My first encounter with John Archibald Wheeler was in the fall of 1945 in the reading room of the Science Library in London, a warm and comfortable place where anyone could walk in off the street to escape from rain and fog or to browse at leisure in scientific books and journals. I had just been released from war service and was eager to get back into science. I found the classic paper of Bohr and Wheeler, “The mechanism of nuclear fission,” in volume 56 of the Physical Review, pages 426–450. It was published on September 1, 1939, the day on which Hitler's armies marched into Poland and the Second World War began. Bohr and Wheeler wrote the paper in Princeton, where Bohr was visiting in the spring of 1939, a few months after the discovery of fission. The paper is a masterpiece of clear thinking and lucid writing. It reveals, at the center of the mystery of fission, a tiny world where everything can be calculated and everything understood. The tiny world is a nucleus of uranium 236, formed when a neutron is freshly captured by a nucleus of uranium 235.

The uranium 236 nucleus sits precisely on the border between classical and quantum physics. Seen from the classical point of view, it is a liquid drop composed of a positively charged fluid. The electrostatic force that is trying to split it apart is balanced by the nuclear surface tension that is holding it together.

The ups and downs of oscillating universes

John Wheeler was one of the first to stress the physical significance of the fundamental Planck scales of mass, length, and time. He recognized their quantum gravitational significance and speculated upon the strange things that might happen when the universe crossed that mysterious threshold where general relativity and quantum theory meet to consummate their arranged marriage. For Wheeler, Einstein's conception of cosmology always implied a universe that was finite in size and total lifetime, a “closed” universe evolving from a Big Bang in the past to a Big Crunch in the future. We still do not know whether these two singular points of the evolution signal merely a breakdown of the nonquantum theory of gravity that we are using or whether they have special significance and will remain even in a future quantum theory of cosmology.

If our expanding universe of stars and galaxies did not appear spontaneously out of nothing at all, then from what might it have arisen? One option that has an ancient pedigree is to sidestep the question and propose that it had no beginning. It always existed.

Introduction

Of John Wheeler's “Really Big Questions,” the one on which the most progress has been made is “It from bit?” – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other questions, such as “How come existence?”, because it does not necessarily require a metaphysical answer. And unlike, say, “Why the quantum?”, it does not require the discovery of new laws of nature: there was room for hope that it might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation.

How might our conception of the quantum physical world have been different if “It from bit” had been a motivation from the outset? No one knows how to derive it (the nature of the physical world) from bit (the idea that information plays a significant role at the foundations of physics), and I shall argue that this will never be possible. But we can do the next best thing: we can start from the qubit.

Qubits

To a classical information theorist, a bit is an abstraction: a certain amount of information. To a programmer, a bit is a Boolean variable. To an engineer, a bit is a “flip-flop” – a piece of hardware that is stable in either of two physical states.

Introduction

The quantum measurement problem – how does an apparently “classical” definite world arise out of the random world of quantum superpositions – was and continues to be one of the fundamental philosophical issues in quantum mechanics. What we mean by a classical world, for example, is one in which macroscopic objects are not in superposition states of being simultaneously in several locations at once, and cats are never in coherent superpositions of being alive and dead. This lack of coherence is actually a loss of the coherence that exists at the level of the isolated quanta, but somehow does not survive the transition to the classical level of measuring apparatus. Such incoherent states are known as mixed states. Therefore, to study the quantum–classical interface, or even to investigate whether such an interface exists at all other than in the minds of “classical sympathizers,” one should look carefully at mixed states, how they arise and how they behave. Here we describe a set of experiments, both real and gedanken, investigating the subtleties of quantum interference when mixed states are involved. We start by describing the well-known double-slit experiment, and the loss of interference when which-path information can be had.

Introduction

One of the most obvious and compelling aspects of the physical world is that it has an “arrow of time.” Certain processes (such as breaking a glass or burning fuel) appear all the time in our everyday experience, but the time reverse of these processes is never seen. In the modern understanding, special nongeneric initial conditions of the universe are used to explain the time-directed nature of the dynamics we see around us.

On the other hand, modern cosmologists believe it is possible to explain the initial conditions of the universe. The theory of cosmic inflation (and a number of competitors) claims to use physical processes to set up the initial conditions of the standard Big Bang. So in one case initial conditions are being used to explain dynamics, and in the other, dynamics are being used to explain initial conditions. In this chapter I explore the relationship between two apparently different perspectives on initial conditions and dynamics.

