Atoms are now such a commonplace idea that it is hard to remember how radical they used to seem. When scientists first hypothesized atoms centuries ago, they despaired of ever observing anything so small, and many questioned whether the concept of atoms could even be called scientific. Gradually, however, evidence for atoms accumulated and reached a tipping point with Albert Einstein's 1905 analysis of Brownian motion, the random jittering of dust grains in a fluid. Even then, it took another 20 years for physicists to develop a theory explaining atoms—namely, quantum mechanics—and another 30 for physicist Erwin Müller to make the first microscope images of them. Today entire industries are based on the characteristic properties of atomic matter.
Physicists' understanding of the composition of space and time is following a similar path, but several steps behind. Just as the behavior of materials indicates that they consist of atoms, the behavior of space and time suggests that they, too, have some fine-scale structure—either a mosaic of spacetime “atoms” or some other filigree work. Material atoms are the smallest indivisible units of chemical compounds; similarly, the putative space atoms are the smallest indivisible units of distance. They are generally thought to be about 10
The most promising involve observations of the cosmos. If we imagine rewinding the expansion of the universe back in time, the galaxies we see all seem to converge on a single infinitesimal point: the big bang singularity. At this point, our current theory of gravity—Einstein's general theory of relativity—predicts that the universe had an infinite density and temperature. This moment is sometimes sold as the beginning of the universe, the birth of matter, space and time. Such an interpretation, however, goes too far because the infinite values indicate that general relativity itself breaks down. To explain what really happened at the big bang, physicists must transcend relativity. We must develop a theory of quantum gravity, which would capture the fine structure of spacetime to which relativity is blind.
The details of that structure came into play under the dense conditions of the primordial universe, and traces of it may survive in the present-day arrangement of matter and radiation. In short, if spacetime atoms exist, it will not take centuries to find the evidence, as it did for material atoms. With some luck, we may know within this decade.
Pieces of Space
Physicists have devised several candidate theories of quantum gravity, each applying quantum principles to general relativity in a distinct way. My work focuses on the theory of loop quantum gravity (“loop gravity,” for short), which was developed in the 1990s using a two-step procedure. First, theorists mathematically reformulated general relativity to resemble the classical theory of electromagnetism; the eponymous “loops” of the theory are analogues of electric and magnetic field lines. Second, following innovative procedures, some that are akin to the mathematics of knots, they applied quantum principles to the loops. The resulting quantum gravity theory predicts the existence of spacetime atoms [see “Atoms of Space and Time,” by Lee Smolin; Scientific American, January 2004].
Other approaches, such as string theory and so-called causal dynamical triangulations, do not predict spacetime atoms per se but suggest other ways that sufficiently short distances might be indivisible [see “The Great Cosmic Roller-Coaster Ride,” by Cliff Burgess and Fernando Quevedo; Scientific American, November 2007, and “The Self-Organizing Quantum Universe,” by Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll; Scientific American, July 2008]. The differences among these theories have given rise to controversy, but to my mind the theories are not contradictory so much as complementary. String theory, for example, is useful for a unified view of particle interactions, including gravity when it is weak. For the purpose of disentangling what happens at the singularity, where gravity is strong, the atomic constructions of loop gravity are more useful.
The theory's power is its ability to capture the fluidity of spacetime. Einstein's great insight was that spacetime is no mere stage on which the drama of the universe unfolds. It is an actor in its own right. It not only determines the motion of bodies within the universe, but it evolves. A complicated interplay between matter and spacetime ensues. Space can grow and shrink.
Loop gravity extends this insight into the quantum realm. It takes our familiar understanding of particles of matter and applies it to the atoms of space and time, providing a unified view of our most basic concepts. For instance, the quantum theory of electromagnetism describes a vacuum devoid of particles such as photons, and each increment of energy added to this vacuum generates a new particle. In the quantum theory of gravity, a vacuum is the absence of spacetime—an emptiness so thorough we can scarcely imagine it. Loop gravity describes how each increment of energy added to this vacuum generates a new atom of spacetime.
