The arrow of time

In T.H. White’s fantasy novel The Once and Future King, Merlyn the magician suffers from a rare and incurable condition: He experiences time in reverse. He knows what will happen, he laments, but not what has happened. “I have to live backwards from in front, while surrounded by a lot of people living forwards from behind,” he explains to a justifiably confused companion.

While Merlyn is fictional, the backward flow of time should not be. As the society of ants in White’s novel proclaimed, “everything not forbidden is compulsory,” and the laws of physics do not forbid time to run backward. Equations that determine the acceleration of a rocket or the momentum of a billiard ball all work just as well with time flowing backward as forward. Yet unlike Merlyn, we remember the past but not the future. We get older but never younger. There is a distinct arrow of time pointing in one direction.

For nearly 140 years, scientists have tried to rule out the backward flow of time by way of nature’s preference for disorder. Left alone, nature transforms the neat into the messy, a one-way progression that many physicists have used to define time’s direction. But if nature prefers disorder now, it always has. The challenge is figuring out why the universe started out so orderly — thereby allowing disorder to grow and time to march forward — when the early universe should have been messy. Despite many proposals, physicists have not been able to agree on a satisfying explanation.

A new paper offers a solution. The secret ingredient, the authors say, is gravity. Using a simple simulation of gravitationally interacting particles, the researchers show that an orderly universe should always arise naturally at one point in time. From there, the universe branches in opposing temporal directions. Within each branch, time flows toward increasing disorder, essentially creating two futures that share one past. “It’s the only clear, simple idea that’s been put forward to explain the basis of the arrow of time,” says physicist Julian Barbour, a coauthor of the study published last October in Physical Review Letters.

It may be clear and simple, but it’s far from being the only idea attempting to explain the mystery of time’s arrow. Many scientists (and philosophers) over the decades have proposed ideas for reconciling nature’s time-reversible laws with time’s irreversible flow. Barbour and colleagues admit that the arrow of time issue is far from settled — there’s no guarantee that their simple simulation captures all the complexities of the universe we know. But their study offers an unusually elegant mechanism for explaining time’s arrow, along with some tantalizing implications. Attacking the arrow-of-time mystery along the lines Barbour and colleagues suggest may reveal that the universe is eternal.

Mixing marbles

Nobody knows exactly why time doesn’t flow backward. But most scientists have suspected that the explanation depends on the second law of thermodynamics, which describes nature’s fondness for messiness. Consider a jar containing 100 numbered marbles, 50 of them red and 50 blue. Someone with way too much free time then takes a picture of every possible arrangement of the marbles (yes, this would take far longer than a human lifetime) and creates a giant collage. Even though every photo depicts a different arrangement of numbered marbles, the vast majority of images would look very similar: a jumble of red and blue. Very few photos would have all the red marbles on one side of the jar and all the blue on the other. A photo picked at random would be far more likely to show a state of disorder than one of order.

Physicists in the 19th century recognized this propensity for disorder by thinking about the flow of heat in steam engines. When two containers of gas are exposed to each other, the faster-moving molecules of the higher-temperature container (think the blue marbles) tend to mix with the slower molecules (red marbles) of the cooler container. Eventually the combined contents of the containers will settle at an equilibrium temperature because a disordered state of blended hot and cold is most likely.

In the mid-19th century, physicists introduced the notion of entropy to quantify the disorder of a heat-shifting system. Austrian physicist Ludwig Boltzmann sharpened the definition by relating entropy to the number of ways that one could arrange microscopic components to produce an indistinguishable macroscopic state. The jar with segregated red and blue marbles, for example, has low entropy because only a few arrangements of the numbered marbles could produce that color pattern. Similarly, there are many combinations of speedy and sluggish molecules that will produce a gas at equilibrium temperature, the highest possible entropy. The fact that there are far more ways to achieve high entropy than low provides the foundation for the second law of thermodynamics: The entropy of a closed system tends to increase until reaching equilibrium, the maximum state of disorder.

The second law explains why cream easily mixes into coffee but doesn’t unmix, and why Humpty Dumpty won’t spontaneously reassemble after his fateful fall. Crucially, the second law also defines a thermodynamic arrow of time. The drive toward maximum entropy is an irreversible process in a universe governed by time-reversible physical laws. The second law suggests that time flows from past to present to future because the universe is progressing from an ordered low-entropy state to a disordered high-entropy one.

