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.

    • Kaslo

      How does Ilya Prigogine fit into all this…? I know Lee has advocated for this view, to also help motivate humanity to act on AGW. As a layman, I don’t understand why this view on time and irreversibility is still not mainstream? For example, Al Gore’s book “The Future” talks about Prigogine, and the profound impact Prigogine’s work had on him personally, but I guess in physics many remained unconvinced…? In any case, I’m glad Lee is here today to hopefully wake people up.

    • Ian Ray Hawke

      Fascinating thoughts … especially since most people seem to have interpreted from Einstein’s theories that TIME is a supremely “fundamental aspect of nature” as the “4th dimension”. Of course, according to Einstein, TIME is not a dimension — TIME is merely an artifact of our one way transition through the 4th dimension. So now I’m wondering if this article is really about “time”, as stated — or about the 4th dimension (as might be implied)?

    • Emilio Alvarez


    • Jay Thompson

      Now this is the type of knowledge as well understandings I wish more would take part in as well deeply think on, it would change the very nature of how “we” as humans see our existence.

    • randy

      Claiming the assumption that time as observed goes in one direction as a new theory is a bit of a stretch. You don’t need a new theoretical framework to take space and unidirectional time as a priori properties of the universe. All you really need to get from the big bang to now, as pointed out, is the right set of initial conditions. You can run the film backwards, but that is not the same as reversing the state so that it implodes with time running forward. Your claim that we do not have to take space as an a priori property is also dubious. The fact that our observations can not exist independent of the physics of energy, does not imply that space is not fundamental.

    • T Clark

      If I drop a deck of cards, it is more likely to form a pile in apparently random order because there are many fewer states I define as ordered than there are those I define as disordered.

      If I double the size of a pressurized cylinder by moving a piston, I have reduced the probability that all the gas particles will be on one side of the cylinder from 1 to almost 0.

      Why isn’t that enough to explain the irreversibility of events and the direction of time? The universe moves towards more probable states.

    • johnwerneken


    • seescaper

      I personally believe in the WSM theory of the universe. In this theory there are no particles, but rather “particle-like” standing wave structures of spacetime, formed from the combination of an “in-wave” derived from all other particles in the universe, which then flips to generate an “out-wave” that propagates to all other wave centers. The wave centers are where energy exchanges occur. The author of this theory is former NASA scientist Dr. Milo Wolff. Dr. Wolff believes that each wave center forms the center of its own observable universe. Wave centers outside that radius do not interact. The weaker interactions of faraway wave-centers account for the so-called red-shift. In this model there is no need for a big bang. Each wave-center forms an observable universe within a larger eternal universe. There are 3 main principles from which relativity, gravity, and quantum mechanics, as well as many other physics principles and laws all derive.The largest structures in the universe are intimately linked to the smallest via an equation of the universe. see http://www.spaceandmotion.com/cosmology-equation-of-cosmos.htm one can also google “beyond the point particle for a more thorough discussion.

    • Anonymous

      Wow. Very well written. This article has substance, in contrast to many recent articles on this site characterized by some readers as flowery metaphysics masquerading as science. That thinking and those articles have their place, but articles like this are deeply satisfying to read.

      As a layman I am still puzzled by the conclusion that fundamental laws permit reversibility…that the broken coffee cup is equally as likely to jump back onto the table and reassemble itself as to break – and that this is essentially the same phenomenon as galaxy formation (i.e., moving opposite entropy).

    • Ron

      How do we know which direction time is moving? We assume it’s moving forward but how do we know that is actually moving backwards. Maybe the forward order of things is death, life, birth rather than the inverse. May gravity is a repelant force and thinks fall up rather than down and we’re just living in time going backwards.

      • Alderak1 .

        Ron, you thought is fundamentally flawed, cyclical, and irrelevant. “Forward” is just a word to describe the “direction” that time flows relative to our perception. It doesn’t matter if gravity or time or whatever is repellent or attractive. “Repellent” and “attractive” are just words. The laws of the universe don’t change based on the rules human vocabulary. We observe time “moving” in one “direction, ” and it just so happens that we call that “direction” the future, or “forward.”

    • Jerome Ogden

      “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.”

