From Eternity to Book Club: Chapter One

By Sean Carroll | January 19, 2010 9:14 am

Welcome to the first installment of the From Eternity to Here book club. We’re starting at the beginning, with Chapter One, “The Past is Present Memory.”


The world does not present us with abstract concepts wrapped up with pretty bows, which we then must work to understand and reconcile with other concepts. Rather, the world presents us with phenomena, things that we observe and make note of, from which we must then work to derive concepts that help us understand how those phenomena relate to the rest of our experience. For subtle concepts such as entropy, this is pretty clear. You don’t walk down the street and bump into some entropy; you have to observe a variety of phenomena in nature and discern a pattern that is best thought of in terms of a new concept you label “entropy.” Armed with this helpful new concept, you observe even more phenomena, and you are inspired to refine and improve upon your original notion of what entropy really is.

For an idea as primitive and indispensable as “time,” the fact that we invent the concept rather than having it handed to us by the universe is less obvious—time is something we literally don’t know how to live without. Nevertheless, part of the task of science (and philosophy) is to take our intuitive notion of a basic concept such as “time” and turn it into something rigorous. What we find along the way is that we haven’t been using this word in a single unambiguous fashion; it has a few different meanings, each of which merits its own careful elucidation.

The book is divided into four major parts — Part One gives an overview of the issues, Part Two discusses relativity and time travel, Part Three (the longest and best part of the book) is about reversibility, entropy, and the arrow of time proper, and Part Four puts it all into a cosmological context. So Part One is somewhat out of logical order — it’s an attempt to survey the terrain and raise some ideas that will come to fruition later in the book.

The basic point of Chapter One is to examine the ways in which we use the concept of “time.” I’ll readily admit that this doesn’t sound like the sexiest idea for an opening chapter. (In my next book, an important character will be murdered within the first few pages, after which his beautiful daughter will be compelled to search for his killer in various exotic locales.) The first chapter has to serve multiple purposes — it obviously needs to provide some background for the rest of the book, but this is not a classroom where you can assume the audience will necessarily follow you to the end. So the first chapter also has to be fun and engaging, hinting at some of the mysteries to come.

In fact, I juggled the first three chapters back and forth. Chapter Two explains the basics of entropy and the arrow of time, while Chapter Three explains the basics of cosmology. At one point I had the current Chapter One placed after these two chapters, on the theory that we could be precise about definitions after we had been exposed to some of the big and exciting ideas. This was a well-intentioned theory, but not an especially good one. Test readers balked, so the current Chapter One was put back in the beginning.

Despite being about definitions and so forth, I think Chapter One turned out to be pretty interesting — indeed, I wonder now whether it shouldn’t have been longer. When you talk to people on the street about “time,” the first questions they ask tend to be along the lines of “what is time, really?” or “is time real, or just an illusion?” This chapter tries to answer those questions, or at least spell out the perspective I’ll be taking for the rest of the book. And they’re important questions, interesting in their own right, even if I breeze through them — lots of philosophical work, not to mention physics, has been addressed to these issues.

We distinguish between three ideas of time — time is a coordinate, time is what clocks measure, and time is the agent of change. These aren’t really “definitions” in any careful sense, so much as “ways we use the notion of time.” And my readers were right — it’s important to set out these different senses right from the start, as I’ve discovered that even physicists tend to blur them together in their minds.

The most important non-obvious stance I take in this chapter is to come down firmly on the side of an “eternalist” or “block universe” conception of time. The past, present, and future are equally real. Philosophers and other deep thinkers have been arguing about this for years, and I kind of dismiss the whole discussion in a couple of paragraphs. Sorry, philosophers! It’s an important issue, but we have other conceptual fish to fry.

So let me know what you thought, and what questions still remain — either about the substance of the chapter, or the stylistic choices made along the way. I’ll try to respond, although I reserve to right to say “hold that thought until we get to Chapter X.” And of course everyone else is encouraged to chime in, too.

  • Fenn

    I thought it was a good and necessary opener. I’d never really considered just how little I’ve considered what exactly time is. It set the table nicely.

    My only quibble with the book so far is I’d have preferred foot notes to end notes. I don’t like having to flip back and forth, but I’m sure the choice wasn’t made haphazardly (maybe footnotes scare people off like equations).

    I’m coming at this topic as a layman who hasn’t read much on the topic. Stocked up at Xmas on some Susskind and Feynman as well, but starting off with yours.

    Looking forward to your takes on the possibility of “many worlds” (especially), a deterministic universe, Boltzman brains, the anthropic principle and getting hit, I’m sure, with plenty of stuff I’ve never heard of or considered before.

    I get tired of hearing/reading concepts that can’t be empirically tested dismissed as out of the realm of science, as if this means they aren’t worth considering. Sounds like this book will take on a lot of those subjects.

  • Sean

    Yeah, the footnotes/endnotes debate raged quite a bit. In the end, endnotes aren’t quite as convenient, but they’re much less off-putting for the general reader. And I tried hard not to put anything crucial in there, and make it easy to cross-reference back and forth.

  • CW

    As a layman also, I thought the discussion about “clocks” was very good. I don’t think it’d been brought up before in other physics/philosophical writings that I have read. I thought the “block universe” element was good, and probably necessary for what you present in the later chapters. At this point, I don’t think I grasped the significance of it.

  • Metre

    “Time is the agent of change.” I always thought of that the other way around – time emerges from change; when nothing changes – such as when the universe reaches thermal equilibrium – time stands still. Time emerges from the grind of the universe toward thermal equilibrium, doesn’t it? Might be a chicken-and-egg argument (or maybe I misunderstood what you meant by “agent”), but I think time is the emergent property.