My goal in pursuing this question is to gain a deeper insight into what we are actually able to accomplish with theories of cosmic initial conditions. Can these two perspectives coexist, perhaps even allowing one to conclude that cosmic inflation explains the arrow of time? Or do these two different ideas about relating dynamics and initial conditions point to some deep contradiction, leading us to conclude that a fundamental explanation of both the arrow of time and the initial conditions of the universe is impossible?

Introduction

Does Schrödinger's wave function describe physical reality (“it” in John Wheeler's terminology (Wheeler 1994)) or some kind of information (“bit”)? The answer to this question must crucially depend on the definition of these terms. Is it then merely a matter of words? Not quite – I feel. Inappropriate words may be misleading, while reasonably chosen terms are helpful.

A bit is usually understood as the binary unit of information, which can be physically realized in (classical) computers, but also by neuronal states of having fired or not. This traditional physical (in particular, thermodynamical) realization of information (“bit from it”) has proven essential in order to avoid paradoxes otherwise arising from situations related to Maxwell's demon. On the other hand, the concept of a bit has a typical quantum aspect: the very word quantum refers to discreteness, while, paradoxically, the quantum bit is represented by a continuum (the unit sphere in a two-dimensional Hilbert space) – more similar to an analog computer. If this quantum state describes “mere information,” how can there be real quantum computers that are based on such superpositions of classical bits?

The problematic choice of words characterizing the nature of the wave function (or a general “quantum state”) seems to reflect the common uneasiness of physicists, including the founders of quantum theory, about its fundamental meaning. However, it may also express a certain prejudice.

The three origins: how come us?

We cannot but wonder about our origin. Cultures throughout history have created mythical narratives that attempt to answer this most vexing of questions, “Why is there something rather than nothing?” Hard questions inspire further thought, and the harder they are, the more inspiring they can be. The rich variety of creation myths is testimony to this. Most of the myths bypass the issue of “something from nothing” by eliminating the nothing: an absolute reality, in the form of a deity or deities, exists outside space and time and originates the cosmos, the order of material things. Creation involves the transition from the absolute to the relative, from a spaceless and timeless reality to a reality within space and time. Myths that don't invoke a deity presume some form of absolute reality which encompasses all opposites, order and chaos, light and darkness. The cosmos emerges spontaneously out of the tension between the opposites, and differentiation follows. A curious exception comes from the Maori people of New Zealand, who describe the origin of all things as coming from nothing, without the action of a god: the cosmos simply comes into being out of a universal urge to exist, a sort of irresistible impulse of creation (Gleiser 1997).

A more detailed study of creation myths shows that they describe the origin of the cosmos through two distinct uses of the concept of emergence: driven emergence and spontaneous emergence.

Introduction

The topics that have been discussed in this volume are generally very difficult ones. They involve some of the big questions that philosophers have pondered for centuries. The wonderful thing about physics is that sometimes, by pondering “little” tractable problems, you uncover deep truths. Little inconsistencies or new results from old theories can lead to wisdom. These advances are not anticipated but by having the big questions in mind, one recognizes them when they appear.

In trying to understand deeper truths about cosmology, extra dimensions are a good place to begin. The equations are well grounded in general relativity at scales where quantum gravitational effects should be under control. Nevertheless, by not exclusively focusing on four–dimensional cosmological solutions, one can discover new phenomena. These might even lead to fundamental truths that can impinge on the four-dimensional appearing universe that we observe.

The plan of this chapter is to first go over some of the major questions in cosmology. I will then discuss some new gravitational solutions in more than four dimensions, and what new aspects of gravity they reveal. The other nice thing about these solutions is that they can be used as a testing ground for ideas about gravity that have been developed based on four-dimensional intuition. I will then sketch some of the newer developments in extra dimensions, and how new geometries continue to reveal unanticipated features.

It has to be a jolting culture shock, or at any rate a severe case of the bends, for someone who has spent the past 60 years since completing the Gymnasium in 1942 studying, reading, translating, and interpreting St Augustine and St Thomas Aquinas, Martin Luther and the other sixteenth-century reformers, and the fourth-century Greek church fathers together with the Greek and Russian Orthodox tradition coming out of them, suddenly to be plunged into the rarefied atmosphere of this volume. Why, back where I come from, quantum is still a Latin interrogatory adjective in the neuter singular! One thing that I did learn, however, from Thomas Aquinas and his fellow scholastics was the doctrine of the analogia entis, the analogy of Being, which enables even a finite mind to speak by analogy about the Infinite (as the old proverb says, “A cat may look on a king”), because in some sense, at any rate in an analogous sense, it may be said that both of them “are,” even though only God “is” noncontingently; it has been brilliantly discussed in the Gifford Lectures of Professor Etienne Gilson at Aberdeen (Gilson 1944).