The spacetime atoms form a dense, ever shifting mesh. Over large distances, their dynamism gives rise to the evolving universe of classical general relativity. Under ordinary conditions, we never notice the existence of these spacetime atoms; the mesh spacing is so tight that it looks like a continuum. But when spacetime is packed with energy, as it was at the big bang, the fine structure of spacetime becomes a factor, and the predictions of loop gravity diverge from those of general relativity.
Attracted to Repulsion
Applying the theory is an extremely complex task, so my colleagues and I use simplified versions that capture the truly essential features of the universe, such as its size, and ignore details of lesser interest. We have also had to adapt many of the standard mathematical tools of physics and cosmology. For instance, theoretical physicists commonly describe the world using differential equations, which specify the rate of change of physical variables, such as density, at each point in the spacetime continuum. But when spacetime is grainy, we instead use so-called difference equations, which break up the continuum into discrete intervals. These equations describe how a universe climbs up the ladder of sizes that it is allowed to take as it grows. When I set out to analyze the cosmological implications of loop gravity in 1999, most researchers expected that these difference equations would simply reproduce old results in disguise. But unexpected features soon emerged.
Gravity is typically an attractive force. A ball of matter tends to collapse under its own weight, and if its mass is sufficiently large, gravity overpowers all other forces and compresses the ball into a singularity, such as the one at the center of a black hole. But loop gravity suggests that the atomic structure of spacetime changes the nature of gravity at very high energy densities, making it repulsive. Imagine space as a sponge and mass and energy as water. The porous sponge can store water but only up to a certain amount. Fully soaked, it can absorb no more and instead repels water. Similarly, an atomic quantum space is porous and has a finite amount of storage space for energy. When energy densities become too large, repulsive forces come into play. The continuous space of general relativity, in contrast, can store a limitless amount of energy.
Because of the quantum-gravitational change in the balance of forces, no singularity—no state of infinite density—can ever arise. According to this model, matter in the early universe had a very high but finite density, the equivalent of a trillion suns in every proton-size region. At such extremes, gravity acted as a repulsive force, causing space to expand; as densities moderated, gravity switched to being the attractive force we all know. Inertia has kept the expansion going to the present day.
In fact, the repulsive gravity caused space to expand at an accelerating rate. Cosmological observations appear to require such an early period of acceleration, known as cosmic inflation. As the universe expands, the force driving inflation slowly subsides. Once the acceleration ends, surplus energy is transferred to ordinary matter, which begins to fill the universe in a process called reheating. In current models, inflation is somewhat ad hoc—added in to conform to observations—but in loop quantum cosmology, it is a natural consequence of the atomic nature of spacetime. Acceleration automatically occurs when the universe is small and its porous nature still quite significant.
Time before Time
Without a singularity to demarcate the beginning of time, the history of the universe may extend further back than cosmologists once thought possible. Other physicists have reached a similar conclusion [see “The Myth of the Beginning of Time,” by Gabriele Veneziano; Scientific American, May 2004], but only rarely do their models fully resolve the singularity; most models, including those from string theory, require assumptions as to what might have happened at this uneasy spot. Loop gravity, in contrast, is able to trace what took place at the singularity. Loop-based scenarios, though admittedly simplified, are founded on general principles and avoid introducing new ad hoc assumptions.
Using the difference equations, we can try to reconstruct the deep past. One possible scenario is that the initial high-density state arose when a preexisting universe collapsed under the attractive force of gravity. The density grew so high that gravity switched to being repulsive, and the universe started expanding again. Cosmologists refer to this process as a bounce.
The first loopy bounce model investigated thoroughly was an idealized case in which the universe was highly symmetrical and contained just one type of matter. Particles had no mass and did not interact with one another. Simplified though this model was, understanding it required a set of numerical simulations that were completed only in 2006 by Abhay Ashtekar, Tomasz Pawlowski and Parampreet Singh, all then at Pennsylvania State University. They considered the propagation of waves representing the universe both before and after the big bang. The model clearly showed that a wave would not blindly follow the classical trajectory into the abyss of a singularity but would stop and turn back once the repulsion of quantum gravity set in.
