How did the universe come to be? We don’t know yet, of course, but we know enough about cosmology, gravitation, and quantum mechanics to put together models that standing a fighting chance of capturing some of the truth.
Stephen Hawking‘s favorite idea is that the universe came out of “nothing” — it arose (although that’s not really the right word) as a quantum fluctuation with literally no pre-existing state. No space, no time, no anything. But there’s another idea that’s at least as plausible: that the universe arose out of something, but that “something” was simply “chaos,” whatever that means in the context of quantum gravity. Space, time, and energy, yes; but no order, no particular arrangement.
It’s an old idea, going back at least to Lucretius, and contemplated by David Hume as well as by Ludwig Boltzmann. None of those guys, of course, knew very much of our modern understanding of cosmology, gravitation, and quantum mechanics. So what would the modern version look like?
That’s the question that Anthony Aguirre, Matt Johnson and I tackled in a paper that just appeared on arxiv. (Both of my collaborators have also been guest-bloggers here at CV.)
Out of equilibrium: understanding cosmological evolution to lower-entropy states
Anthony Aguirre, Sean M. Carroll, Matthew C. JohnsonDespite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.
It was Boltzmann who long ago realized that the Second Law, which says that the entropy of a closed system never decreases, isn’t quite an absolute “law.” It’s just a statement of overwhelming probability: there are so many more ways to be high-entropy (chaotic, disorderly) than to be low-entropy (arranged, orderly) that almost anything a system might do will move it toward higher entropy. But not absolutely anything; we can imagine very, very unlikely events in which entropy actually goes down.
In fact we can do better than just imagine: this has been observed in the lab. The likelihood that entropy will increase rather than decrease goes up as you consider larger and larger systems. So if you want to do an experiment that is likely to observe such a thing, you want to work with just a handful of particles, which is what experimenters succeeded in doing in 2002. But Boltzmann teaches us than any system, no matter how large, will eventually fluctuate into a lower-entropy state if we wait long enough. So what if we wait forever?
It’s possible that we can’t wait forever, of course; maybe the universe spends only a finite time in a lively condition like we see around us, before settling down to a truly stable equilibrium that never fluctuates. But as far as we currently know, it’s equally reasonable to imagine that it does last forever, and that it is always fluctuating. This is a long story, but a universe dominated by a positive cosmological constant (dark energy that never fades away) behaves a lot like a box of gas at a fixed temperature. Our universe seems to be headed in that direction; if it stays there, we will have fluctuations for all eternity.
Which means that empty space will eventually fluctuate into — well, anything at all, really. Including an entire universe.
This basic story has been known for some time. What Anthony and Matt and I have tried to add is a relatively detailed story of how such a fluctuation actually proceeds — what happens along the way from complete chaos (empty space with vacuum energy) to something organized like a universe. Our answer is simple: the most likely way to go from high-entropy chaos to low-entropy order is exactly like the usual way that systems evolve from low entropy to high-, just played backward in time.
Here is an excerpt from the paper:
The key argument we wish to explore in this paper can be illustrated by a simple example. Consider an ice cube in a glass of water. For thought-experiment purposes, imagine that the glass of water is absolutely isolated from the rest of the universe, lasts for an infinitely long time, and we ignore gravity. Conventional thermodynamics predicts that the ice cube will melt, and in a matter of several minutes we will have a somewhat colder glass of water. But if we wait long enough … statistical mechanics predicts that the ice cube will eventually re-form. If we were to see such a miraculous occurrence, the central claim of this paper is that the time evolution of the process of re-formation of the ice cube will, with high probability, be roughly equivalent to the time-reversal of the process by which it originally melted. (For a related popular-level discussion see From Eternity to Here, ch. 10.) The ice cube will not suddenly reappear, but will gradually emerge over a matter of minutes via unmelting. We would observe, therefore, a series of consecutive statistically unlikely events, rather than one instantaneous very unlikely event. The argument for this conclusion is based on conventional statistical mechanics, with the novel ingredient that we impose a future boundary condition — an unmelted ice cube — instead of a more conventional past boundary condition.
