The nature of time has perplexed philosophers and scientists from the ancient Greeks (and probably before) to the present day. Despite two and half millennia of reflexion upon the problem and spectacular success in understanding many other aspects of the universe we inhabit, not only has little progress been made on the question of time, but to a large extent we are still puzzling over the same problems which vexed thinkers in the time of Socrates: Why does there seem to be an inexorable arrow of time which can be perceived in physical processes (you can scramble an egg, but just try to unscramble one)? Why do we remember the past, but not the future? Does time flow by us, living in an eternal present, or do we move through time? Do we have free will, or is that an illusion and is the future actually predestined? Can we travel to the past or to the future? If we are typical observers in an eternal or very long-persisting universe, why do we find ourselves so near its beginning (the big bang)?
Indeed, what we have learnt about time makes these puzzles even more enigmatic. For it appears, based both on theory and all experimental evidence to date, that the microscopic laws of physics are completely reversible in time: any physical process can (and does) go in both the forward and reverse time directions equally well. (Actually, it’s a little more complicated than that: just reversing the direction of time does not yield identical results, but simultaneously reversing the direction of time [T], interchanging left and right [parity: P], and swapping particles for antiparticles [charge: C] yields identical results under the so-called “CPT symmetry” which, as far is known, is absolute. The tiny violation of time reversal symmetry by itself in weak interactions seems, to most physicists, inadequate to explain the perceived unidirectional arrow of time, although some disagree.)
In this book, the author argues that the way in which we perceive time here and now (whatever “now” means) is a direct consequence of the initial conditions which obtained at the big bang—the beginning of time, and the future state into which the universe is evolving—eternity. Whether or not you agree with the author’s conclusions, this book is a tour de force popular exposition of thermodynamics and statistical mechanics, which provides the best intuitive grasp of these concepts of any non-technical book I have yet encountered. The science and ideas which influenced thermodynamics and its practical and philosophical consequences are presented in a historical context, showing how in many cases phenomenological models were successful in grasping the essentials of a physical process well before the actual underlying mechanisms were understood (which is heartening to those trying to model the very early universe absent a theory of quantum gravity).
Carroll argues that the Second Law of Thermodynamics entirely defines the arrow of time. Closed systems (and for the purpose of the argument here we can consider the observable universe as such a system, although it is not precisely closed: particles enter and leave our horizon as the universe expands and that expansion accelerates) always evolve from a state of lower probability to one of higher probability: the “entropy” of a system is (sloppily stated) a measure of the probability of finding the system in a given macroscopically observable state, and over time the entropy always stays the same or increases; except for minor fluctuations, the entropy increases until the system reaches equilibrium, after which it simply fluctuates around the equilibrium state with essentially no change in its coarse-grained observable state. What we perceive as the arrow of time is simply systems evolving from less probable to more probable states, and since they (in isolation) never go the other way, we naturally observe the arrow of time to be universal.
Look at it this way—there are vastly fewer configurations of the atoms which make up an egg as produced by a chicken: shell outside, yolk in the middle, and white in between, as there are for the same egg scrambled in the pan with the fragments of shell discarded in the poubelle. There are an almost inconceivable number of ways in which the atoms of the yolk and white can mix to make the scrambled egg, but far fewer ways they can end up neatly separated inside the shell. Consequently, if we see a movie of somebody unscrambling an egg, the white and yolk popping up from the pan to be surrounded by fragments which fuse into an unbroken shell, we know some trickster is running the film backward: it illustrates a process where the entropy dramatically decreases, and that never happens in the real world. (Or, more precisely, its probability of happening anywhere in the universe in the time since the big bang is “beyond vanishingly small”.)
Now, once you understand these matters, as you will after reading the pellucid elucidation here, it all seems pretty straightforward: our universe is evolving, like all systems, from lower entropy to higher entropy, and consequently it’s only natural that we perceive that evolution as the passage of time. We remember the past because the process of storing those memories increases the entropy of the universe; we cannot remember the future because we cannot predict the precise state of the coarse-grained future from that of the present, simply because there are far more possible states in the future than at the present. Seems reasonable, right?