Unfortunately, physicists had to make a major assumption to connect entropy and the arrow of time. If entropy has been increasing since the Big Bang, 13.8 billion years ago, then the universe’s original entropy must have been low enough that even today the universe is not close to equilibrium. Yet as the jar of marbles reveals, there are not many ways for entropy to be low. If you randomly picked the universe’s initial entropy value out of a hat, “you’d almost certainly pick equilibrium,” says Anthony Aguirre, a cosmologist at the University of California, Santa Cruz. A universe in equilibrium would be like the thoroughly mixed container of gas molecules: unchanging, with no heat flowing, no eggs to break, no pockets of order remaining to transform into disorder. And that’s not what scientists see when they look at the universe, both in the past and today.

This early-universe entropy dilemma bothers many physicists. They want to prove that the universe is typical, that it did not need an exceptionally lucky break to evolve into its current condition. But framing the Big Bang era in terms of entropy is a slippery proposition. Back then, matter and energy were confined to a hot, dense ball. Some physicists consider that to be an orderly, low-entropy state; others say it resembles a packed container of gas molecules in equilibrium. Most physicists agree that the second law of thermodynamics is vital for explaining time’s arrow, but they still want to develop a simple theory that explains the flow of time.

The Janus point

Barbour is in this camp of time thinkers. Like a random low-entropy state, he is a rarity in physics: a freelancer. After completing his Ph.D. in 1968 at the University of Cologne in Germany, he quit academia so that he could focus on fundamental physics rather than obtaining tenure. He lives in a small English parish (population 285) where the rural charm and centuries-old houses create the illusion that time has slowed since the Age of Enlightenment.

Barbour’s dive into the arrow-of-time question began several years ago. He was thinking about the n-body problem, which requires determining the motion of multiple objects that are tugging on each other due to gravity. He wondered whether gravity, which clearly influences the movement of matter, could also impact the movement of time. Barbour worked on the problem with Tim Koslowski of the University of New Brunswick in Fredericton, Canada, and Flavio Mercati of the Perimeter Institute for Theoretical Physics in Waterloo, Canada. They set up a toy universe — a simple simulation used to examine the workings of the complex cosmos without all the messy details. This universe consisted of 1,000 particles in limitless space that interacted solely through Newtonian gravity.

Barbour, Koslowski and Mercati did not just toss in some particles and press play. Assuming a forward flow of time would have defeated the purpose of the exercise. Instead, they let the simulation rip and recorded a series of snapshots, like frames in a movie. Each frame captured the positions of the particles and recorded the system’s complexity — a measure that quantified the spread and clustering of the particles. (For the most part, complexity increases along with entropy.) Then the researchers pieced together the frames to create a coherent motion picture, much like someone ordering stills from a video that captures the motion of a swinging pendulum.

After running the simulation many times with varying numbers of particles, Barbour and colleagues noticed an unmistakable pattern. At some instant during each simulation, all the particles would clump together into a homogeneous ball, a moment of minimum complexity. Then the complexity would increase. As the elapsed time from the instant of minimum complexity increased in either direction of time, so did the number of clumps and the distances between them.

Barbour and his team immediately made a connection to our universe and its arrow of time. At a single instant, the toy universe’s 1,000 particles had formed a packed, uniform ball, which resembles the conditions at the Big Bang. From there the ball had expanded into a sparse, clumpy arrangement that is more reminiscent of today’s galaxy cluster–dotted cosmos. This expansion, the shift from simplicity to complexity, occurred in both directions of time. That means that all the matter and energy that have evolved to create the cosmos we see today could also be evolving independently in the other direction of time. What we know as the universe could actually be just one of a pair that exists in the same space but at different times.

The researchers concluded that an observer living in either universe would perceive time as flowing in the direction of increasing complexity, from the Big Bang–esque blob to the present. The arrow of time for an observer on one side of the timeline would appear to run backward from the perspective of an observer on the other side, but that would be academic: An observer could never compare notes with his or her counterpart because that would require burrowing backward through time.

Crucially, the researchers’ proposal demonstrates what Boltzmann could not nearly 140 years ago: that asymmetry in time can arise naturally from time-symmetric physical laws. In fact, Barbour and colleagues proved mathematically that if the real universe behaves like the toy one, then a gravity-driven arrow of time must have arisen. This inevitability could solve the problem of why entropy in the early universe was so low. Barbour and colleagues say that the Big Bang could represent the one minimum-complexity moment in time that always arises when gravity is at work. The researchers named this pivotal instant the Janus point, after the Roman god of beginnings, who has one face looking toward the past and another toward the future.

“The proof that they give is nice and elegant,” Aguirre says. But he warns that Barbour has a long way to go to prove that his simulation, which simplifies gravity and ignores quantum physics, can approximate the actual universe. Barbour says his team is working to confirm that particles would behave similarly in a universe governed by general relativity, Einstein’s all-encompassing theory of gravity.