Let’s imagine that you want to wait long enough to see something like the Big Bang fluctuate randomly out of empty space. How will it actually transpire? It will not be a sudden WHAM! in which nothingness turns into the Big Bang. Rather, it will be just like the observed history of our universe — just played backward. A collection of long-wavelength photons will gradually come together; radiation will focus on certain locations in space to create white holes; those white holes will spit out gas and dust that will form into stars and planets; radiation will focus on the stars, which will break down heavy elements into lighter ones; eventually all the matter will disperse as it contracts and smooths out to create a giant Big Crunch. Along the way people will un-die, grow younger, and be un-born; omelets will convert into eggs; artists will painstakingly remove paint from their canvases onto brushes.
Now you might think: that’s really unlikely. And so it is! But that’s because fluctuating into the Big Bang is tremendously unlikely. What we argue in the paper is simply that, once you insist that you are going to examine histories of the universe that start with high-entropy empty space and end with a low-entropy Bang, the most likely way to get there is via an incredible sequence of individually unlikely events. Of course, for every one time this actually happens, there will be countless times that it almost happens, but not quite. The point is that we have infinitely long to wait — eventually the thing we’re waiting for will come to pass.
And so what?, you may very rightly ask. Well for one thing, modern cosmologists often imagine enormously long-lived universes, and events like this will be part of them, so they should be understood. More concretely, we are of course all interested in understanding why our actual universe really does have a low-entropy boundary condition at one end of time (the end we conventionally refer to as “the beginning”). There’s nothing in the laws of physics that distinguishes between the crazy story of the fluctuation into the Big Crunch and the perfectly ordinary story of evolving away from the Big Bang; one is the time-reverse of the other, and the fundamental laws of physics don’t pick out a direction of time. So we might wonder whether processes like these help explain the universe in which we actually live.
So far — not really. If anything, our work drives home (yet again!) how really unusual it is to get a universe that passes through such a low-entropy state. So that puzzle is still there. But if we’re ever going to solve it, it will behoove us to understand how entropy works as well as we can. Hopefully this paper is a step in that direction.
Neal, I am impressed. I didn’t expect anybody would notice….it was just my very lame attempt at mathematical humor….
Here is another way to see my point that not all states need to occur after an infinite amount of time. Suppose all possible states can be represented as points on a plane. There are an infinite number of such points. Now imagine an infinitely long path drawn on this plane, representing the succession of states actually occupied by our universe. This path can be infinitely long without going through most of the points on the plane. Indeed, it can even be infinitely long without crossing itself. So I do not see how the mere fact of infinite time obliges the universe to occupy all possible states, or to repeat previous states. This appears to be an abuse of the concept of infinity.
Hawking: “Because there is a law like gravity, the universe can and will create itself from nothing.”
Smith: “…explanation of the creation of a universe from literally nothing subject to the
laws of quantum mechanics.”
Smith: “This is what physicists mean by “nothing”. Nonexistent space-time, subject to the
laws of quantum mechanics.”
Yes, But Are These Wordings *Really* Describing “Absolute Nothingness” As Noted (or
implied?) – Or Something *Less* (or more?) Than “Absolute Nothingness” – After All,
Conditions Are Noted (“law of gravity,” “laws of quantum mechanics,” and the like) As,
Perhaps, Pre-Existing(?) When Discussing “Absolute Nothingness” – Wouldn’t “Absolute
Nothingness” Be Entirely Un-Conditional, And Without Such Pre-Existing (original/initial/a
priori?) Conditions Also? – If Not, Aren’t Such Noted Conditions “Something”? – And Maybe,
Require An Explanation Of Their Beginnings From True “Absolute Nothingness” As Well?
In Any Case – Enjoy! 🙂
I think whether Mr. Jost is correct or not depends on the definition of possible events, and how the number of them changes over time. I think of an event which has non-zero probability as one which has a finite probability of occurring in a finite amount of time. Under that definition, it seems to me at first that all non-zero-probability events would have to occur within infinite time. This may be a naive way of defining probabilities, however. At any time in this universe, (as far as I know) there are a finite number of particles and a finite amount of energy, which can only exist in a finite number of quantum states, so there is not an infinite set of events – yet. But maybe the number of different “possible” events is growing faster than the amount of time is increasing, so the probability of a specific event is decreasing with time.
JimV, if space and time are continuous variables, then the set of all possible position states is uncountably infinite and has the cardinality of the set of real numbers. This implies any particular state has measure 0, and hence zero probability.
Certainly you are right that any physical constraints that make the set of states finite will change the argument.
