How Is the Universe Built? Grain by Grain

            By GEORGE JOHNSON
            Slightly smaller than what Americans quaintly insist on
            calling half an inch, a centimeter (one-hundredth of a
        meter) is easy enough to see. Divide this small length into
        10 equal slices and you are looking, or probably squinting,
        at a millimeter (one-thousandth, or 10 to the minus 3
        meters). By the time you divide one of these tiny units into
        a thousand minuscule micrometers, you have far exceeded
        the limits of the finest bifocals.

        But in the mind's eye, let the
        cutting continue, chopping the
        micrometer into a thousand
        nanometers and the
        nanometers into a thousand
        picometers, and those in steps
        of a thousandfold into
        femtometers, attometers,
        zeptometers, and
        yoctometers. At this point, 10
        to the minus 24 meters, about
        one-billionth the radius of a
        proton, the roster of
        convenient Greek names runs
        out. But go ahead and keep
        dividing, again and again until
        you reach a length only a
        hundred-billionth as large as
        that tiny amount: 10 to the
        minus 35 meters, or a decimal
        point followed by 34 zeroes
        and then a one.

        You have finally hit rock bottom: a span called the Planck
        length, the shortest anything can get. According to recent
        developments in the quest to devise a so-called "theory of
        everything," space is not an infinitely divisible continuum.
        It is not smooth but granular, and the Planck length gives
        the size of its smallest possible grains.

        The time it takes for a light beam to zip across this
        ridiculously tiny distance (about 10 to the minus 43
        seconds) is called the Planck time, the shortest possible
        tick of an imaginary clock. Combine these two ideas and
        the implication is that space and time have a structure.
        What is commonly thought of as the featureless void is
        built from tiny units, or quanta.

        "We've long suspected that space-time had to be
        quantized," said Dr. Steven B. Giddings, a theorist at the
        University of California at Santa Barbara. "Recent
        developments have led to some exciting new proposals
        about how to make these ideas more concrete."

        The hints of graininess come from attempts to unify
        general relativity, Einstein's theory of gravity, with quantum
        mechanics, which describes the workings of the three other
        forces: electromagnetism and the strong and weak nuclear
        interactions. The result would be a single framework --
        sometimes called quantum gravity -- that explains all the
        universe's particles and forces.

        The most prominent of these unification efforts,
        superstring theory, and a lesser-known approach called
        loop quantum gravity, both strongly suggest that
        space-time has a minute architecture. But just what the void
        might look like has physicists straining their imaginations.

        As Dr. John Baez, a theorist at the University of California
        at Riverside put it: "There's a lot we don't know about
        nothing."

        Since the days of ancient Greece, some philosophers have
        insisted that reality must be perfectly smooth like the
        continuum of real numbers: pick any two points, no matter
        how close together, and there is an infinity of gradations in
        between. Others have argued that, on the smallest scale,
        everything is surely divided into irreducible units like the
        so-called natural or counting numbers, with nothing
        between, say, 3 and 4.

        The development of modern atomic theory, in the 19th
        century, pushed science toward viewing the universe as
        lumpy instead of smooth. At the beginning of this century,
        sentiments swung further in that direction when Max
        Planck found that even light was emitted in packets. From
        that unexpected discovery emerged quantum field theory,
        in which all the forces are carried by tiny particles, or
        quanta -- all, that is, except gravity.

        This force continues to be explained, in entirely different
        terms, by general relativity: as the warping of a perfectly
        smooth continuum called space-time. A planet bends the
        surrounding space-time fabric causing other objects to
        move toward it like marbles rolling down a hill.

        Scientists have long assumed that unification would reveal
        that gravity, like the other forces, is also quantum in nature,
        carried by messenger particles called gravitons. But while
        the other forces can be thought of as acting within an arena
        of space and time, gravity is space-time. Quantizing one is
        tantamount to quantizing the other.

        It is hardly surprising that space-time graininess has gone
        unnoticed here in the macroscopic realm. Even the tiny
        quarks that make up protons, neutrons and other particles
        are too big to feel the bumps that may exist on the Planck
        scale. More recently, though, physicists have suggested
        that quarks and everything else are made of far tinier
        objects: superstrings vibrating in 10 dimensions. At the
        Planck level, the weave of space-time would be as
        apparent as when the finest Egyptian cotton is viewed
        under a magnifying glass, exposing the warp and woof.

        It was Planck himself who first had an inkling of a smallest
        possible size. He noticed that he could start with three
        fundamental parameters of the universe -- the gravitational
        constant (which measures the strength of gravity), the
        speed of light, and his own Planck's constant (a gauge of
        quantum graininess) -- and combine them in such a way
        that the units canceled one another to yield a length. He
        was not sure about the meaning of this Planck length, as it
        came to be called, but he felt that it must be something
        very basic.