Everlasting universe

If Barbour’s proposal holds up, it will offer intriguing evidence that the universe is eternal, with no beginning and no end of time. Today, many cosmologists consider the Big Bang as the start of the universe’s forward-pointing arrow of time. But Barbour’s simulation suggests the Big Bang serves as the starting point of two arrows that both point toward increasing disorder. The universe we know, which is guided by one of the arrows, has evolved to enable the development of stars, galaxies and life; the universe on the other side of the Janus point, undetectable to us but made of the same starting ingredients, may be very similar.

In some ways, Barbour’s proposal is much like one made in 2004 by cosmologists Sean Carroll and Jennifer Chen when they were at the University of Chicago. They also envisioned an eternal universe, though it existed in an equilibrium state. The catch was that occasional quantum fluctuations could spark the birth of low-entropy universes that break away, expand and evolve toward higher entropy (SN: 6/19/10, p. 26). Baby universes could pinch off in either temporal direction, ensuring a local arrow of time while preserving an overall time symmetry.

Aguirre, who described an eternal multiverse with local arrows of time in 2003, says these recent studies should give cosmologists pause when they consider whether the Big Bang truly marked the beginning of time. The idea of a universe with a beginning “has become so entrenched that many cosmologists seem unwilling to entertain the notion of an eternal universe,” he says. While he doesn’t expect that his work or that of Carroll, Chen or Barbour will sway his colleagues, he says that future astronomical observations might support the case for an eternal multiverse (SN: 6/7/08, p. 23).

Barbour’s findings also open up a possibility that would get Boltzmann rolling in his grave. If gravity is the crucial ingredient that explains why time flows forward, Barbour says, then perhaps a new measure that incorporates gravity should replace the steam engine–inspired concept of entropy. Barbour is not arguing that entropy is useless or that the second law is wrong, but he questions whether entropy can be usefully applied to describe the universe as a whole.

Lawrence Schulman, a physicist at Clarkson University in Potsdam, N.Y., shares Barbour’s entropy trepidation. “It’s very hard to define entropy for the entire universe,” says Schulman, who suggested in 1999 that time could run backward in some regions of the cosmos. A box of gas molecules has boundaries, he says, making it easy to describe the entire large-scale configuration of the gas; the universe stretches beyond the billions of light-years in all directions that are visible to us. And gravity plays a far greater role in the evolution of the universe than it does in a small container of lightweight gas molecules.

As a replacement for entropy, Barbour, Koslowski and Mercati, in an upcoming paper, suggest a metric called “entaxy.” From the Greek for “toward order,” entaxy measures the degree of order created by gravity. It is essentially the opposite of entropy. Based on their simulation, maximum entaxy occurs at the Janus point, when gravity pulls matter and energy together into one orderly clump. As the universe evolves in both directions from that orderly point, entaxy decreases as matter spreads apart and forms ever-smaller clumps. The entaxy of the universe has been decreasing ever since the Big Bang, Barbour says.

Carroll, who is now at Caltech and wrote a 2010 book on the arrow of time, remains staunchly on Team Boltzmann. Gravity is essential for understanding what an increasing-entropy universe looks like, he says, but that doesn’t mean that gravity should be integrated into the measurement of the universe’s disorder. “You know entropy when you see it,” he says, even if the universe presents more challenges than a steam engine or a jar of marbles.

Carroll praises the work of Barbour and colleagues, but he thinks similar simulations would work just as well if the particles exerted no gravitational influence on each other. He is working with MIT cosmologist Alan Guth to create a simulation without gravity. Barbour’s toy universe is simple but “specific,” Carroll says. “We want our model to be simple and generic. We literally have no forces or interactions.” The particles move in a straight line and bounce off each other like billiard balls. While Carroll and Guth have yet to produce a paper, Carroll says their toy universe also results in a Janus-like point with diverging arrows of time toward increasing entropy.

Guth and Carroll may indeed demonstrate that arrows of time can emerge without gravity’s involvement. Alternatively, Barbour and his team may devise a more complete theory that incorporates general relativity and entaxy. Or maybe these simulations have nothing to say about time’s arrow in the actual universe. Regardless of where the research leads, Barbour says he takes satisfaction in the simplicity of the approaches. It would be fitting, he says, if observing the behavior of a simple set of particles, which provided the first vital clue toward understanding the arrow of time, ends up finally resolving the problem once and for all. 

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This article appears in the July 25, 2015, Science News with the headline, “Time’s Arrow: Maybe gravity shapes the universe into two opposing futures.”