  • Beltstars

    When our mind perceives something even if its just 10 feet away it is away from us in space and in time, a fraction of a second that light travels. So for an individual what is the present in time? Is it always the past? Does the concept of past mean different things if you are in different places (Earth or Andromeda Galaxy)? Please comment.

  • Oded

    I’m having a bit of trouble understanding the “flow” of time.. Maybe this is tackled later on. While I have no problem accepting that there is a certain unique state, at 10:00am, with Bob and water boiling on the stove, and a mental state of Bob anticipating making coffee, together with a unique state of 10:05am, with a mental state of Bob actively making coffee and so on, I fail to understand the “flow” between them, and why is it that Bob’s mental state feels a forward “flow” of time…
    Is this perhaps the whole subject of the book? :) I’m not sure yet, as I am reading a chapter a week…

  • Sean

    Metre– I think it is chicken-and-egg, at least with respect to what I had in mind. I wasn’t actively suggesting that time is prior to change, just referring to the role of time as what keeps track of change.

    Beltstars– We’ll get into this more in Chapters 4&5. Obviously “the present” is something of an approximation, useful over the scale of meters but less so over the scale of light-years.

    Oded– Not sure what to say, this might be more of a psychology question. Time exists as a label that ties all those moments together in a particular order. The increase of entropy allows for a directionality to that set of mental states, so that at each moment we perceive ourselves as having traveled from the past into the future. I don’t have much to say beyond that, I’m afraid.

  • David Lucas

    I agree that it is more practical to see time as a unit of measurement as well as a ubiquitous aspect of our space-time universe. I have always felt that time in a way is akin to gravity. Gravity seems overwhelmed by the other forces sometimes, and only becomes increasingly powerful at the quantum levels, as will be shown even further if the LHC manages to create micro black holes. In the same way, I feel that time may have a further role to play, but that it has more of an effect in extra dimensions, and will not be discovered until we are able to somehow measure the effects of quantum mechanics below the Planck length. Thoughts?

  • Sean

    David– I don’t have any specific suspicions that extra dimensions will change the way we view time. Quantum gravity very likely will; I tend to think that time is more fundamental than space, but there’s obviously a lot we don’t know.

  • Mikey G

    I just tried to buy it from my Local Barnes and Noble on my lunch hour and they were sold out. I hate waiting on the Mail. I hope it’s as good as a “Brief History of Time” –I can’t wait for another book to blow my mind away.
    There is Nothing better than feeding your baby his nighttime bottle, and reading something, that someday he will read and be blown away as his daddy was. Ahh time…….

  • Andreas

    I read chapters 1 &2 yesterday. These cover the psychological feel of time (time speeds up, slows down); time of memory (I remember yesterday, etc.); time in physics (entropy, many events can go forwards or backwards), and so on.

    Okay, it’s an opening chapter, and I’m willing to let a few pages go by. I hope the book gets down to business.

    By the way, I’ve read Brian Greene’s “Fabric of the Cosmos” and Frank Wilczek’s “Lightness of Being” (along with a number of other similar books). Green argues that the key to physics is space: by understanding space, dimensions, string theory, we can understand the world. Wilczek writes that being is based on energy (mass is a form of energy, and thus space is a result of mass and energy). Sean Carroll presents the role of time in physics.

    It’s interesting that space, energy, and time are now the leading actors in physics. From a human’s perspective, mass and gravity seem to be the basis of reality, but for physics, mass is a form of energy and gravity is an effect of mass. As all three writers point out, common mass and energy is only about 4% of the universe: it’s mostly dark energy.

    This is yet another step away from the human-centric worldview: the Earth is no longer the center of the solar system; Newton’s “mass-centric world” is now only a minor part of the universe.

    (By the way, I strongly recommend Greene’s “Fabric of the Cosmos”. Well-written, clearly written, etc. Wilczek’s “Lightness of Being” however… well, he’s not a good writer. Doesn’t explain items, doesn’t position an issue in context, etc.)

  • David Lucas

    Do you see any correspondence to our perceptual arrow of time and the fact that we live “in” time? Compared to the fact that we live in at least 3 dimensions, and yet only perceive space in 2 dimensions? In other words, is the unidirectionality of time a perceptual anomaly (such as space seeming to be two-dimensional)? Also, do you believe that the mechanism of collapsing wave functions is time irreversible, or do we not have enough knowledge in this area yet?

  • lk

    I love philosophy of time stuff so would have been very happy to have more on the block universe/ presentism business, but I can see why you’ve accepted the block universe quickly seeing as you want to go on to relativity, where it’s the natural choice. Oded, that’s a pretty important question I think – the subjective experience of a flow of time is the thing that’s difficult to reconcile with the block time view and (I think) the main reason why some philosophers don’t go along with it. Saying ‘it’s a psychology question’ is how we block time people normally escape at this point!

    On the exciting footnotes/endnotes subject, I don’t care which but can I just say thanks for not starting the numbering afresh with each chapter! Normally I really hate having to work out *which* footnote 6 I want every time I flip to the back of the book…

  • Plato

    I will buy the book next visit to the book store.

    Would it be safe to say that all contents o the book mirror your discussions on the blog format? I know you had dispensed with the philosophical view , but I found your conversation with David Albert an important one.

