Time

Reality, Pushed From Behind

Teleology” is a naughty word in certain circles — largely the circles that I often move in myself, namely physicists or other scientists who know what the word “teleology” means. To wit, it’s the concept of “being directed toward a goal.” In the good old days of Aristotle, our best understanding of the world was teleological from start to finish: acorns existed in order to grow into mighty oak trees; heavy objects wanted to fall and light objects to rise; human beings strove to fulfill their capacity as rational beings. Not everyone agreed, including my buddy Lucretius, but at the time it was a perfectly sensible view of the world.

These days we know better, though the knowledge has been hard-won. The early glimmerings of the notion of conservation of momentum supported the idea that things just kept happening, rather than being directed toward a cause, and this view seemed to find its ultimate embodiment in the clockwork universe of Newtonian mechanics. (In technical terms, time evolution is described by differential equations fixed by initial data, not by future goals.) Darwin showed how the splendid variety of biological life could arise without being in any sense goal-directed or guided — although this obviously remains a bone of contention among religious people, even respectable philosophers. But the dominant paradigm among scientists and philosophers is dysteleological physicalism.

However. Aristotle was a smart cookie, and dismissing him as an outdated relic is always a bad idea. Sure, maybe the underlying laws of nature are dysteleological, but surely there’s some useful sense in which macroscopic real-world systems can be usefully described using teleological language, even if it’s only approximate or limited in scope. (Here’s where I like to paraphrase Scott Derrickson: The universe has purposes. I know this because I am part of the universe, and I have purposes.) It’s okay, I think, to say things like “predators tend to have sharp teeth because it helps them kill and eat prey,” even if we understand that those causes are merely local and contingent, not transcendent. Stephen Asma defends this kind of view in an interesting recent article, although I would like to see more acknowledgement made of the effort required to connect the purposeless, mechanical underpinnings of the world to the purposeful, macroscopic biosphere. Such a connection can be made, but it requires some effort.

Of course loyal readers all know where such a connection comes from: it’s the arrow of time. The underlying laws of physics don’t work in terms of any particular “pull” toward future goals, but the specific trajectory of our actual universe looks very different in the past than in the future. In particular, the past had a low entropy: we can reconcile the directedness of macroscopic time evolution with the indifference of microscopic dynamics by positing some sort of Past Hypothesis (see also). All of the ways in which physical objects behave differently toward the future than toward the past can ultimately be traced to the thermodynamic arrow of time.

Which raises an interesting point that I don’t think is sufficiently appreciated: we now know enough about the real behavior of the physical world to understand that what looks to us like teleological behavior is actually, deep down, not determined by any goals in the future, but fixed by a boundary condition in the past. So while “teleological” might be acceptable as a rough macroscopic descriptor, a more precise characterization would say that we are being pushed from behind, not pulled from ahead.

The question is, what do we call such a way of thinking? Apparently “teleology” is a word never actually used by Aristotle, but invented in the eighteenth century based on the Greek télos, meaning “end.” So perhaps what we want is an equivalent term, with “end” replaced by “beginning.” I know exactly zero ancient Greek, but from what I can glean from the internet there is an obvious choice: arche is the Greek word for beginning or origin. Sadly, “archeology” is already taken to mean something completely different, so we can’t use it.

I therefore tentatively propose the word aphormeology to mean “originating from a condition in the past,” in contrast with teleology, “driven toward a goal in the future.” (Amazingly, a Google search for this word on 3 February 2014 returns precisely zero hits.) Remember — no knowledge of ancient Greek, but apparently aphorme means “a base of operations, a place from which a campaign is launched.” Which is not a terribly bad way of describing the cosmological Past Hypothesis when you think about it. (Better suggestions would be welcome, especially from anyone who actually knows Greek.)

We live in a world where the dynamical laws are fundamentally dysteleological, but our cosmic history is aphormeological, which through the magic of statistical mechanics gives rise to the appearance of teleology in our macroscopic environment. A shame Aristotle and Lucretius aren’t around to appreciate the progress we’ve made.

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Is Time Real?

I mentioned some time back the Closer to Truth series, in which Robert Lawrence Kuhn chats with scientists, philosophers, and theologians about the Big Questions. Apparently some excerpts are now appearing on YouTube — here I am talking about whether time is real.

Sean Carroll - Is Time Real?

