A Universe Out of Chaos

By Sean Carroll | August 3, 2011 8:55 am

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. Johnson

Despite 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 <a href="http://blogs.discovermagazine.com/cosmicvariance/2010/03/16/from-eternity-to-book-club-chapter-ten/" 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.

CATEGORIZED UNDER: arxiv, Science, Time, Top Posts
  • Mike

    Sean,

    In the second to last paragraph on page three the first sentence reads “[t]his story seem surprising not because the net result is unlikely, but because it consists of such a large number of individually unlikely events.”

    I think the third word should be “seems”.

    How’s that for a deep, thoughtful comment on the substance of the paper? ;)

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Oh no! This changes everything!

    Thanks for the catch.

  • Mike

    No problem at all. When the revision is posted, as now it must be, I expect to be listed in the acknowledgments ;)

  • http://calamitiesofnature.com Tony

    Sean,

    During the very long time needed to wait for an ice cube to “unmelt” won’t there be many instances where the ice cube starts to unmelt but the unmelting doesn’t go to completion?

    Similarly, if our Universe was formed in a random fluctuation like you describe, wouldn’t it be more likely that the Universe only proceeded partially toward a big crunch rather all the way to a big crunch?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Tony, yes, that is exactly right. Which is why the idea that the universe is a fluctuation is very hard to make work — it’s very difficult to see why it would be such a big fluctuation.

    This intuitive notion becomes a little tricky when gravity and curved spacetime are involved; the prospect of inflation in the early universe confuses things a bit. One of our motivations was to un-confuse things as much as we can. And our tentative conclusion is that inflation doesn’t really help in this particular case.

  • Anthony A.

    Tony: yes to both. In fact this is, in essence, the major reason why a fluctuation is not a viable explanation for the universe we see.

  • Sean Nicholson

    Well Sean. I’ve come to the conclusion that your a bit of a one trick pony.
    I’ve read your book from eternity twice. Your your obsession with statistical mechanics and the 2nd law of thermodynamics assumes too much. You make wild leaps from small humps my friend. Waiting forever doesn’t mean every possibility will happen. Entropy is an easy subject to get stuck in and confuse the listener when discussing the origins of the universe and analysing time. Sorry I just distrust your logic.
    Change the record or at least make a better job of your argument.
    Kind regards

  • george briggs

    i think instwad of fluctuations we had a transfer of matter from the preceeding universe. this matter was of E8 symmetry, see papers of lisi et al. this matter had very low entropy

  • http://j.mp/drb123p Dr. Dennis Bogdan

    Thanks For Your Comments – Seems Your Proposal Is That The Universe Did NOT Come From “Nothing” – But From “Something” (“Chaos” and/or “Fluctuations”) Instead – Is This Type Of “Somethingness” *Always* Present? – And Related Perhaps – Is True Absolute “Nothingness” *Always* NOT Present? – In Any Case – Thanks For Your Comments – And – Enjoy! :)

  • Ian Ward

    It actually might be a good idea to believe in a creator: that way we can leave it up to him/her to figure out how the universe they found themselves in, before they created this one, came to be ie. it puts off all the brain-wracking on them!

  • William

    Sean,

    There has been lots of thought and discussion about how the universe came about and what there was before the Big Bang, but I haven’t seen anything on how the “laws of physics” came about. They seem to be constant and unchanging. We just assume that they have always been so. I know we can see back in time to nearly the beginning (edge?) of the universe and the physical “constants” seem to be constant (taking into accout general relativity), but how do we know that the “laws of physics” remained the same through the Big Crunch?

    Just wondering.

  • Chris

    So if we go along with the idea that the big bang arose from a fluctuation, why do we think that fluctuation actually proceeded all the way to the big bang? Isn’t it more likely that the fluctuation “almost” got there, and then reversed? Or is that even less likely then going all the way to the big bang and proceeding from there? Am I even making sense?

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  • FmsRse12

    “we impose a future boundary condition — an unmelted ice cube — instead of a more conventional past boundary condition.”

    …doesn’t this mean that future is definetely an unmelted ice cube if this is also the boundary condition….my understanding is that regarding any theory of universe the only interesting parts are the boundary conditions at time zero and approaching infinity, what happens at those points to the universe…. so how can you derive a theory by just assuming certain boundary conditions when its the boundary conditions we are trying to understand in the first place….

  • David Santo Pietro

    I’ve always liked this idea, but what about Boltzmann Brains? If you are going to use the 2nd law to prove anything here you are going to have to use statistics. Don’t the statistics overwhelmingly say that I (as a conscious observer) should be a Boltzmann Brain?