An exciting result of these simulations was that the notorious uncertainty of quantum mechanics seemed to remain fairly muted during the bounce. A wave remained localized throughout the bounce rather than spreading out, as quantum waves usually do. Taken at face value, this result suggested that the universe before the bounce was remarkably similar to our own: governed by general relativity and perhaps filled with stars and galaxies. If so, we should be able to extrapolate from our universe back in time, through the bounce, and deduce what came before, much as we can reconstruct the paths of two billiard balls before a collision based on their paths after the collision. We do not need to know each and every atomic-scale detail of the collision.
Unfortunately, various subsequent analyses dashed this hope. The model as well as the quantum waves used in the numerical simulations turned out to be a special case. In general, I found that waves spread out and that quantum effects were strong enough to be reckoned with. So the bounce was not a brief push by a repulsive force, like the collision of billiard balls. Instead it may have represented the emergence of our universe from an almost unfathomable quantum state—a world in highly fluctuating turmoil. Even if the preexisting universe was once very similar to ours, it passed through an extended period during which the density of matter and energy fluctuated strongly and randomly, scrambling everything—even the passage of time itself.
The fluctuations before and after the big bang were not strongly related to each other. The universe before the big bang could have been fluctuating very differently than it did afterward, and those details did not survive the bounce. The universe, in short, has a profound case of forgetfulness. It may have existed before the big bang, but quantum effects during the bounce wiped out almost all traces of this prehistory.
Some Scraps of Memory
This picture of the big bang is subtler than the classical view of the singularity. Whereas general relativity simply fails at the singularity, loop quantum gravity is able to handle the extreme conditions there. The big bang is no longer a physical beginning or a mathematical singularity, but it does put a practical limitation on our knowledge. Whatever survives cannot provide a complete view of what came before.
Frustrating as this may be, it might be a conceptual blessing. In physical systems as in daily life, disorder tends to increase. This principle, known as the second law of thermodynamics, is an argument against an eternal universe. If order has been decreasing for an infinite span of time, the universe should by now be so disorganized that structures we see in galaxies as well as on Earth would be all but impossible. The right amount of cosmic forgetfulness may come to the rescue by presenting the young, growing universe with a clean slate irrespective of all the mess that may have built up before.
According to traditional thermodynamics, there is no such thing as a truly clean slate; every system retains a memory of its past in the configuration of its atoms [see “The Cosmic Origins of Time's Arrow,” by Sean M. Carroll; Scientific American, June 2008]. But by allowing the number of spacetime atoms to change, loop quantum gravity allows the universe more freedom to tidy up than classical physics would suggest.
All that is not to say that cosmologists have no hope of probing the quantum-gravitational period. Gravitational waves and neutrinos are especially promising tools because they barely interact with matter and therefore penetrated the primordial plasma with minimal loss. These messengers might well bring us news from a time near to, or even before, the big bang.
One way to look for gravitational waves is by studying their imprint on the cosmic microwave background radiation [see “Echoes from the Big Bang,” by Robert R. Caldwell and Marc Kamionkowski; Scientific American, January 2001]. If quantum-gravitational repulsive gravity drove cosmic inflation, these observations might find some hint of it. Theorists must also determine whether this novel source of inflation could reproduce other cosmological measurements, especially of the early density distribution of matter seen in the cosmic microwave background.
At the same time, astronomers can look for the spacetime analogues of random Brownian motion. For instance, quantum fluctuations of spacetime could affect the propagation of light over long distances. According to loop gravity, a light wave cannot be continuous; it must fit on the lattice of space. The smaller the wavelength, the more the lattice distorts it. In a sense, the spacetime atoms buffet the wave. As a consequence, light of different wavelengths travels at different speeds. Although these differences are tiny, they may add up during a long trip. Distant sources such as gamma-ray bursts offer the best hope of seeing this effect [see “Window on the Extreme Universe,” by William B. Atwood, Peter F. Michelson and Steven Ritz; Scientific American, December 2007].
In the case of material atoms, more than 25 centuries elapsed between the first speculative suggestions of atoms by ancient philosophers and Einstein's analysis of Brownian motion, which firmly established atoms as the subject of experimental science. The delay should not be as long for spacetime atoms.