In one sense, it’s a silly question. The “reality” of something is only an interesting issue if its a well-defined concept whose actual existence is in question, like Bigfoot or supersymmetry. For concepts like “time,” which are unambiguously part of a useful vocabulary we have for describing the world, talking about “reality” is just a bit of harmless gassing. They may be emergent or fundamental, but they’re definitely there. (Feel free to substitute “free will” for “time” if you like.) Temperature and pressure didn’t stop being real once we understood them as emergent properties of an underlying atomic description.

The question of whether time is fundamental or emergent is, on the other hand, crucially important. I have no idea what the answer is (and neither does anybody else). Modern theories of fundamental physics and cosmology include both possibilities among the respectable proposals.

Note that I haven’t actually watched the above video, and it’s been more than three years since the interview. Let me know if I said anything egregiously wrong. (I’m sure you will.)

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The Higgs Boson vs. Boltzmann Brains

Kim Boddy and I have just written a new paper, with maybe my favorite title ever.

Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains?
Kimberly K. Boddy, Sean M. Carroll
(Submitted on 21 Aug 2013)

The standard ΛCDM model provides an excellent fit to current cosmological observations but suffers from a potentially serious Boltzmann Brain problem. If the universe enters a de Sitter vacuum phase that is truly eternal, there will be a finite temperature in empty space and corresponding thermal fluctuations. Among these fluctuations will be intelligent observers, as well as configurations that reproduce any local region of the current universe to arbitrary precision. We discuss the possibility that the escape from this unacceptable situation may be found in known physics: vacuum instability induced by the Higgs field. Avoiding Boltzmann Brains in a measure-independent way requires a decay timescale of order the current age of the universe, which can be achieved if the top quark pole mass is approximately 178 GeV. Otherwise we must invoke new physics or a particular cosmological measure before we can consider ΛCDM to be an empirical success.

We apply some far-out-sounding ideas to very down-to-Earth physics. Among other things, we’re suggesting that the mass of the top quark might be heavier than most people think, and that our universe will decay in another ten billion years or so. Here’s a somewhat long-winded explanation.

A room full of monkeys, hitting keys randomly on a typewriter, will eventually bang out a perfect copy of Hamlet. Assuming, of course, that their typing is perfectly random, and that it keeps up for a long time. An extremely long time indeed, much longer than the current age of the universe. So this is an amusing thought experiment, not a viable proposal for creating new works of literature (or old ones).

There’s an interesting feature of what these thought-experiment monkeys end up producing. Let’s say you find a monkey who has just typed Act I of Hamlet with perfect fidelity. You might think “aha, here’s when it happens,” and expect Act II to come next. But by the conditions of the experiment, the next thing the monkey types should be perfectly random (by which we mean, chosen from a uniform distribution among all allowed typographical characters), and therefore independent of what has come before. The chances that you will actually get Act II next, just because you got Act I, are extraordinarily tiny. For every one time that your monkeys type Hamlet correctly, they will type it incorrectly an enormous number of times — small errors, large errors, all of the words but in random order, the entire text backwards, some scenes but not others, all of the lines but with different characters assigned to them, and so forth. Given that any one passage matches the original text, it is still overwhelmingly likely that the passages before and after are random nonsense.

That’s the Boltzmann Brain problem in a nutshell. Replace your typing monkeys with a box of atoms at some temperature, and let the atoms randomly bump into each other for an indefinite period of time. Almost all the time they will be in a disordered, high-entropy, equilibrium state. Eventually, just by chance, they will take the form of a smiley face, or Michelangelo’s David, or absolutely any configuration that is compatible with what’s inside the box. If you wait long enough, and your box is sufficiently large, you will get a person, a planet, a galaxy, the whole universe as we now know it. But given that some of the atoms fall into a familiar-looking arrangement, we still expect the rest of the atoms to be completely random. Just because you find a copy of the Mona Lisa, in other words, doesn’t mean that it was actually painted by Leonardo or anyone else; with overwhelming probability it simply coalesced gradually out of random motions. Just because you see what looks like a photograph, there’s no reason to believe it was preceded by an actual event that the photo purports to represent. If the random motions of the atoms create a person with firm memories of the past, all of those memories are overwhelmingly likely to be false.