    Assuming this is the case, the thing that flex’s one position on the idea of time is the close association to reverse chronology you presented in your Incompatible Arrows I(Martin Amis),II(Kurt Vonnegut),III( Lewis Carroll ),IV(Scott Fitzgerald). It was a fun exercise.

    Also, how far back in time was set in regard to Steven Weinberg’s First three Minutes to have now concluded with the term micro-seconds has helped us push our perspective back toward the beginning of time with The First Few Microseconds, by Michael Riordan and Willaim A. Zajc and as to how particles came to be, served to see that a Supercosmologist who actually thinks outside the box helps to set up what came before the beginning of time.

    So the question then might be approached as to the substance of the beginning of this universe and the “continuity expressed inside” some blackhole, while thinking of the quantum gravity issue?

    I think this method is a good exercise and I hope I have not gone beyond the boundaries to which time might have been expressed in the book. How it is described from “some horizon” with a conformal field theory approach.


  • Sean

    David– You should hang in there for the rest of the book. The perception of time is ultimately driven by the arrow of time and increasing entropy, although there are many details remaining to be worked out, to say the least.

    lk– given that we put the notes at the end of the book, I tried hard to make them as user-friendly as possible. It’s a dilemma! (Until everyone is using electronic readers. By the way, the Kindle edition came out pretty well.)

    Plato– some of the book mirrors stuff that appeared on the blog, but there’s much more in the book.

  • Tom Clark

    “The most important non-obvious stance I take in this chapter is to come down firmly on the side of an “eternalist” or “block universe” conception of time. The past, present, and future are equally real. Philosophers and other deep thinkers have been arguing about this for years, and I kind of dismiss the whole discussion in a couple of paragraphs. Sorry, philosophers! It’s an important issue, but we have other conceptual fish to fry.”

    Do you know whether there’s any consensus on this in the physics community? In any case, the block universe view seems to have direct implications for one common conception of free will, in which the future is thought to be metaphysically open for us to determine, not sitting there in spacetime. I’ll be curious to see if this gets covered in the book. Meanwhile, folks might want to check out the ABC sci-fi series FlashForward which takes up issues of time and free will, which I’ve posted about over at the Garden of Forking Paths.

    Love the book club concept, thanks.

  • David Lucas

    So you think the mechanism of wave function collapse is related to the entropic arrow of time?

  • Clifford Hall

    I am very glad Dr. Carroll gave the philosophical definitions at the end of the chapter: block universe, eternalism, and presentism. I was in desperate need to label these concepts. That being said, I am a PRESENTIST. Time for me is merely a bookeeping variable in physics equations; otherwise, it is an illusion. I believe that there is something in the geometry of the universe which is a “cause” of our emergent experience of linear time, and I cannot believe that there is a block universe where the worldlines of every elementary particle extend indefinitely in two directions. We can move freely in space, but not in time; therefore, I have no evidence of its existence as its very own dimension in space-time.
    The keyword here is ‘believe.’ Thus far, I see no means for science to falsify this belief. I am quite surprised that Dr. Carroll would so adamantly take the opposite stance as neither stance appears to contradict physical law.

  • Jon Claerbout

    I’ve seen too many theoretical physics popularizations and far too few on real phenomena, measurements, and experiments.

  • Sean

    Tom– I think most physicists are block-universe believers, even if they never lay out that belief explicitly. That seems to be the most natural reading of the differential equations that we think govern fundamental physics.

    David– yes, and we’ll get around to that later (Ch. 11). But I don’t think all the details are anywhere near worked out.

    Clifford– I didn’t think I was all that adamant.

    Jon– those books are certainly there, if you look for them.

  • RGG

    I’m here because of your fine lectures on Dark Matter and Energy. As a philosopher I found your analysis and theory clear. Here I’m less comfortable. We can ask ‘What’s supper?’ and when’s supper? We can even say ‘What’s when’? and begin a discussion about time. But When’s what?’ doesn’t compute, which makes time unhandsome, or without a handle.

    PS, I’m reading your wife’s useful and friendly book at the same time.

  • Sean

    RGG– I’m not sure if you’re looking for a specific response, or exactly what it is that makes you uncomfortable. I tried my best to lay out (very briefly) in Chapter 1 how I thought we should think about time, so that we can spend the rest of the book digging into it more deeply.

  • Bill Rockenbeck

    I liked how the date and time in some example is January 20, 2010. Hey, that’s tomorrow! A bonus of being an early buyer and reader of the book is its timeliness (er, heheh).

  • TS

    What did you mean by “a straight trajectory between two events in spacetime describes the longest elapsed duration”? is there another way to get from event A to Event B that would be ‘shorter’? I am having a hard time understanding this.

    I have other questions regarding the end of the chapter, but I guess I will try to figure them out on my own. Pages 19-25 — do you go into these concept further as the chapters move on, or should a person understand these concepts before going any farther into the book?


  • Sean

    Bill– Had I known the actual publication date I would have chosen that.

    TS– That’s explained more thoroughly in Chapter 4, but yes — the path of shortest duration between two events in spacetime (not points in space!) is one where you zoom out near the speed of light and then zoom back in time to reach the event.

    And yes, these are developed in more detail through the rest of the book.

  • Andreas

    The discussion of perceived time is too simple. We look down, see a broken coffee cup, and we remember the cup fell a moment ago and broke. That’s the past. But that’s also a very simple (and too simple) description of time.