Introduction

A volume in honor of a visionary thinker such as John Archibald Wheeler is a rare license to exercise in the kind of speculation and exploration for which Wheeler is famous, but which most of the rest of us usually feel we had better keep to ourselves. We have all – even those of us who never had the fortune to work directly with him – been inspired and motivated by Wheeler's creativity and open-mindedness. For all of our apparent understanding of quantum mechanics, our ability to calculate remarkable things using this theory, and the regularity with which experiment has borne out these predictions, at the turn of the twenty-first century it seems there are as many puzzles on the road to a true understanding of quantum theory as there were at the start of the previous century. Then, at least, one could hope to be guided by the mysteries of unexplained experiment. Now, by contrast, we may seem to have lost our way, as even though our experiments are all “explained” (in some narrow sense which can only be deemed satisfactory out of fear to leap beyond the comfortable realm of formalism), the theory itself is mysterious. Further explorations, without the anchor of experiment, certainly run the risk of becoming mere flights of metaphysical fancy, giving rise to factions characterized less by intellectual rigor than by fundamentalist zeal. Yet it would be premature to give up the journey before at least trying to establish a foothold on the terrain ahead.

Why quantum gravity?

In the twentieth century we gained an enormous amount of knowledge about the basic fundamental laws that govern the physical world. We can summarize this knowledge by saying that particles experience four kinds of forces: electromagnetic, weak, strong, and gravitational. For the first three we have a quantum mechanical description but for gravity we have Einstein's theory, which is rather difficult to quantize. It is not logically consistent to describe particles with quantum mechanics but spacetime with classical physics since matter causes spacetime curvature. So we should be able to consider a particle which is in a quantum mechanical superposition of two states with different positions. These particles should create a gravitational field which contains a similar superposition. This is possible only if the gravitational field itself is quantized. Finding a theory of quantum gravity is not just a question of mathematical consistency, there are physical processes that we cannot describe with current theories. The most notable of these is the beginning of the universe, the initial moments of the Big Bang. We need a quantum gravity theory to be able to understand that moment. The moment is very important since it sets the initial conditions for the subsequent classical evolution of spacetime. Quantum gravity is important when the typical energies of the particles involved are very high. We know from the form of Einstein's action that quantum gravity must be important when particle energies are close to 1019 GeV, which is called the Planck energy.

Beyond the black hole

In 1979 we held a symposium at the Institute for Advanced Study to celebrate the hundredth birthday of Albert Einstein. Unfortunately Einstein could not be there, but John Wheeler made up for Einstein's absence. Wheeler gave a marvelous talk with the title “Beyond the black hole,” sketching with poetic prose and Wheelerian pictures his grand design for the future of science. Wheeler's philosophy of science is much more truly relativistic than Einstein's. Wheeler would make all physical law dependent on the participation of observers. He has us creating physical laws by our existence. This is a radical departure from the objective reality in which Einstein believed so firmly. Einstein thought of nature and nature's laws as transcendent, standing altogether above and beyond us, infinitely higher than human machinery and human will.

One of the questions that has always puzzled me is this. Why was Einstein so little interested in black holes? To physicists of my age and younger, black holes are the most exciting consequence of general relativity. With this judgment the man-in-the-street and the television commentators and journalists agree. How could Einstein have been so indifferent to the promise of his brightest brainchild? I suspect that the reason may have been that Einstein had some inkling of the road along which John Wheeler was traveling, a road profoundly alien to Einstein's philosophical preconceptions.

Introduction

In this volume honoring John Archibald Wheeler, I would like to take a fresh look at the intersection between two fields to which he devoted much of his research life: general relativity (GR) and quantum mechanics (QM). As evidence of his keen interest in these two subjects, I would cite two examples from my own experience. When I was an undergraduate at Princeton University during the years from 1957 to 1961, he was my adviser. One of his duties was to assign me topics for my junior paper and for my senior thesis. For my junior paper, I was assigned the topic: “Compare the complementarity and the uncertainty principles of quantum mechanics: Which is more fundamental?” For my senior thesis, I was assigned the topic: “How to quantize general relativity?” As Wheeler taught me, more than half of science is devoted to the asking of the right question, while often less than half is devoted to the obtaining of the correct answer, but not always!

In the same spirit, I would like to offer up here some questions concerning conceptual tensions between GR and QM, which hopefully can be answered in the course of time by experiments, with a view towards probing the tension between the concepts of locality in GR and nonlocality in QM. I hope that it would be appropriate and permissible to ask some questions here concerning this tension.