How Time Got Its Arrow

I believe in time.

I haven’t always believed in it. Like many physicists and philosophers, I had once concluded from general relativity and quantum gravity that time is not a fundamental aspect of nature, but instead emerges from another, deeper description. Then, starting in the 1990s and accelerated by an eight year collaboration with the Brazilian philosopher Roberto Mangabeira Unger, I came to believe instead that time is fundamental. (How I came to this is another story.) Now, I believe that by taking time to be fundamental, we might be able to understand how general relativity and the standard model emerge from a deeper theory, why time only goes one way, and how the universe was born.

Flickr user Robert Couse-Baker, adapted under a Creative Commons license.

The story starts with change. Science, most broadly defined, is the systematic study of change. The world we observe and experience is constantly changing. And most of the changes we observe are irreversible. We are born, we grow, we age, we die, as do all living things. We remember the past and our actions influence the future. Spilled milk is hard to clean up; a cool drink or a hot bath tend towards room temperature. The whole world, living and non-living, is dominated by irreversible processes, as captured mathematically by the second law of thermodynamics, which holds that the entropy of a closed system usually increases and seldom decreases.

It may come as a surprise, then, that physics regards this irreversibility as a cosmic accident. The laws of nature as we know them are all reversible when you change the direction of time. Film a process described by those laws, and then run the movie backwards: the rewound version is also allowed by the laws of physics. To be more precise, you may have to change left for right and particles for antiparticles, along with reversing the direction of time, but the standard model of particle physics predicts that the original process and its reverse are equally likely.

The same is true of Einstein’s theory of general relativity, which describes gravity and cosmology. If the whole universe were observed to run backwards in time, so that it heated up while it collapsed, rather than cooled as it expanded, that would be equally consistent with these fundamental laws, as we currently understand them.

This leads to a fundamental question: Why, if the laws are reversible, is the universe so dominated by irreversible processes? Why does the second law of thermodynamics hold so universally?

Gravity is one part of the answer. The second law tells us that the entropy of a closed system, which is a measure of disorder or randomness in the motions of the atoms making up that system, will most likely increase until a state of maximum disorder is reached. This state is called equilibrium. Once it is reached, the system is as mixed as possible, so all parts have the same temperature and all the elements are equally distributed.

But on large scales, the universe is far from equilibrium. Galaxies like ours are continually forming stars, turning nuclear potential energy into heat and light, as they drive the irreversible flows of energy and materials that characterize the galactic disks. On these large scales, gravity fights the decay to equilibrium by causing matter to clump,,creating subsystems like stars and planets. This is beautifully illustrated in some recent papers by Barbour, Koslowski and Mercati.

But this is only part of the answer to why the universe is out of equilibrium. There remains the mystery of why the universe at the big bang was not created in equilibrium to start with, for the picture of the universe given us by observations requires that the universe be created in an extremely improbable state—very far from equilibrium. Why?

So when we say that our universe started off in a state far from equilibrium, we are saying that it started off in a state that would be very improbable, were the initial state chosen randomly from the set of all possible states. Yet we must accept this vast improbability to explain the ubiquity of irreversible processes in our world in terms of the reversible laws we know.

In particular, the conditions present in the early universe, being far from equilibrium, are highly irreversible. Run the early universe backwards to a big crunch and they look nothing like the late universe that might be in our future.

In 1979 Roger Penrose proposed a radical answer to the mystery of irreversibility. His proposal concerned quantum gravity, the long-searched-for unification of all the known laws, which is believed to govern the processes that created the universe in the big bang—or transformed it from whatever state it was in before the big bang.

Penrose hypothesized that quantum gravity, as the most fundamental law, will be unlike the laws we know in that it will be irreversible. The known laws, along with their time-reversibility, emerge as approximations to quantum gravity when the universe grows large and cool and dilute, Penrose argued. But those approximate laws will act within a universe whose early conditions were set up by the more fundamental, irreversible laws. In this way the improbability of the early conditions can be explained.

In the intervening years our knowledge of the early universe has been dramatically improved by a host of cosmological observations, but these have only deepened the mysteries we have been discussing. So a few years ago, Marina Cortes, a cosmologist from the Institute for Astronomy in Edinburgh, and I decided to revive Penrose’s suggestion in the light of all the knowledge gained since, both observationally and theoretically.

Dr. Cortes argued that time is not only fundamental but fundamentally irreversible. She proposed that the universe is made of processes that continuously generate new events from present events. Events happen, but cannot unhappen. The reversal of an event does not erase that event, Cortes says: It is a new event, which happens after it.

