not fall afoul of Bell's results because, as we discussed toward the end of Chapter 4, possessing definite properties forbidden by quantum uncertainty is not ruled out; only locality is ruled out, and Bohm's approach is not local. 9 Instead, Bohm imagined that the wavefunction of a particle is another, separate element of reality, one that exists in addition to the particleitself. It's not particles or waves, as in Bohr's complementarity philosophy; according to Bohm, it's particles and waves. Moreover, Bohm posited that a particle's wavefunction interacts with the particle itself—it "guides" or "pushes" the particle around—in a way that determines its subsequent motion. While this approach agrees fully with the successful predictions of standard quantum mechanics, Bohm found that changes to the wavefunction in one location are able to immediately push a particle at a distant location, a finding that explicitly reveals the nonlocality of his approach. In the double-slit experiment, for example, each particle goes through one slit or the other, while its wavefunction goes through both and suffers interference. Since the wavefunction guides the particle's motion, it should not be terribly surprising that the equations show the particle is likely to land where the wavefunction value is large and it is unlikely to land where it is small, explaining the data in Figure 4.4. In Bohm's approach, there is no separate stage of wavefunction collapse since, if you measure a particle's position and find it here, that is truly where it was a moment before the measurement took place.