        In the 1950's,
        the physicist
        John Wheeler
        suggested that
        the Planck length
        marked the
        boundary where
        the random roil
        of quantum
        mechanics
        scrambled space
        and time so
        violently that
        ordinary notions
        of measurement
        stopped making
        sense. He called the result "quantum foam."

        "So great would be the fluctuations that there would
        literally be no left and right, no before and no after," Dr.
        Wheeler recently wrote in his memoir, "Geons, Black
        Holes and Quantum Foam" (Norton, 1998). "Ordinary
        ideas of length would disappear. Ordinary ideas of time
        would evaporate."

        Half a century later, physicists are still trying to work out
        the bizarre implications of a minimum length. In superstring
        theory, a mathematical relationship called T duality
        suggests that one can shrink a circle only so far. As the
        radius contracts, the circle gets smaller and smaller and
        then bottoms out, suddenly acting as though it is getting
        bigger and bigger.

        "This behavior implies that there is a minimum 'true size' to
        the circle," Dr. Giddings said. Many believe this will turn
        out to be roughly comparable to the Planck scale.

        There are other indications of graininess. According to the
        Heisenberg uncertainty principle, certain pairs of quantities
        are "noncommutative": you cannot simultaneously measure
        a particle's position and momentum, for example, or its
        energy and life span. The more precisely you know one,
        the fuzzier your knowledge of the other becomes.

        In string theory, the very geometry of space may turn out
        to be noncommutative, making it impossible to measure
        simultaneously the horizontal and vertical position of a
        particle to perfect precision. The graininess of space itself
        would get in the way.

        Not everyone in the unification business is a string theorist.
        Coming from an entirely different direction, researchers in
        a discipline called loop quantum gravity have devised a
        theory in which space is constructed from abstract
        mathematical objects called spin nets.

        Imagine a tiny particle spinning like a top on its axis. Now
        send it on a roundtrip journey, a loop through space.
        Depending on the Einsteinian shape of the space the
        particle traverses, it will return home with its axis tilted in a
        different direction. This change then provides a clue about
        how the space is curved.

        Using particles with various spins, theorists can probe
        space in more detail. The different trajectories can then be
        combined into a web, called a spin network, that captures
        everything you need to know about how the space is
        curved -- what physicists call its geometry.

        "Our space in which we live is just this enormously
        complicated spin network," said Dr. Carlo Rovelli of the
        University of Pittsburgh. He and Dr. Lee Smolin of the
        Center for Gravitational Physics and Geometry at
        Pennsylvania State University have figured out how to use
        spin nets to calculate area and volume -- all this information
        is encoded within the weblike structure.

        Suppose you are sitting at a table. To calculate its area you
        would add up the spins of all the links of the spin net that
        are passing through it, and multiply by the square of the
        Planck length. A table with an area of about one square
        meter would be impinged by some 10 to the 65th of these
        trajectories. The implication is that the very idea of a
        surface is an illusion generated by the spin network.

        The picture gets even weirder. In quantum mechanics, an
        electron orbiting an atomic nucleus is thought of as a cloud
        of probability: a "superposition" in which all the electron's
        possible locations hover together. In the view of Dr.
        Rovelli, Dr. Smolin and their colleagues, the universe itself
        is a superposition of every conceivable spin net -- all the
        possible ways that it can be curved.

        Where does time fit into the picture? A spin net provides a
        snapshot of the geometry of three-dimensional space at a
        particular instant. To describe space-time, Dr. Baez and
        other theorists have stretched spin nets into the fourth
        dimension, devising what they call spin foam. Slice it and
        each infinitely thin cross section is a spin net.

        Most perplexing of all, spin nets and spin foam cannot be
        thought of as existing in space and time. They reside on a
        more fundamental level, as a deep structure that underlies
        and gives rise to space-time.

        "That is the core of the matter," Dr. Rovelli said. "They
        don't live somewhere. They are the quantum space-time."

        The universe, in this view, is conjured up from pure
        mathematics. And the old idea of space and time as the
        stage on which everything happens no longer seems to
        apply.

        "If we believe what we really have discovered about the
        world with quantum mechanics and general relativity, then
        the stage fiction has to be abandoned," Dr. Rovelli said,
        "and we have to learn to do physics and to think about the
        world in a profoundly new way. Our notions of what are
        space and time are completely altered. In fact, in a sense,
        we have to learn to think without them."