    – 1861 was in the past. Does anyone remember 1861? No. None of us can personally remember that year. We know from teachers and books that the US Civil War started at Ft. Sumter in 1861. But even that isn’t clear. All we know as a fact is that there was a blockade and cannon fire. But what happened in the Civil War? That isn’t a “fact” in the same way that my broken coffee cup is a fact. The meaning of the “Civil War” changes every few decades. If you read books and articles written at the time, you’ll realize that what we “know” about the past is different from what they experienced at the time. Thus the perceived past can change: it can evolve (look at the change in understanding over the Great Depression), it can change radically (the War Between the States, which was fought over states’ rights, is now seen as a war over slavery), and it can even disappear (the history of the USSR is disappearing).

    – Did the past ever exist? Christians say the world was created by their sky god in seven days. Archbishop Ussher calculated this to a late afternoon on Sunday, October 23, 4004 BC. They know the past quite clearly (and you have any doubts, just try talking with a fundamentalist Christian). But for everyone else, their “past” never existed.

    What about the “past” of science? That’s clearly defined, isn’t it? But 200 years ago, we had no idea of galaxies. 100 years ago, we realized how far away they were. Ten years ago, the issue of the expansion of the universe was solved. Our scientific, objective past itself is changing radically, constantly being updated.

    The past itself is as malleable and up-for-grabs as the future, according to politics, religion, and cultural trends. A few things can be said with certainty (such as “Sean Carroll was born in 1966”), but even that can change (“Carroll, the 2018 Nobel Prize winner, was born Oct. 5, 1966″) (or… The modern Age of Carroll started as the year zero, which replaced the previous Gregorian Calendar, previously known as 1966.”).

    What about the broken coffee cup? Isn’t that clearly “in the past”? Not if your house has three kids, two dogs, and a cat. You’ll get 24 different explanations why your Nobel Prize coffee cup got broken until you finally give up and switch to whiskey.

    So, it’s only for very simple (and very trivial) events that we can talk with certainty about a past. Everything else recedes into a fog of conflicting interpretations.

    All of this applies to the future as well. “The future isn’t what it used to be” captures it very well: The expected perception of the future is a cultural construct, and it changes as well. 2010 certainly isn’t what we expected back in 1980. We construct and maintain the future, just as we construct and maintain the present and the past.

    Thus I find it very problematic (okay, wrong) when Sean writes “we remember the past due to entropy” (p.40-41). How does entropy explain different pasts (Bishop Ussher vs. Charles Darwin) or that the understanding of the French Revolution has changed several times? And we very well can remember the future: Back in the 80s, the future had flying cars, house robots, and no web.

    So the discussion of time in these opening chapters isn’t useful. Too many issues are mixed up; there isn’t a clear analysis.

  • Sean

    Andreas– I’m not sure if there’s a particular point in there you’d like me to answer. General tip: to increase the likelihood of a useful response, keep the questions relatively pithy!

  • TS

    By the way, I read Slaughterhouse-Five a week before I started reading this book and was excited to see the reference to it. I was also thinking of how the Grand Canyon gives us the ability to see all events at once (maybe not the future, but if we pick a spot in the middle then we could see past present future with a little help from our imagination). You can see millions of years at once if you know how to ‘read’ the walls and rocks.

  • NicoleS

    I am coming to this book as a complete and total laymen, interested in the subject of time and eager to go on this quest for the ultimate theory, but a little frightened by how smart all of you are!

    That being said, I thoroughly enjoyed the first chapter. The only place that I stumbled was when you said, “For subtle concepts such as entropy…” and I thought to myself, “Oh crap, I have no idea what entropy is.” I tried to have someone explain it to me and I managed to somehow understand how human beings are the anti-entropy, but the concept is still lost on me. But I guess you’ll be getting more into that in the second chapter?

    Anyway, being that I didn’t feel at all lost or bored in this chapter means that I think you’ve done a really excellent job.

    Excited to read and discuss more.

  • NicoleS

    Oh! I also wanted to say that imagining myself as Dr. Manhattan really helped in understanding a lot of the chapter. I sort of wanted to leave a comment in the book club announcement that said, “It’s 3:34 on April 19th and I’ve already finished reading the book.”

    Also – for those of you having a hard time finding it at B&N – I’m pretty sure the stores have the books modeled in on a display, so if you go to and click the find in store option, it should give you a list of other stores near you that have the book.

  • J

    I got a Kindle for Christmas and this was the second book I put on there. The notes work great on it! I, like Tom, would have liked to have seen more on the block universe concept, but I can live with that given the way the perception of time was broken down into the 3 aspects. I had long ago given up trying to wrap my head around the “the medium through which we move” and was quite happy counting ticks and plotting points. It was good to revisit and I look forward to seeing the 3 aspects get tied closer together (at least I hope they get tied closer together) as the book progresses.

  • Sean

    TS– digging up the literary references was lots of fun.

    NicoleS– more on entropy in Chapter Two, and *lots* more in Chapters 8, 9, 10. If nothing else, you’ll know what entropy is when we’re all done. (It’s [the logarithm of] the number of ways you can re-arrange a system without changing its macroscopically observable features.)

    J– hopefully things will be tied more together. And I agree, the Kindle works well.

  • Lab Lemming

    The purpose of science is to solve problems. So the assuption of an actual past makes solving questions about it a lot easier. Geologists regularly use multiple working models for particular past (and present) problems where different methods of analysis produce different results. But the assumption of anything other than a single tractable reality decreases our ability to constrain that reality, so it is not a productive approach.