      As I was reading this I was fumbling with a Rubik’s cube, and an image occurred to me that may help understand what Dr. Cortes is saying about a “reversal” being a “new event:”

      Imagine a Rubik’s cube composed of a near infinite number of pieces that starts out in perfect order, each face one color, just as a cube you bring back from the store. Let’s assume gravity holds it together, and your energy flips the rows and columns. If you move rows and columns randomly, over time almost all of the outcomes will appear chaotic, but on rare occasions, purely by accident, you will do an enormously long series of moves that will put all the pieces into their original perfect configuration. This will appear as a “reversal,” but will really be a “new event.” There will also be multiple repetitions of chaotic patterns that appear as new events.

      There are probably flaws to this analogy, as it just popped into my head. I look forward to hearing critiques or suggestions for improvements.

      • Mike

        Calling it a “new” event requires an a priori assumption of time moving in one direction. A Rubik’s Cube is completely reversible in that when you move it back to a previous position, it is exactly as it was before. Let’s say the cubes came with an internal counter that incremented every time the pieces were moved, only then would it be irreversible because the pieces would be in the same position but the counter would be at a higher number, therefore it would not be the same. But fundamental processes don’t have a counter like that, clocks and counters are something we build and we can also turn them back if they are designed so that we can do it.

        A better theory is based on the many-worlds hypothesis, in that initial conditions lead to possibilities that are both entropic and negentropic, but because observing a possibility requires information to be transferred to the observer we can only see the entropic ones, therefore everything looks entropic to us.

        • Jerome Ogden

          Thanks for your very informative response. Perhaps the analogy would work better as a near-infinite number of Rubik’s cubes, each with a near-infinite number of pieces, each Rubik’s cube in a different configuration. Then both Barbour’s conception of the universe as timeless and the multiverse hypothesis might both apply. Certain arrangements would appear coherent in our universe, other arrangements equally coherent in other universes.
          In any case, the Rubik’s cube analogy might be useful, but clearly requires refinements.

    • Alex Simonelis

      “The reversal of an event does not erase that event, Cortes says: It is a new event, which happens after it.”
      Assume that EVERYTHING “reversed” back 1 second. How could you test whether it was a true time reversal or the new, old universe? And if you can’t test it …

    • ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


      This is interesting… if you could put everything back the way it was in the past, has time itself also reverted to that period? That would mean “time” is just the way things are arranged.

      If I had a time machine, I (just myself) could travel back to 1947 and drive out to Roswell in a 1947 Chevy and see what really crashed there.

      But what if I use the time machine and transferred the whole planet back to 1947? It would leave the planet exactly as it is now but in universal time it is 1947. I could still drive to Roswell in a modern car and the UFO crash would still happen because it originated from off-world.

      Taking this one step further… I transfer the whole Universe back to 1947.
      Everything is exactly the way it is now but Universal time is 1947. Now the crash does not happen. Even though it is actually 1947… the arrangement of stuff in the entire Universe is 2015

    • Mongo

      “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.”

      God’s Engineering.

      • Kaslo

        Lee Smolin has been quoted as saying: “One possibility is: God is nothing but the power of the universe to organize itself.” If the universe is biocentric, then God could be akin to an evolving super-organism. And just like in our bodies we have trillions of cells we are unaware of, God may not be aware of of each individual or piece of the puzzle either, but that doesn’t mean it’s still not concerned with its evolution. In fact, Smolin has proposed that not only the laws of nature could evolve over time, but that new universes could be born from black holes. He does however, believe there is only one universe at a time, thus his new book “The Singular Universe and the Reality of Time”.

        • Jon Harris

          God gave up trying to organize my pantry!

    • antonio carlos motta

      The time macroscópic is reflected in the microscópicas world thr ou ghosts of the violation of symmetry t and in the generating of the spacetime is the pt symmetry breaking, that deformations the spacetime topological geometry, nottotally smooth.the time does the spspacetime bê curve and splitted by two non oriental e manifold that if interceptação. The né have the extradimensions.the that has hídden symmetries that occur the extradimensions The né have the continuar and discreteness in the spacetime, it is the quântica gravity, than the império of the extradimensions generated the spacetime

    • Liam Uber

      Great essay. Thinking about the reality of time is difficult, it may even be wrong. It helps me to visualize the universe as a matrix of clocks. These are pretty obvious as solar and biological clocks, but it seems to me that no system can function without its clock or system of clocks. Our bodies contain innumerable clocks. Multitudes of such has been postulated even within our neurons where Drs. Penrose and Hameroff have postulated quantum processes generate consciousness. Interesting stuff!