This is easy to solve. Nothing is unstable. Since its ‘nothing’ there is nothing to confine what can and will arise from it. Anything can come out of nothing. So this nothingness quantumagically fluctuated and God came out of it and then decided to create the Universe as we see it.
This is easy to solve. Nothing is unstable. Since its ‘nothing’ there is nothing to confine what can and will arise from it. Anything can come out of nothing. So this nothingness quantumagically fluctuated and God came out of it and then decided to create the Universe as we see it.
@gnome – Thanks For Your Comments – *Really* Enjoyed Your “quantumagical fluctuated” Phrasing – Nonetheless, Even Positing “Nothing is unstable” May Be Setting A Condition (or property of sorts?) And Perhaps, May Need Some Explaining? – Seems That Descriptions Of “Nothing,” Even Those Noted Earlier In This Blog-Thread (by Smith/Guth/Vilenkin) As “Absolute Nothingness,” Actually Contains “Something” (noted or implied) (ie, “law of gravity,” “laws of quantum mechanics,” “quantum gravity,” “fluctuations,” “chaos,” “low/high entropy,” etc) Instead – The “Spontaneous Creation” Of “Something” From “Nothing” To, In Hawking’s Poetic Phrasing, “light the blue touch paper and set The universe going” Seems To Be Getting A Bit “curiouser and curiouser”? – In Any Case – Thanks Again – And – Enjoy! 🙂
I like these ideas. That was really nice to read the whole paper, get it, and learn so much… sections III and IV are very beautiful. Love the math.
Hi Dennis,
I was being tongue-in-cheek and using terminology I’ve heard before loosely, I wasn’t being literally serious. A “true” nothing would really be devoid of all properties and that is why no limits can be set on what could/would emerge from it, if anything. Part of the problem is that it’s difficult to talk about nothing without assigning some properties to it.
The main reason for my very tongue-in-cheek statement above was to call attention to how speculative and esoteric some cosmologists have become. I was just joining in the speculation game. Anyhow, I think in these cases we’re reaching well beyond good empirical science. And scientists look down on metaphysics.
@gnome – Thanks For Your Latest Comments – I *Entirely* Agree With Your Thinking – Also, I Was Well Aware, And *Thoroughly Enjoyed*, Your Earlier Tongue-In-Cheek Statements But, Nonetheless, Took The Occasion To Try And Add A Bit More To The Main Discussion – Seems We’re *Very* Similar In Our Viewpoints – Thanks Again For Your Comments – And – Enjoy! 🙂
Sean is utterly confused about entropy and thermodynamics and time. His confusion seems to be the origin of all these papers, rather than there being a real physical issue to solve.
If the universe is in a pure state, and the laws are unitary, then BY DEFINITION the universe BEGAN in a state of ZERO ENTROPY. That is the thermodynamic definition of the BEGINNING. Sean thinks that the universe should have begun with lots of entropy. But that is nonsense. If the universe was born with high entropy, it would have been born in a highly mixed state, which contradicts the assumption (that most people agree with) that the universe is in a pure state. Instead the entropy at the beginning was of course zero. And its entropy grew over time as we lost track of the details of the micro-state of the universe. That is how entropy works. Sean is utterly confused to think that the universe should have began with high entropy – thats thermodynamically a contradiction in terms.
By the way, if one imposes an (unphysical) future low entropy boundary condition, as Sean has done in this paper, then I think everyone would agree that the evolution from high to low would be the time reversed version of low to high – how is this a new result? I thought this is obvious. Am I missing the novelty here?
Speaking of confusion, why is Lou Jost so confused about infinity?
Hi Fireworks,
I don’t know, why don’t you tell me? My point was that an infinitely long path does not have to cross every point in an infinite multi-dimensional state space. That seems obvious, and it is easy to give simple examples of curves that are infinitely long and yet do not cover an unbounded plane.
Just watched Hawkin’s Discovery special. Please bear in mind, I’m not a scientist. But the Hawkin’s explanation leaves out “the spark” (order) element. What triggered the Bang? Whatever it was, it’s occurrence might have been in/with time. Not before. Therefore, I think a conception of chaos previous to the bang is more consistent with the behavior of the universe as we know it. So yes, Dr. Carroll, I look forward to your posts on the subject. You have a fan rooting for you in Panama. Central America.