    Here is a practical example: A decade ago, the two main radiological methods of determining time (The uaranium/ lead and potassium argon systems) systematically differed by 1-2%. Assuming a single “real” timescale allows two thigs: firstly, an intercalibration between the two systems can be produced. Secondly, the assuption that one or both is wrong can lead to attempts to improve them by refining analytical procedures and the physical constants used in those procedures. It is not clear to me how a different view of time would increase the tarctability of the problem. Since science is ultimately a utilitarian endeavor, we pick the approach that works best.

    In fact, the appeal to utilitarianism is useful not only here, but for confronting anti-evolutionary and other antiscientific suggestions as well.

  • Lab Lemming

    Do you go into the history of entropy at all? The thing I lvoe about it is that it was defined and put into routine use decades before atomic theory was accepted. So the

  • Sean

    I go into the pre-Boltzmann history a bit in Chapter 2, and the Boltzmann history a lot in later chapters.

  • badinage

    I am surprised that with all the recent recourse to dualism nobody has stated the obvious; that the presentism and eternalism views are dual descriptions of the same concept (time). The analogy to wave-particle duality is self evident. I think Orzel’s dog figured that out in chapter one of his book.

  • Susan

    I see in Chapter One the same thoroughness I liked so much in your dark energy lectures. Sometimes I think I understand a concept, sometimes not. But I know that if I keep at it I WILL understand it, because it is All there. One idea, discussion around it, next idea more explaination, and so on. Each one a block of thought, that I can return too. And the layering of ideas is useful. Since I only read, or even “think deeply”, in bits and pieces, I often have to go back over things many times. But in this back and forth manner I have learned a lot. I hope I am correct in thinking this book will lend itself to that method. To help out I have the book, and the audio book is ordered. I do expect you to be reading it.

  • Sean

    Susan, thanks, I hope the book lives up to it! I’m not the one reading the audio book; the guy who is doing it is a professional who is frankly better at it than I would have been.

  • Andreas

    Lab Lemming writes that it’s useful to assume an actual past. He means “an actual physical past”, namely, the history of broken cups and factual, physical things.

    I’m pointing out that Sean is moving back and forth between “physical past in memory” (I remember my cup fell and broke) and “the social past in memory” (the various interpretations of the Civil War.)

    The second one isn’t something that physics can address. I don’t see how entropy has to do with that type of memory, since it changes according to politics, historians, etc. There simply isn’t an objective historical past in the Newtonian sense.

    The first type of past (physical events) is also a problem. Let’s say ten minutes ago, Xsdf (who lives on a planet around Sirius) broke his coffee cup. Sirius is about eight light years away, which means Xsdf is outside our light cone. There is no meaningful way for us to say Xsdf’s cup fell ten minutes ago in our past. There is no objective Newtonian past. We can’t assume an actual physical past.

    Sean asked if I’m asking a question. It’s not a question. I’m pointing out that the common sense ideas of past and memories are very complicated (or, better said, very muddled). Sean’s book is forcing me to think about these. I’ll admit: I want to say that Xsdf’s cup broke ten minutes ago, but Einstein’s ideas tell me I can’t do that.

    Here’s another note: A few months ago, I converted our family’s Super8mm films into digital files and began editing them on my computer. I haven’t seen these movies in 20-30 years. If you ask me what is in my memory, it’s a series of fuzzy scenes, somewhat like what I see in dreams. When I watch the videos, it doesn’t match my memory at all. I have to adjust my memory to match the video. I bring this up because Sean writes quite a bit about memory and entropy, but that doesn’t match my experience of memory, that is to say, my experience of the past.

  • Sam Wolk

    Hi –
    I guess I am a layman (I am a freshman in high school and I should probably be studying for finals right now… this is more fun though so whatever…), but I love reading books like this (I just finished A Brief History of Time and Why Does E=mc^2, both of which I would highly recommend to anyone who likes this sort of book). I do have a few questions from the start of the book, both of them about entropy, so I guess I should wait until next week but one of them is more directly related to time, so here it is: I completely understand that the Second Law of Thermodynamics combined with the fact that entropy must have originally been very low leads to the Arrow of Time and thus why we seem to move from and remember the past while journey (so to speak) into the future. My question though is this: if a universe were to evolve in which the reverse were true (perhaps this is impossible and a silly hypothetical, but it seems conceivable), i.e. the universe started with high entropy and entropy decreases, what would that mean for perception? Would we “remember” the future and forget the past? Also would this universe actually seem no different, just as if every timekeeping device of any sort slowed down, you wouldn’t notice?

    This is something else that I find interesting but isn’t really a question: if one were to apply the concept of slowing down all the time-keepers to a single individual, it seems to me analogous to the idea of one person seeing everything in negative; the person who experiences time slower would be like the person who sees everything in negative relative to everyone else. If someone else were to experience time or see color the way the special person does, they would notice the difference, but if they were to just talk, it would be impossible to tell the difference. As I’m sure you know the idea of seeing in negative is a famous philosophical concept, and although I mean not be explaining it well, I was wondering if you agree that the same idea applies to time.


    Sorry if my first question should have waited for the next chapter, but I am already saving one and I just had to ask.

  • Sean

    Sam– the direction in which time points is ultimately arbitrary. What is real and measurable is the direction in which entropy increases. Everything goes along with that; so in any particular universe, inhabitants would always think of the direction of lower entropy as “the past,” and that’s what they would remember. There would be absolutely no difference between that type of universe and the one in which we live. (In fact, there’s nothing to stop you from using a time coordinate that runs in the opposite direction of the usual one — coordinates aren’t very meaningful, they’re just labels.)

  • Phillip Helbig

    My only quibble with the book so far is I’d have preferred foot notes to end notes. I don’t like having to flip back and forth, but I’m sure the choice wasn’t made haphazardly (maybe footnotes scare people off like equations).