This thought experiment was originally relevant because Boltzmann himself (and before him Lucretius, Hume, etc.) suggested that our world might be exactly this: a big box of gas, evolving for all eternity, out of which our current low-entropy state emerged as a random fluctuation. As was pointed out by Eddington, Feynman, and others, this idea doesn’t work, for the reasons just stated; given any one bit of universe that you might want to make (a person, a solar system, a galaxy, and exact duplicate of your current self), the rest of the world should still be in a maximum-entropy state, and it clearly is not. This is called the “Boltzmann Brain problem,” because one way of thinking about it is that the vast majority of intelligent observers in the universe should be disembodied brains that have randomly fluctuated out of the surrounding chaos, rather than evolving conventionally from a low-entropy past. That’s not really the point, though; the real problem is that such a fluctuation scenario is cognitively unstable — you can’t simultaneously believe it’s true, and have good reason for believing its true, because it predicts that all the “reasons” you think are so good have just randomly fluctuated into your head!

All of which would seemingly be little more than fodder for scholars of intellectual history, now that we know the universe is not an eternal box of gas. The observable universe, anyway, started a mere 13.8 billion years ago, in a very low-entropy Big Bang. That sounds like a long time, but the time required for random fluctuations to make anything interesting is enormously larger than that. (To make something highly ordered out of something with entropy S, you have to wait for a time of order eS. Since macroscopic objects have more than 1023 particles, S is at least that large. So we’re talking very long times indeed, so long that it doesn’t matter whether you’re measuring in microseconds or billions of years.) Besides, the universe is not a box of gas; it’s expanding and emptying out, right?

Ah, but things are a bit more complicated than that. We now know that the universe is not only expanding, but also accelerating. The simplest explanation for that — not the only one, of course — is that empty space is suffused with a fixed amount of vacuum energy, a.k.a. the cosmological constant. Vacuum energy doesn’t dilute away as the universe expands; there’s nothing in principle from stopping it from lasting forever. So even if the universe is finite in age now, there’s nothing to stop it from lasting indefinitely into the future.

But, you’re thinking, doesn’t the universe get emptier and emptier as it expands, leaving no particles to fluctuate? Only up to a point. A universe with vacuum energy accelerates forever, and as a result we are surrounded by a cosmological horizon — objects that are sufficiently far away can never get to us or even send signals, as the space in between expands too quickly. And, as Stephen Hawking and Gary Gibbons pointed out in the 1970’s, such a cosmology is similar to a black hole: there will be radiation associated with that horizon, with a constant temperature.

In other words, a universe with a cosmological constant is like a box of gas (the size of the horizon) which lasts forever with a fixed temperature. Which means there are random fluctuations. If we wait long enough, some region of the universe will fluctuate into absolutely any configuration of matter compatible with the local laws of physics. Atoms, viruses, people, dragons, what have you. The room you are in right now (or the atmosphere, if you’re outside) will be reconstructed, down to the slightest detail, an infinite number of times in the future. In the overwhelming majority of times that your local environment does get created, the rest of the universe will look like a high-entropy equilibrium state (in this case, empty space with a tiny temperature). All of those copies of you will think they have reliable memories of the past and an accurate picture of what the external world looks like — but they would be wrong. And you could be one of them.

That would be bad. …

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Cosmology and the Past Hypothesis

Greetings from sunny Santa Cruz, where we’re in week three of the Summer School on Philosophy of Cosmology. I gave two lectures yesterday afternoon, and in a technological miracle they’ve already appeared on YouTube. The audio and video aren’t perfect quality, but hopefully viewers can hear everything clearly.

These are closer to discussions than lectures, as I was intentionally pretty informal about the whole thing. Rather than trying to push any one specific model or idea, I gave an overview of what I take to be the relevant issues confronting someone who wants to build a cosmological model that naturally explains why the early universe had a low entropy. They are a little bit technical, as the intended audience is grad students in physics and philosophy who have already sat through two weeks of lecturing.

If there is one central idea, it’s the concept of a “cosmological realization measure” for statistical mechanics. Ordinarily, when we have some statistical system, we know some macroscopic facts about it but only have a probability distribution over the microscopic details. If our goal is to predict the future, it suffices to choose a distribution that is uniform in the Liouville measure given to us by classical mechanics (or its quantum analogue). If we want to reconstruct the past, in contrast, we need to conditionalize over trajectories that also started in a low-entropy past state — that the “Past Hypothesis” that is required to get stat mech off the ground in a world governed by time-symmetric fundamental laws.