In December of 2011, Dr. Cortes began a three-month visit to Perimeter Institute, where I work, and challenged me to collaborate with her on realizing these ideas. The first result was a model we developed of a universe created by events, which we called an energetic causal set model.

This is a version of a kind of model called a causal set model, in which the history of the universe is considered to be a discrete set of events related only by cause-and-effect. Our model was different from earlier models, though. In it, events are created by a process which maximizes their uniqueness. More precisely, the process produces a universe created by events, each of which is different from all the others. Space is not fundamental, only the events and the causal process that creates them are fundamental. But if space is not fundamental, energy is. The events each have a quantity of energy, which they gain from their predecessors and pass on to their successors. Everything else in the world emerges from these events and the energy they convey.

We studied the model universes created by these processes and found that they generally pass through two stages of evolution. In the first stage, they are dominated by the irreversible processes that create the events, each unique. The direction of time is clear. But this gives rise to a second stage in which trails of events appear to propagate, creating emergent notions of particles. Particles emerge only when the second, approximately reversible stage is reached. These emergent particles propagate and appear to interact through emergent laws which seem reversible. In fact, we found, there are many possible models in which particles and approximately reversible laws emerge after a time from a more fundamental irreversible, particle-free system.

This might explain how general relativity and the standard model emerged from a more fundamental theory, as Penrose hypothesized. Could we, we wondered, start with general relativity and, staying within the language of that theory, modify it to describe an irreversible theory? This would give us a framework to bridge the transition between the early, irreversible stage and the later, reversible stage.

In a recent paper, Marina Cortes, PI postdoc Henrique Gomes and I showed one way to modify general relativity in a way that introduces a preferred direction of time, and we explored the possible consequences for the cosmology of the early universe. In particular, we showed that there were analogies of dark matter and dark energy, but which introduce a preferred direction of time, so a contracting universe is no longer the time-reverse of an expanding universe.

To do this we had to first modify general relativity to include a physically preferred notion of time. Without that there is no notion of reversing time. Fortunately, such a modification already existed. Called shape dynamics, it had been proposed in 2011 by three young people, including Gomes. Their work was inspired by Julian Barbour, who had proposed that general relativity could be reformulated so that a relativity of size substituted for a relativity of time.

Using the language of shape dynamics, Cortes, Gomes and I found a way to gently modify general relativity so that little is changed on the scale of stars, galaxies and planets. Nor are the predictions of general relativity regarding gravitational waves affected. But on the scale of the whole universe, and for the early universe, there are deviations where one cannot escape the consequences of a fundamental direction of time.

Very recently I found still another way to modify the laws of general relativity to make them irreversible. General relativity incorporates effects of two fixed constants of nature, Newton’s constant, which measures the strength of the gravitational force, and the cosmological constant, which measures the density of energy in empty space. Usually these both are fixed constants, but I found a way they could evolve in time without destroying the beautiful harmony and consistency of the Einstein equations of general relativity.

These developments are very recent and are far from demonstrating that the irreversibility we see around us is a reflection of a fundamental arrow of time. But they open a way to an understanding of how time got its direction that does not rely on our universe being a consequence of a cosmic accident.

Go Deeper
Editor’s picks for further reading

About.com: Does Time Exist?
Science writer Andrew Zimmerman Jones on the problem of time and the origin of time’s arrow.

FQXi: Setting Time Aright
Watch video and slides from this wide-ranging interdisciplinary 2011 conference on the nature of time.

Lee SmolinDiscover more general-audience and scientific writing from Lee Smolin, along with links to videos and interviews.

The Nature of Reality: Are Space and Time Fundamental?
Why some physicists believe that time and space may emerge from deeper physics.

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Lee Smolin

    Lee was born in New York City in 1955 and raised there and in Cincinnati. In September of 2001 he moved to Canada to be a founding member of the Perimeter Institute for Theoretical Physics, where he has been ever since. Lee's main contributions to research are so far to the field of quantum gravity. He was, with Abhay Ashtekar and Carlo Rovelli, a founder of the approach known as loop quantum gravity, but he has contributed to other approaches including string theory and causal dynamical triangulations. He is also known for proposing the notion of the landscape of theories, based on his application of Darwinian methods to Cosmology. He has contributed also to the foundations of quantum mechanics, elementary particle physics and theoretical biology. He also has a strong interest in philosophy and his books "Life of the Cosmos," "Three Roads to Quantum Gravity" and "The Trouble with Physics," and "Time Reborn" are in part philosophical explorations of issues raised by contemporary physics. His latest book, "The Singular Universe and the Reality of Time," with Roberto Mangabeira Unger, was published by Cambridge University Press in November, 2014.