Well, up to a point, Lord Copper. The real mystery, to which Roger Penrose and others have been calling attention for some years, is not that entropy is increasing in our universe, but rather why it is presently so low compared to what it might be expected to be in a universe in a randomly chosen configuration, and further, why it was so absurdly low in the aftermath of the big bang. Given the initial conditions after the big bang, it is perfectly reasonable to expect the universe to have evolved to something like its present state. But this says nothing at all about why the big bang should have produced such an incomprehensibly improbable set of initial conditions.
If you think about entropy in the usual thermodynamic sense of gas in a box, the evolution of the universe seems distinctly odd. After the big bang, the region which represents today’s observable universe appears to have been a thermalised system of particles and radiation very near equilibrium, and yet today we see nothing of the sort. Instead, we see complex structure at scales from molecules to superclusters of galaxies, with vast voids in between, and stars profligately radiating energy into space with a temperature less than three degrees above absolute zero. That sure doesn’t look like entropy going down: it’s more like your leaving a pot of tepid water on the counter top overnight and, the next morning, finding a village of igloos surrounding a hot spring. I mean, it could happen, but how probable is that?
It’s gravity that makes the difference. Unlike all of the other forces of nature, gravity always attracts. This means that when gravity is significant (which it isn’t in a steam engine or pan of water), a gas at thermal equilibrium is actually in a state of very low entropy. Any small compression or rarefaction in a region will cause particles to be gravitationally attracted to volumes with greater density, which will in turn reinforce the inhomogeneity, which will amplify the gravitational attraction. The gas at thermal equilibrium will, then, unless it is perfectly homogeneous (which quantum and thermal fluctuations render impossible) collapse into compact structures separated by voids, with the entropy increasing all the time. Voilà galaxies, stars, and planets.
As sources of energy are exhausted, gravity wins in the end, and as structures compact ever more, entropy increasing apace, eventually the universe is filled only with black holes (with vastly more entropy than the matter and energy that fell into them) and cold dark objects. But wait, there’s more! The expansion of the universe is accelerating, so any structures which are not gravitationally bound will eventually disappear over the horizon and the remnants (which may ultimately decay into a gas of unbound particles, although the physics of this remains speculative) will occupy a nearly empty expanding universe (absurd as this may sound, this de Sitter space is an exact solution to Einstein’s equations of General Relativity). This, the author argues, is the highest entropy state of matter and energy in the presence of gravitation, and it appears from current observational evidence that that’s indeed where we’re headed.
So, it’s plausible the entire evolution of the universe from the big bang into the distant future increases entropy all the way, and hence there’s no mystery why we perceive an arrow of time pointing from the hot dense past to cold dark eternity. But doggone it, we still don’t have a clue why the big bang produced such low entropy! The author surveys a number of proposed explanations, some of which invoke fine-tuning with no apparent physical explanations, summon an enormous (or infinite) “multiverse” of all possibilities and argue that among such an ensemble, we find ourselves in one of the vanishingly small fraction of universes like our own because observers like ourselves couldn’t exist in all the others (the anthropic argument), or that the big bang was not actually the beginning and that some dynamical process which preceded the big bang (which might then be considered a “big bounce”) forced the initial conditions into a low entropy state. There are many excellent arguments against these proposals, which are clearly presented. The author’s own favourite, which he concedes is as speculative as all the others, is that de Sitter space is unstable against a quantum fluctuation which nucleates a disconnected bubble universe in which entropy is initially low. The process of nucleation increases entropy in the multiverse, and hence there is no upper bound at all on entropy, with the multiverse eternal in past and future, and entropy increasing forever without bound in the future and decreasing without bound in the past.