The goal I am pursuing is to find cosmological scenarios in which the Past Hypothesis is predicted by the dynamics, not merely assumed. We imagine a “large universe,” one in which local macroscopic situations (like a box of gas or a lecture hall full of students) occur many times. Then we can define a measure over the microconditions corresponding to such situations by looking at the ways in which those situations actually appear in the cosmic history. The hope — still just a hope, really — is that familiar situations like observers or lecture halls or apple pies appear predominantly in the aftermath of low-entropy Big-Bang-like states. That would stand in marked contrast to the straightforward Boltzmannian expectation that any particular low-entropy state is both preceded by and followed by higher-entropy configurations. I don’t think any particular model completely succeeds in this ambition, but I’m optimistic that we can build theories of this type. We shall see.

Initial state/origin of the universe (Part 1) by Sean Carroll

Initial state/origin of the universe (Part 2) by Sean Carroll

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Philosophy of Cosmology Summer School

Going on right now, up at UC Santa Cruz — I guess the official name is the UCSC Institute for the Philosophy of Cosmology. It’s a three-week event, with talks by some top-notch people: David Albert, David Wallace, Tim Maudlin, Joel Primack, Anthony Aguirre, Matt Johnson, Leonard Susskind, and a bunch more. To my great regret I can’t be there for the whole thing, but I will be popping in during the last week to say some things about cosmology and the arrow of time. (Is it possible that not everything worth saying will have already been said?)

If you’re not actually there, they seem to be doing a great job of putting lectures on YouTube almost as soon as they appear. Almost like being there, except that you won’t get to walk outside into the redwood forest.

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Time, Born Again

Lee Smolin has a new book out, Time Reborn: From the Crisis in Physics to the Future of the Universe. His previous subtitle lamented “the fall of a science,” while this one warns of a crisis in physics, so you know things must be pretty dire out there.

I’m not going to do a full-fledged review of the book, which gives Lee’s argument for why “time” needs to be something more than just a label on spacetime or a parameter in an evolution equation, but a distinct fundamental piece of reality with respect to which the laws of physics and space of states can change. (Sabine Hossenfelder does offer a review.) There are also suggestions as to how this paradigm-changing viewpoint gives us new ways to talk about economics and social problems.

Over at Edge, John Brockman has posted an interview with Lee, and is accumulating responses from various interested parties. I did contribute a few words to that, which I’m reproducing here.


Time and the Universe

Cosmology and fundamental physics find themselves in an unusual position. There are, as in any area of science, some looming issues of unquestioned importance: how to reconcile quantum mechanics and gravity, and the nature of dark matter and dark energy, to name two obvious ones. But the reality is that particle physicists, gravitational physicists, and cosmologists all have basic theories that work extraordinarily well in the regimes to which we have direct access. As a result, it is very hard to make progress; we know our theories are not absolutely final, but without direct experimental contradictions to them it’s hard to know how to do better.

What we have, instead, are problems of naturalness and fine-tuning. Dark energy is no mystery at all, if we are simply willing to accept a cosmological constant that is 120 orders of magnitude smaller than its natural value. We take fine-tunings to be clues that something deeper is going on, and try to make progress on that basis. Sadly, these are subtle clues indeed.

“Time” is something that physicists understand quite well. Quantum gravity remains mysterious, of course, so it’s possible that the true status of time in the fundamental ontology of the world is something that remains to be discovered. But as far as how time works at the level of observable reality, we’re in good shape. Relativity has taught us how to deal with time that is non-universal, and it turns out that’s not such a big deal. The arrow of time—the manifold differences between the past and future – is also well-understood, as long as one swallows one giant fine-tuning: the extreme low entropy of the early universe. Given that posit, we know of nothing in physics or cosmology or biology or psychology that doesn’t fit into our basic understanding of time.

But the early universe is a real puzzle. Is it puzzling enough, as Smolin suggests, to demand a radical re-thinking of how we conceive of time? He summarizes his view by saying “time is real,” but by “time” he really means “the arrow of time” or “an intrinsic directedness of physical evolution,” and by “real” he really means “fundamental rather than emergent.” (Opposing “real” to “emergent” is an extremely unfortunate vocabulary choice, but so be it.)

This is contrary to everything we think we understand about physics, everything we think we have learned about the operation of the universe, and every experiment and observation we have ever performed. But it could be true! It’s always a good idea to push against the boundaries, try something different, and see what happens.

I have two worries. One is that Smolin seems to be pushing hard against a door that is standing wide open. With the (undeniably important) exceptions of the initial-conditions problem and quantum gravity, our understanding of time is quite good. But he doesn’t cast his work as an attempt to (merely) understand the early universe, but as a dramatic response to a crisis in physics. It comes across as a bit of overkill.