  • Neal

    So … of all histories that include a low-probability bottleneck in the future, the highest probability history is one which gradually approaches that low-probability bottleneck? Reminds me very vaguely of “climbing Mt Improbable.”

  • BackAlleySUSY

    Hi Sean,

    I just have a question regarding this general idea of the universe from a high-entropy state. If the universe is the result of a stochastic fluctuation we would expect this to be the minimal fluctuation, as this is much more probable than anything else. Now we can use anthropic reasoning here to say that it is the minimal fluctuation to create scientist to observe it. However, judging by the vastness of the universe, this fluctuation is much more gratuitous (this is of course the “Boltzmann’s brain paradox”). Does modern cosmology have anything to say about this improbable state of the universe? In other words, is there any reason at all to believe that the universe is a minimal fluctuation?

  • george briggs

    concerning #11: the laws of physics have only one chance to change: at each big bang, and E8 symmetry is involved in setting the rules for the next universe. in this way we can have an evolving
    universe with anthropic characteriistics, which has long been a mystery.

  • Cutter McCool

    “the idea that the universe is a fluctuation is very hard to make work — it’s very difficult to see why it would be such a big fluctuation.”–Sean

    @Sean. Not to get all William-Blakean, but if we’re inside that fluctuation then isn’t that fluctuation only “big” from our perspective? While outside it, within the mother universe that our daughter universe fluctuated from, that fluctuation might be less than a nanoparticle grain of sand?

  • http://skepticsplay.blogspot.com miller

    I was imagining a world in which there are fossils, but the fossils are of creatures that clearly couldn’t have evolved by natural selection. Such a world would be unlikely to come about from a big bang initial state, and would therefore be unlikely to evolve into a big bang state. But then, everything is unlikely to evolve into a big bang state because it’s such low entropy. If we’re already positing a path from chaos to our universe, is it really so unlikely that the path will happen to include fossils of non-evolved animals?

    If I understand your description of the paper, the answer is, “Yes, it is much more unlikely.” Do I understand correctly?

  • Neal

    Been mulling this. You’re arguing that the probability of some history leading up to the Big Bang, conditional upon there being a Big Bang, is maximized when that history looks like a time-reversed Big Bang. Right?

  • george briggs

    i’m saying we may have had millions of big bangs, recycling the same immortal matter over and over again, recycling it thru an E8 symmetry entity each time. the laws of phyics can change only while the E8 symmetry is controlling things. in this way the physical laws could gradually change over time (evolve), resulting in the anthropic universe we observe.

  • Trevor

    So if our current Universe is one of those fluctuations going backward to the Big Bang (but of course we perceive time the other way) AND it is much more likely to not make it all the way back to the Big Bang (a larger fluctuation), doesn’t that mean the creationists might be right?! The Universe was much more likely “created” Just So in order to fool us; it really “started” (ends) at some point well “after” the Big Bang.

  • Cosmonut

    Regarding Hawking’s idea – I fail to understand how the “laws of physics” could “allow” the universe to come into existence from nothing.

    The laws of physics are not transcendent entities – they are just the properties of the various constituents of the universe.

    But nothing would imply no universe and hence no “laws of physics” to allow anything.

  • Dave

    Can a Boltzmann brain be conscious? Who observes the states of the Boltzmann brain? Who observes the observer of the states of the Boltzmann brain?

  • George

    Is there a transcendent timeless reality out there from which our universe emerged? Could this explain the existence of our universe? What can we discover about this transcendent reality? Do we have direct experience of this transcendent reality?

  • Nick

    In Tegmark’s Ultimate Ensemble of all possible mathematical structures, what is the spotlight in the darkness shining upon a particular mathematical structure actualizing it in the sea of potential mathematical structures? If all which can exists exist, why are we not all?

  • http://www.jonstraveladventures.blogspot.com Jonathan

    “Along the way people will un-die, grow younger, and be un-born”

    and along this path which way will their memories point? To what is (from our perspective) going to happen (this seems somewhat acausal – memories created before the event occurs), or the other way around, in which case they remember their ‘old’ years and look forward to their ‘young’ years – all seems pretty strange to me. If it’s the former then we could just as well be in the devolving universe state, but wouldn’t know because all we remember is what is to come, which we think is our past.