The Carezani’s Cosmology elevating the Mass Decay-Energy absorption to a Universal Law prove that the Thermodynamics seconf law is incorrect. As consequence the Universe’s Entropy is constant because energy absorption is creating low entropy. See the whole blog at: http://autodynamicslborh.blogspot.com/
Lucy Haye Ph. D.
SAA’s representative.
lucyhaye22@gmail.com
@Lou Jost 63.
in any useful statement about a continuous phase, one must coarse grain. This leads to a countable set of allowed states. If the probability for each is non-zero (e.g., they are all equally likely), then each allowed state will occur if one waits long enough. So what are you so confused about?
Fireworks, look at my Comment 55. I was very clear that if you add physical assumptions such as your “coarse-grain” assumption, the argument changes. My point was a mathematical one about infinity, and you said I was confused about that. I stand by my point that an infinitely long path through an unbounded state space does not have to pass through every point in the space.
I think that coarse-graining also does not escape my point. If the state space (which has many dimensions) is unbounded, even if it is coarse-grained, most infinitely-long paths will not cover every grain.
Even in a bounded, finite universe, the allowed wavelengths of a particle are (countably) infinite. The energy states of bound particles are also countably infinite. Therefore even with reasonable physical conditions, an infinitely long path through state space will not hit every point in that space. So even with realistic physical conditions, Sean’s statement that “eventually, the thing we’re waiting for will come to pass” is not true.
@ 37 Bill Davis
Your thoughts are mine – but no one answered. Your clarity is admirable, and you stated better than I could have. Salute. –Dan
@Lou Jost 68.
apparently you don’t understand bound states or free particles. There are 2 kinds of states: (1) those whose energy spectrum goes up to infinity, such as the harmonic oscillator or free particles, and (2) those whose energy spectrum approaches a finite fixed point, such as the hydrogen atom. In both cases the number of states naively appears infinite, but under realistic physical conditions, it is finite.
In (1), a realistic physical condition is that the universe only has a finite amount of energy, so there is a maximum energy that individual states can carry. This truncates the available states to a finite set. This is true for bound states or free particles. And even if you allow arbitrary energy to the whole universe, individual particles cannot meaningfully have energies greater than the Planck scale; such sub-Planckian wavelengths cannot be resolved.
In (2), a realistic physical condition is that we cannot discern the difference between the asymptotically high orbital states, which all have asymptotically similar energies. So the asymptotically high orbital states are all grouped into one common state (that we might call “loosely bound”). This is the effect of coarse graining.
An all encompassing way of saying this, is that the known finiteness of the entropy of the universe, restricts the number of effectively dissimilar states to a finite set. This appears to disprove your point.
I am not sure….given that the temporal evolution of the universe is chaotic (tiny variations in conditions can lead to macroscopically different trajectories), coarse graining may not be appropriate. Even if the energy of the universe is finite, any of the infinite number of higher-energy states could be occupied for very short periods of time. So it appears to me that there are still a countably infinite number of states available, and that coarse-graining is inappropriate in a chaotic universe. Which means the universe will never repeat itself.
@Lou Jost and interlocutors,
Mathematically speaking, it is perfectly possible to have an infinite path that does not hit every point. The path just needs to go in a loop that does not pass through every state. If there are an infinite number of states, we could also have a non-repeating path that does not hit every point, just as the sequence of odd numbers is infinite, non-repeating, and fails to hit every natural number. I am not convinced that coarse-graining leads to a finite set of states (it depends on how the coarse-graining is done), but it doesn’t even matter here.
But neither is it clear to me that Sean was making a claim that the trajectory of the universe must go through every state. I think it is simply highly probable that the any given state of the universe will eventually reach at least one low entropy state.
@miller, the reason I interpreted Sean that way was because of this statement: “The point is that we have infinitely long to wait — eventually the thing we’re waiting for will come to pass.” Or again, “But if we wait long enough … statistical mechanics predicts that the ice cube will eventually re-form.” I do not think this really follows from the properties of infinity, if state space is unbounded or if it is continuous in some dimensions, and if the universe is chaotic so that we cannot do coarse-graining.
@Lou
Yes, I have a different interpretation of the same statement. *shrugs*
@Miller, how did you interpret the statement about the ice cube reforming if we wait long enough?