    I also vastly prefer footnotes to endnotes. Those who aren’t interested can ignore either one; those who are have a more difficult time with the endnotes. After reading a book, sometimes I want to go back and re-read something, and have a feel for where it was in the book. With footnotes, I’ll find it easily, whether it was in the main text or not, but with endnotes it is more difficult.

  • Phillip Helbig

    The most important non-obvious stance I take in this chapter is to come down firmly on the side of an “eternalist” or “block universe” conception of time.

    I used to be rather sceptical of the many-worlds interpretation due to the “but where are they” argument. However, while reading Deutsch’s The Fabric of Reality, I realised that this question is no more puzzling than asking where the many worlds (infinitely many, or perhaps finitely separated by the Planck time or whatever) of the past are.


  • Sean

    Philip– yes, I feel the same way, and we talk about it a bit in Chapter 11.

  • Will

    I’m interested in the concept of “nowhen”, but it seems to me that everyone’s nowhen is unique. An earlier poster asked about the concept of “past” in the context of far removed locales, and you promised we would get into it more in later chapters. But does the role of the observer have similar effects on time as it does on quantum mechanics? I’m probably not making sense, but it seems to me that my perception of time (past, present or future) must be different than an observer (hypothetical) in the Andromeda galaxy. Really looking forward to chapters 4 and 5!

  • Blake Stacey

    In my next book, an important character will be murdered within the first few pages, after which his beautiful daughter will be compelled to search for his killer in various exotic locales.

    Huh. I waited until the bottom of p. 35 to kill off a character. No wonder my sales have been so slow.

    <John Hammond voice> “Next time, it will be flawless!”

  • PhilG

    I got my copy just in TIME to join in. First chapter is very solid except I have no idea who or what a “running back” is or why they would run around like that :-)

    You said above that you dont have “any specific suspicions that extra dimensions will change the way we view time”. Of course if there were extra time dimensions (as in F-theory) then that would have some influence on the way people view time. Some ideas about time would not make sense if there were actually more than one time dimension even if they only show up at very small scales. For example a lot of what Lee Smolin says about time being more fundamental and different from space would be hard to justify. I prefer the viewpoints that would not fall apart in the face of many time dimensions.

  • Sean

    Will– time is not an observable in quantum mechanics; the wave function takes on values at every different moment of time. But the perception of time depends on lots of things, including the arrow of time based on entropy. For most purposes, there’s every reason to think that the perception of time is similar at all points within the observable universe, but in regions where they might not be an arrow of time it’s hard to know what that would even mean.

    Blake– study your Dan Brown, and get back to me.

    PhilG– sorry about the running back business; the only current edition of the book is aimed at Americans. The number of time dimensions is of course an empirical question, to the extent that it’s a well-posed question at all. I tend to think that quantum mechanics is fundamental, so that there is just one time direction at a deep level, but obviously that’s a tentative opinion.

  • Mark Weitzman

    Your above quote ” time is not an observable in quantum mechanics” while the conventional view has always made me a little unconfortable especially with regard to relativistic QM. I love Mark Srednicki’s dicussion in his QFT text P. 10 about the two alternatives demoting space operators to parameters ( conventional QFT approach ) or promoting time to an operator – any thoughts about the second option?

  • Sean

    Mark– I don’t have any very deep thoughts about it. It doesn’t seem obviously necessary to promote time to an operator; in quantum mechanics, time is very different from anything else, as the history of the wave function is a path through the Hilbert space as a function of time. I kind of like it that way.

  • Blake Stacey

    Blake– study your Dan Brown, and get back to me.

    “Fluctuations, in this equilibrated Universe, could come in countless forms. Renowned physicist Ludwig Boltzmann staggered out onto the Ringstrasse, knowing that he had only moments before his brain dissolved once more into formless Chaos. . . .”

  • Godfather

    No question yet, but I thank you for this excellent book :-)

  • Josh

    Time being a Lorentzian complimentary coordinate to space emerges from the second derivatives of time that appear in gauge-invariant vacuum solutions to Maxwell’s Equations. So, is the comparable lack of a temporal observable in QM due to the fact that solutions to Schrodinger’s Equation are linear in time?

  • Susan

    I developed an interest in cosmology late in life. I’m now 64. Feeling I don’t have time to learn from the basics up, I use another method. I start with the new and most interesting, “good stuff” and the I learn down just far enough to understand the theory. It may take reading many books to “get it” or it may be just one word I need defined. This is working well for me overall, and who cares if I know more about generalativity than chemestry, or that I never took a physics class. It does however set me up for some embarassing misconceptions. I wasn’t sure what a “field theory” was for a long time. I would be going along understanding the material and then it would talk about some famous scientist’s field theory, and I would wonder why do they call it that! The notion that these folk were out measuring things in the woods didn’t fit the material at all. I tried to find out what it mean many times but just couldn’t. It is hard to look up a phrase, and if it isn’t on TV with cool pictures, my friends don’t know. Finally I just made up my own definition. I decided it meant any work or experiment that wasn’t done in a lab or collider etc. and let it go. It wasn’t until I was thinking about Bosons being force particles that it came clear. “Forces and fields”, or maybe it was “forcefield” that brought it home. I am still laughing at that one! Now I think I know what “as a funtion of time” means, but I have been wrong before. Please indulge me and clarify it.

    PS. I bet I could understand what Josh just said if I worked at it, but I think I’ll pass, and continue reading “Chapter Two”.