    If indeed we are in the devolving universe state and heading in the direction of what we think of as the big bang, then there would be a very large chance that this fluctuation will stop pretty soon and we’ll start going back in the ‘normal’ direction – it seems that in this scenario you never actually need to reach the big bang: The ice cube can half freeze, and then start melting again.

    If this is the case, then the big bang need never have happened, but we could just have appeared to have come from it.

    My thought is that the fault in the argument is that the progress towards a lower entropy state should take us through the state with complex structures we see around us…ie. the egg coming back together etc. Surely there are simpler paths to a low entropy state than civilisation undoing itself in perfect unison (though this may be precisely what the US administration is attempting ;-).

  • BrianC

    Following up on Jonathan’s comment, and Sean’s statement that artists will ‘painstakingly remove paint from their canvases’ in this scenario:

    It seems to me that these hypothetical artists will believe that they are actually applying paint to their canvases, not removing it. The reason is that their neurons etc. are simply following a time-reversal of what we consider ‘normal’, and thus their consciousness at any instant in time is identical whether cosmological entropy is increasing or decreasing. They will not remember the ‘past’, but only their ‘future’.

    Extrapolating this a bit, it seems like this reasoning implies that observers have *no way* of judging whether the universal ice cube is in the process of melting or freezing. Therefore this theory must be necessarily untestable by conscious beings, and thus it is truly a philosophical rather than a physical effort at understanding the world.

  • mtravers

    As an alternative to Quantum Theory there is a new theory that describes and explains the mysteries of physical reality. While not disrespecting the value of Quantum Mechanics as a tool to explain the role of quanta in our universe. This theory states that there is also a classical explanation for the paradoxes such as EPR and the Wave-Particle Duality. The Theory is called the Theory of Super Relativity and is located at Super Relativity Website. This theory is a philosophical attempt to reconnect the physical universe to realism and deterministic concepts. It explains the mysterious.

  • Ian Ward

    If the universe is cyclical and each cycle is larger than the previous cycle, then moving towards the low entropy of a big crunch is also moving towards the higher entropy of the next cycle.

  • Neal

    Ian, I don’t think that follows. Of all possible histories, any which go through a big crunch are lower entropy than any which increase entropy indefinitely. The universe will tend to shy away from low-entropy states (by the definition of low entropy), so any history which goes through a big crunch is less probable than a history which does not.

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  • Jasper

    I understand the reasoning, but why are you making the point that the universe should always be the same. If i just displace or remove some particles it still kind of looks like our universe. even statistical physics tells us that you should be looking at ensembles of universes. Maybe the amount of our-universe-like universes is just quite large.

  • http://rowingpresents.com Tyler

    Looked at from the perspective of a closed system, if we leave an ice cube (low-entropy) in a glass of water at room temperature, in a few minutes it will melt (high-entropy) and cool the water inside. If we then remove a few milliliters of water from the glass (high-entropy) and freeze it back into an ice cube (low-entropy), we have successfully reversed the second law of thermodynamics within the system and can begin the process again. (Also note: freezing is equivalent to ‘unmelting,’ and less of an awkward term). If the above accurately describes a ‘small-scale’ closed system, then it only makes sense that a ‘large-scale’ closed system, such as the universe, works the same way.

    To me, the only issue arises with the concepts of equilibrium, and closed or open system. For example, if two systems are in thermal equilibrium, then their temperatures are the same. Thus if the definition of an open system is that matter may flow in and out of the system boundaries, then when two systems are in thermal equilibrium, it must also be equivalent to say that this equilibrated system is no longer open, but closed because there is no system boundary between them.

    The universe is equivalent to an ice cube melting in a glass of room temperature water, or a lake freezing over in winter and then thawing again in spring; the universe must be a self-regulating process of continual melting and freezing.

    Sean, I look forward to your comments if you have any.

  • http://www.jonstraveladventures.blogspot.com Jonathan

    Tyler, the problem with your argument is that in the re-freezing you are not considering the thing that you are using to re-freeze the water. If you include this then the entropy will increase as you put in energy to freeze the water – your machine will use fuel, will heat up, etc. If you don’t include this, then you are not dealing with a closed system.