The other worry is the frequent appearance of statements like “it seems to me a necessary hypothesis.” Smolin seems quite content to draw sweeping conclusions from essentially philosophical arguments, which is not how science traditionally works. There are no necessary hypotheses; there are only those that work, and those that fail. Maybe laws change with time, maybe they don’t. Maybe time is fundamental, maybe it’s emergent. Maybe the universe is eternal, maybe it had a beginning. We’ll make progress by considering all the hypotheses, and working hard to bring them into confrontation with the data. Use philosophical considerations all you want to inspire you to come up with new and better ideas; but it’s reality that ultimately judges them.

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Sixty Symbols: The Arrow of Time

Completing an action-packed trilogy that began with quantum mechanics and picked up speed with the Higgs boson, here I am talking with Brady Haran of Sixty Symbols about the arrow of time. If you’d like something more in-depth, I can recommend a good book.

Arrow of Time - Sixty Symbols

Will there be more? You never know! The Hitchhiker’s Guide to the Galaxy started out as a trilogy, and look what happened to that. (But I promise no prequels.)

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Explaining Time to Kids

Don’t forget that the deadline for this year’s Flame Challenge is coming up. Your mission: to explain “Time” to a group of 11-year-olds, who will be sternly judging your work. Get your submissions in by March 1, either video or written (less than 300 words).

Here’s my attempt. (Just given the likely number of entries, winning seems like a long shot, so I don’t mind encouraging other submissions or giving away all my best lines.) 300 words is hard, and aiming squarely at 11-year-olds who are judging a bunch of submissions is also no easy feat. But it’s good practice. I personally first fell in love with science when I was 10, so 11-year-olds are a great audience to aim at.

Admittedly the definitions I propose below could be accused of being circular, but without using technical jargon I think it’s appropriate to aim for intuitive understanding rather than perfect rigor.


Time is not hard to understand! How time works can be tricky, but time itself isn’t that mysterious.

We live in a world full of stuff. Chairs, trees, planets, stars, all kinds of things. This stuff is spread throughout space–everything has a location somewhere or another. And all this stuff, at various positions in space, happens over and over again, slightly differently each time. Things move, age, transform. Planets orbit stars, animals eat and sleep, people play and fight and think and learn. The universe doesn’t sit still.

Time is the label we stick on different moments in the life of the world. There is the universe at 2 p.m. July 1st 2013, the universe at 2:01 p.m., and so on. Just like a page number tells you where you are in a book, time tells you when you are in the universe. Moments of time are pages in the book of the universe.

We can measure time using clocks and calendars—things that repeat themselves in a predictable way. Every time the Earth revolves around the Sun, it rotates around its axis about 365 times. Every time the little hand goes around a clock dial, we can be sure the big hand goes around twelve times.

Time gets mysterious when we think about past, present, and future. We can remember what happened yesterday, but we can’t remember tomorrow. It seems obvious, but why is it true? Why does everyone – everyone! – get born young, and then grow old? We can choose what to do next in our lives, but we can’t un-choose events in the past, things that have already happened. The past is in the books, but the future remains to be shaped. Let’s hope we choose wisely!

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Talking Nerdy About Time

Cara Santa Maria, science correspondent for the Huffington Post, does a series of videos there called Talk Nerdy To Me. See Martin Savage on physics and the simulation argument, Mark Jackson on cosmology and string theory, Mark’s PhD advisor Brian Greene on the multiverse, or a collection of interviews about Alan Turing.

The latest one features me talking about the arrow of time. Likely nothing you haven’t heard before, but it’s only five minutes! Could be a useful explainer for your friends who don’t understand why you keep mumbling about entropy under your breath. (People do that, right?)

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What is Time? The Flame Challenge

Of course you know what time is, since you’ve read From Eternity to Here and you don’t buy into the mysterianist gobbledygook that often accrues to the subject. But not everyone is so fortunate. (Or my sales would have been a lot better.) So Alan Alda has laid down the gauntlet: explain time to an 11-year-old.

This is the second iteration of the Flame Challenge, so named because the first question asked was “What is a flame?” The level of abstraction is a bit higher here, and the challenge correspondingly greater.

The deadline is March 1, so plenty of time to come up with a compelling story for those of you who are tempted to rise to the challenge. There are two categories, “Written” and “Visual,” so don’t think that you necessarily have to produce a little movie to be the winner. I might enter myself, although frankly I don’t think it’s possible to do a good job in less than four hundred pages.

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