(If you’re a regular visitor here, you know what’s coming, don’t you?) Paging friar Ockham! We start out having discovered yet another piece of evidence for what appears to be a fantastically improbable fine-tuning of the initial conditions of our universe. The deeper we investigate this, the more mysterious it appears, as we discover no reason in the dynamical laws of physics for the initial conditions to be have been so unlikely among the ensemble of possible initial conditions. We are then faced with the “trichotomy” I discussed regarding the origin of life on Earth: chance (it just happened to be that way, or it was every possible way, and we, tautologically, live in one of the universes in which we can exist), necessity (some dynamical law which we haven’t yet figured out caused the initial conditions to be the way we observe them to have been), or (and here’s where all the scientists turn their backs upon me, snuff the candles, and walk away) design. Yes, design. Suppose (and yes, I know, I’ve used this analogy before and will certainly do so again) you were a character in a video game who somehow became sentient and began to investigate the universe you inhabited. As you did, you’d discover there were distinct regularities which governed the behaviour of objects and their interactions. As you probed deeper, you might be able to access the machine code of the underlying simulation (or at least get a glimpse into its operation by running precision experiments). You would discover that compared to a random collection of bits of the same length, it was in a fantastically improbable configuration, and you could find no plausible way that a random initial configuration could evolve into what you observe today, especially since you’d found evidence that your universe was not eternally old but rather came into being at some time in the past (when, say, the game cartridge was inserted).
What would you conclude? Well, if you exclude the design hypothesis, you’re stuck with supposing that there may be an infinity of universes like yours in all random configurations, and you observe the one you do because you couldn’t exist in all but a very few improbable configurations of that ensemble. Or you might argue that some process you haven’t yet figured out caused the underlying substrate of your universe to assemble itself, complete with the copyright statement and the Microsoft security holes, from a generic configuration beyond your ability to observe in the past. And being clever, you’d come up with persuasive arguments as to how these most implausible circumstances might have happened, even at the expense of invoking an infinity of other universes, unobservable in principle, and an eternity of time, past and present, in which events could play out.
Or, you might conclude from the quantity of initial information you observed (which is identical to low initial entropy) and the improbability of that configuration having been arrived at by random processes on any imaginable time scale, that it was put in from the outside by an intelligent designer: you might call Him or Her the Programmer, and some might even come to worship this being, outside the observable universe, which is nonetheless responsible for its creation and the wildly improbable initial conditions which permit its inhabitants to exist and puzzle out their origins.
Suppose you were running a simulation of a universe, and to win the science fair you knew you’d have to show the evolution of complexity all the way from the get-go to the point where creatures within the simulation started to do precision experiments, discover curious fine-tunings and discrepancies, and begin to wonder…? Would you start your simulation at a near-equilibrium condition? Only if you were a complete idiot—nothing would ever happen—and whatever you might say about post-singularity super-kids, they aren’t idiots (well, let’s not talk about the music they listen to, if you can call that music). No, you’d start the simulation with extremely low entropy, with just enough inhomogeneity that gravity would get into the act and drive the emergence of hierarchical structure. (Actually, if you set up quantum mechanics the way we observe it, you wouldn’t have to put in the inhomogeneity; it will emerge from quantum fluctuations all by itself.) And of course you’d fine tune the parameters of the standard model of particle physics so your universe wouldn’t immediately turn entirely into neutrons, diprotons, or some other dead end. Then you’d sit back, turn up the volume on the MultIversePod, and watch it run. Sure ’nuff, after a while there’d be critters trying to figure it all out, scratching their balding heads, and wondering how it came to be that way. You would be most amused as they excluded your existence as a hypothesis, publishing theories ever more baroque to exclude the possibility of design. You might be tempted to….
Fortunately, this chronicle does not publish comments. If you’re sending them from the future, please use the antitelephone.
(The author discusses this “simulation argument” in endnote 191. He leaves it to the reader to judge its plausibility, as do I. I remain on the record as saying, “more likely than not”.)
Whatever you may think about the Big Issues raised here, if you’ve never experienced the beauty of thermodynamics and statistical mechanics at a visceral level, this is the book to read. I’ll bet many engineers who have been completely comfortable with computations in “thermogoddamics” for decades finally discover they “get it” after reading this equation-free treatment aimed at a popular audience.
Carroll, Sean. From Eternity to Here. New York: Dutton, 2010. ISBN 978-93-5111-694-3.
Here is a talk by the author at Google on “The Origin of the Universe and the Arrow of Time”, the central topic of this book.
Here is an hour long interview (with terrible video) with the author about the book and the nature of time in physics.