  • Bill Davis

    Sean (or anyone!) – I’m reading ‘From Eternity to Here’ at the moment and I’ve been niggled by something since Chapter 10. This post has increased my niggle. The post (and some comments) seem to hint at what I’m thinking, but I haven’t seen it stated explicitly (I’m not a physicist, so more than likely I’m missing something). So: if the arrow of time is determined by the second law (and specifically the fact that memory is a coherent concept only under the assumption of a lower entropy past) then how does it make sense to talk about a fluctuation from maximum entropy at all? You cannot describe a fluctuation without a dimension of time (as in the horizontal axis of figure 54 in the book), but the initial part of the fluctuation involves entropy decreasing in the forward direction of time, which can’t happen by definition. In this context does it make any sense to ask how long you need to wait for a maximum entropy universe to experience a fluctuation of the magnitude that would lead to what we observe? Surely in a uniformly high entropy universe there is no such thing as time?

  • Ian Ward

    Reply to (32): Neal: When a star collapses before going supernova, the total entropy of the star system doesn’t decrease. Maybe big crunches are similar to stellar collapses in that space doesn’t collapse and the entropy of the universe doesn’t actually decrease when moving through them.

  • ian

    Interesting, and in some ways similar both to Nietzsche’s eternal recurrence and Asimov’s last question (just to pick two). Of course, those didn’t make it to arxiv.

  • http://vacua.blogspot.com Jim Harrison

    If a universe really were to revert to its initial state via the same stages by which it got to its endpoint, the conscious animals in that universe would not experience themselves living backwards. They would still remember the future, not the past, assuming, of course, that mental states are absolutely determined by physical ones. So how exactly do you propose to distinguish the road up and the road down in your story? Maybe things are running backwards right now.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    As people have noted (and I’ve said many times myself, although not in this post), the “backwards-living” people in the universe we describe wouldn’t think they were living backwards at all. We always remember the direction in which entropy was lower, so their evolution is internally indistinguishable from an ordinary Big Bang.

    The only difference, therefore, is external. We are talking about processes that happen in a universe that lasts forever. Inside that universe, there will inevitably be universe-creating fluctuations like this (as well as an enormously larger number of smaller fluctuations), and then these fluctuations will decay back to equilibrium. It only makes sense to say that the arrow of time is “backwards” in any one region when we’re comparing it to other regions.

    However, the fact that there are many much smaller fluctuations tends to imply that this is not the right story of the universe. (If it were, we would probably live in a much smaller fluctuation.) So either the universe is not eternal, or something else, as we briefly touch on in the paper.

  • Steve Smith

    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.

    These ideas are receiving a lot more attention in the popular media and press, and I think that a few pointers to the technical ideas that motivate them are necessary. So here’s some scientific background and links on universe ex nihilo theories, a background that isn’t presented widely enough, even at scienceblogs that address the subject specifically.

    Guth’s Inflationary Universe is a must-read, in which Guth explains ex nihilo theories with the colorful statement:

    The question of the origin of the matter in the universe is no longer thought to be beyond the range of science—everything can be created from nothing … it is fair to say that the universe is the ultimate free lunch.

    Guth provides technical reasons for this claim:

    Now we can return to a key question: How is there any hope that the creation of the universe might be described by physical laws consistent with energy conservations? Answer: the energy stored in the gravitational field is represented by a negative number! … The immense energy that we observe in the form of matter can be canceled by a negative contribution of equal magnitude, coming from the gravitational field. There is no limit to the magnitude of energy energy in the gravitational field, and hence no limit to the amount of matter/energy it can cancel. For the reader interested in learning why the energy of a gravitational field is negative, the argument is presented in Appendix A.

    Guth goes on to explain a simple argument for all this that if you grasp, you will understand a fact of gravity that evaded Newton. Unfortunately, Google books doesn’t have Appendix A online.

    Guth’s technical explanation above is what is meant by the nontechnical, poetic description, like Hawking’s: “Because there is a law like gravity, the universe can and will create itself from nothing.”

    Here are some pointers to a quick technical explanation of the creation of a universe from literally nothing subject to the laws of quantum mechanics.

    A technical account of the universe ex nihilo, following Vilenkin, “Creation of universes from nothing”. Physics Letters B Volume 117, Issues 1-2, 4 November 1982, Pages 25–28. Available here.

    1. Observe the Friedmann–Lemaître–Robertson–Walker metric for universal expansion:

    ds² = dt² – a(t)|dx

    This is the space-time geometry with the spatial scale term a(t) describing the growth/contraction of the universe. This is Vilenkin’s equation (2).

    2. Solve the evolution equation:

    a(t) = (1/H)cosh(Ht)

    where H² = (8π/3)Gρ is the Hubble parameter.

    This is Vilenkin’s equation (3). So far, there is no explanation of a universe from nothing because the de Sitter space isn’t nothing, as everyone agrees.