  • Sean

    Josh– not really. Time is just treated completely differently from space in quantum mechanics. The are treated very similarly in relativity, which seems to suggest some kind of tension, but in fact the tension is easy to resolve, until you get to quantum gravity.

    Susan– hooray for getting interested in science of any sort late in life! “As a function of time” simply means that something is changing as time passes. At any one moment, quantum mechanics tells us that we describe the state of the world by a “wave function,” which can be used to calculate the probability of obtaining any particular result for an observation. But that wave function changes as time passes. So the history of the world is described by a series of wave functions, one at each time, which together we call “the wave function as a function of time.” If that makes sense.

  • Susan

    It tells me what I needed to know, Thanks.

  • Andy Jewell

    This might be beyond the scope of chapter 1, but — is there a Plank time? The time cousin to 10^-33 centimeters?

  • TS

    Susan, ‘function’ is a math term, maybe you remember it from precalc or algebra. simply stated: It is an equation with variables (x and y) and y will change with x: 3+x=y … if I let x be 5 then y will be 8. If I let x be 1 then y will be 4. If something is a function of time then it will change with time (or will time change when that ‘something’ changes?!)

  • waveforms

    “In relativity, there’s no such thing as “at the same time,” at least when we’re talking about two truly distinct events at different points in space. If something happens very far away, we can’t say it happens at the same time as something that happens right next to us, because that depends on the reference frame we are using.”

    From This answer leads me to a paradox.

    Doesn’t the collapse of the wavefunction of the universe happen everywhere at once? If you say no then my follow up question will be: split the distance between the two far away events, if they still don’t happen at same time, split distance again, repeat until you find a point where they both occur at same time as collapse of wavefunction of the universe. Now, explain how come that distance is different from step n-1?
    If you say yes, then all events can be related unequivocally to the moment of the collapse of the wavefunction of the universe. We have our universal frame of reference, No?

  • Sean

    Andy– Yes, it’s 10^-44 seconds. Given a distance you can always convert into a time, and vice-versa, by dividing or multiplying by the speed of light.

    waveforms– That’s bothered a lot of people, including Einstein. The thing is, we can describe the wave function as collapsing instantaneously in any reference frame, and all the observational consequences are exactly the same. So there’s no preferred frame.

  • Samuel A. (Sam) Cox

    Sean, Really am enjoying the book. Your comment #41 in answer to #40 was well worth noting…observers always perceive the direction of the “flow” of time as resulting from a (macroscopic) increase in entropy? Even in dual or yet higher dimensional configurations time could only be identified as it resulted from an upward change in entropy? relates to the irreversibility of time?

  • PhilG

    Sean, I don’t know why you would target a physics book at Americans. All Anglophones will find it perfectly readable. Honestly, we dont really mind if you spell “colour” wrongly and use American Football metaphores. There was no difficulty or extra cost getting the “American” version here on They dont even label them as imports anymore. Most of the marketing seems to be web-based and UK science magazines have already reviewed it, so that does not make any difference either. I remember one of Smolin’s books having a UK version released 6 months after the US version. I doubt it sold well because anyone like me who had an interest had already bought the US version without noticing the difference. If your publisher tells you that popular physics books dont sell well in the UK ask them if they are counting sales of the US versions here.

    I dont think two time dimensions stops quantum mechanics being fundamental, otherwise what kind of theory is F-theory? (The answer may depend on exactly what you mean by “quantum mechanics is fundamental.”) Of course two time dimensions is problematic for causality, but as you say, it is open to empirical test and if evidence of two time dimensions is found it will certainly change our view of time. That was the original point.

  • Andreas

    The core idea of the book is the concept “entropy.” What does that mean?

    Entropie, which means “the measure of the disorder of a system,” was coined in 1865 by physicist Rudolph Clausius (1822-1888) based on the German word “Energie” by using the Greek word entropia “a turning toward” (en- “in” + trope “a turning”).

    Look at Wikipedia. It now has at least four different definitions:

    – Entropy is a measure of the number of ways in which a system may be arranged, often taken to be a measure of “disorder” (the higher the entropy, the higher the disorder).

    – Entropy is a measure of a system’s tendency towards spontaneous change.

    – Entropy is a measure of certain aspects of energy in relation to absolute temperature.

    – Entropy is a measure of the uniformity of the distribution of energy.

    It means disorder, change, energy, and distribution? That’s four different ideas. And you can easily find more definitions by reading about entropy.

    This explains the problem with entropy. Writers shift back and forth between various definitions when they talk about entropy.

    Sean, can you give us a clear definition of entropy? Or does this word have multiple shades of meaning?

  • rww

    Is it that the early universe was low entropy or just lower than presently?

    If it is just low-er then it doesn’t seem quite the same puzzle.

    And if it was low in some absolute sense, relative to what?

  • rww

    Sorry, that was probably not very clear. Maybe my problem is this: If the early universe was a fog of photons and particles, why is that considered low entropy? How was it different from my mix of coffee and cream?

  • Sean

    Andreas– There are many definitions of entropy. We’ll talk a little about them in Chapter 2, and in more detail in Chapter 8.

    rww– We’ll get to that, in Chapter 3 and again in great detail in Part Four, especially Chapter 13.

  • TSny

    Just got started reading chapter 1. This is going to be a fun book.

    Sean, on page 10 you imply that John Wheeler is the source of the statement “Time is Nature’s way of keeping everything from happening at once”. Although Wheeler might have been fond of this quote, he was not the originator. On page 351 of Wheeler’s book Geons, Black Holes, and Quantum Foam, Wheeler writes that he found the quote as a graffito in the men’s bathroom at the Pecan Street Café in Austin.

    On page 323 of the April, 1978 issue of The American Journal of Physics you can find essentially the same quote attributed to the physicist C. J. Overbeck. No reference is given. Using the internet I was able to find an article by Overbeck in the August 1973 issue of The Rotarian Magazine in which he writes “What is time? As a physicist I have on occasion answered that question by saying, quite seriously, ‘Time is that great gift of nature which keeps everything from happening at once’.” Of course, Overbeck might have been repeating or rephrasing something that he had heard or read somewhere else!

    Most hits on the internet appear to attribute the quote to Wheeler, so he might very well end up owning it.

  • Sean

    Thanks for the catch. I definitely have seen it attributed to Wheeler, but it’s easy to imagine the Matthew effect at work.

  • TSny

    Also, quite a few internet hits attribute the quote to Woody Allen. I guess we’ll never know for sure.

  • Susan

    I think your book is written for people like me. That is those who are happy with concepts and intriguing ideas. It is science, but well explained and not too hard to understand. I know there is understanding, and deeper understanding, and really understanding. To learn enough for personal satisfaction is the goal. I believe folk put physicists, cosmologists etc in with “brain surgeons and rocket scientists” all very smart people. This is of course is completely true, but by doing so they put themselves in the category of dumb. They are likely “smart enough”. It is the intriguing ideas that may get them to give it a try. I think it is testimony to how far the knowledge of the universe has come that we can ask seriously “whats outside the universe”. Up to now it has been sort of “I’m still trying to figure out what is inside the universe, so I am not going to think about that!” As you point out, some of these ideas have been around for awhile, but thinking about time in terms of natural laws and physics, is all new to most of us. Thanks for putting it out there.

    PS. to Frank and Sean. I haven’t taken any math since Algebra I in highscool, thanks for adding to Seans answer. Who knew I would be buying math learning DVD’s about 37 years later. When I implied I could learn hard technical things, I should have added, if I live long enough! The waveform information makes me want to know more.

  • Susan

    Let me change the above “outside the universe” to “before the low entropy state of the universe”, or something along that line. (I knew I should have read ahead a little).

  • Buffalo Bob

    It “seems’ to me that C itself determines time’s existence and also our perception of it. Were there no speed limit on light, the unfolding of the Universe would be but a wink, over in a flash. BUT, limiting C (but what exactly limits C ?) allows the unfolding of process and events, ie. what we call time. (I am NOT a physicist, just a curiopus stranger.)

    It would further “seem” to me that it is fabric of space itself which puts the brakes on C, and that by delving into that, we will discover a technique for “Warp Drive”, etc. We have been looking at all the stuff that is just along for the ride, as if there answer were there. I think, not! (Now there’s an ambiguous statement.)

    I will buy the book from Amazon and delve in… working through Robert Laughlin right now.

  • Buffalo Bob

    stuck here….. out of entrophy…. delete

  • Andreas

    No, Buffalo Bob, it’s the other way around: you have TOO MUCH entropy!

    In the news this morning. The universe contains 30 times more entropy than earlier estimates.

  • Rex

    Okay, I have an important (to me!) question about chapter 10. Surely you won’t make me wait 8 more weeks (2 months!) to get an answer! (I hope!)

    BUT, I’ll ask it back here on the Chapter 1 discussion from last week, so as not to disrupt the active Chapter 2 thread that just started this week.

    I promise I’ll ask again in March when we get to chapter 10!

    Okay, that’s my groveling. Now the question:

    So, in chapter 10 you rule out the possibility of the eternal recurrence scenario based on the low probability of an observer of our type (human) being surrounded by a non-equilibrium visible universe compared to the probability being a “boltzmann brain” human observer who pops into existence to find himself surrounded by chaos.

    As you say, in the eternal recurrence scenario there should be far far more of the later than of the former.

    Okay. So, my question:

    If the recurrences are really eternal, then shouldn’t there be infinitely many of BOTH types of observers? Countably infinite?

    And aren’t all countably infinite sets of equal size?

    So in an infinite amount of time we would accumulate one countably infinite set of our type of observer. And over that same amount of time we’d could also accumulate another countably infinite set of the “Boltzmann Brain” type of observer.

    The two sets would be of the same size…countably infinite. Right?

    So probabilistic reasoning wouldn’t apply here, would it?

    Especially not in a “block” universe where we don’t even have to wait for an infinite amount of time to pass.

  • Sean

    Rex, this is certainly a good problem, related to the “measure” issue that cosmologists are always talking about. Yes, in an eternal universe there are countably infinite numbers of “ordinary” observers and freak (thermal-fluctuation) observers. But the frequency of the latter — the average number in any particular length of time — is much larger. We generally assume that this is enough to calculate probabilities, although it’s hardly an airtight principle.

  • marcel

    In my next book, an important character …

    Be sure to include hot vampires too.

  • John

    Dr. Carroll, enjoying your new book very much.

    Have a simple logic question that I do not get satisfactory answers to:

    Is Cosmology a subset of Astronomy, or is Astronomy a subset of Cosmology?

    My notions are that Cosmology is everything, not just the visibile universe, including what we can’t see.

  • Sean

    I don’t think there’s a simple universal answer. Cosmology is the study of the structure and evolution of the universe, which involves aspects of physics and astronomy. It’s sometimes considered a subset of astronomy for classification purposes, but I agree that it includes the parts of the universe we can’t see.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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