    3. Observe that at t = 0, the physics has the same form as a potential barrier, for which it is known that quantum tunneling is possible. The description of quantum tunneling involves a transformation tit, with i² = –1.

    Now the evolution equation is

    a(t) = (1/H)cos(Ht) [the cosine “cos”, not the hyperbolic cosine “cosh”]

    valid for |t| < π/2/H. This is Vilenkin’s equation (5). Space-Time is simply the 4-sphere, a compact, i.e, bounded space. At the scale a(t) = 0, this space is literally nothing. No space-time, no energy, no particles. Nothing. The interpretation of (5) is quantum tunneling from literally nothing to de Sitter space, the universe as we know it. See Figure 1a in Vilenkin’s paper for a depiction of the creation of the universe from nothing using this explanation.

    Vilenkin says in the paper, “A cosmological model is proposed in which the universe is created by quantum tunneling from literally nothing into a de Sitter space. After the tunneling, the model evolves along the lines of the inflationary scenario. This model does not have a big-bang singularity and does not require any initial or boundary conditions. … In this paper I would like to suggest a new cosmological scenario in which the universe is spontaneously created from literally nothing, and which is free from the difficulties I mentioned in the preceding paragraph. This scenario does not require any changes in the fundamental equations of physics; it only gives a new interpretation to a well-known cosmological solution. … The concept of the universe being created from nothing is a crazy one. To help the reader make peace with this concept, I would like to give an example of a compact instanton in a more familiar setting. …”

    This is what physicists mean by “nothing”. Nonexistent space-time, subject to the laws of quantum mechanics.

    Guth provides a nontechnical explanation:

    Alexander Vilenkin … suggested that the universe was created by quantum processes starting from “literally nothing,” meaning not only the absence of matter, but the absence of space and time as well. This concept of absolute nothingness is hard to understand, because we are accustomed to thinking of space as an immutable background which could not possibly be removed. Just as a fish could not imagine the absence of water, we cannot imagine a situation devoid of space and time. At the risk of trying to illuminate the abstruse with the obscure, I mention that one way to understand absolute nothingness is to imagine a closed universe, which has a finite volume, and then imagine decreasing the volume to zero. In any case, whether one can visualize it or not, Vilenkin showed that the concept of absolute nothingness is at least mathematically well-defined, and can be used as a starting point for theories of creation.

  • http://www.loujost.com Lou Jost

    I have a problem with the often-repeated idea that if the universe lasts an infinite amount of time, every possible state will happen. Doesn’t this assume the cardinality of the set of all possible states is the same as the cardinality of time?

  • http://www.loujost.com Lou Jost

    “The point is that we have infinitely long to wait — eventually the thing we’re waiting for will come to pass.”

    Even if the cardinalities of the set of all possible times and the set of all possible states were the same, it is still not clear to me that, given an infinite amount of time, every state will occur. Consider a hotel with an infinite number of rooms. (Mathematicians spend an inordinal amount of time in this hotel when they think about infinity.) Suppose it has an infinitely long stream of customers. The receptionist can choose to give every new guest an odd-numbered room. Even though there are in infinite number of guests, the hotel will never need to use the even-numbered rooms, as the hotel will never fill up. (I think this example is given in a book called “Is God a mathematician” by Mario Livio.) If the rooms represent states, this suggests that not all states need to be filled, even given an infinite amount of time.

  • Julien

    Sean, I don’t get why we should consider “backwards-living” peoples in the first place. This would implicate a “backward natural selection”, despite this makes very little difference in the total entropy. Am I wrong to think that a sterile universe would be far more likely for the backward direction?

  • Trevor

    @Lou,

    Usually people talk about the idea that in an infinite Universe (in space and time), anything that can happen with non-zero probability will happen. Some things have zero probability of occurring, and those “states” will not happen. So if there is a law of nature that says no occupation of even-numbered rooms, then indeed, they will not be occupied.

    So for example, even if the Universe is infinite, we don’t expect there to be some part of it where, e.g., like electric charges attract.

    But since there is some non-zero probability of you existing and posting a comment here, and there likely is a non-zero probability of you having done the same thing except with one more sentence, it is quite plausible that in an infinite Universe, that alter-Lou exists.

  • http://www.loujost.com Lou Jost

    But Trevor, ANY particular state has a probability of zero, if states have a one-to-one correspondence with the points on a number line. And again, if the state space has higher cardinality than the time dimension, it is actually impossible that all states will be reached, even given an infinite amount of time.

  • http://www.loujost.com Lou Jost

    And Trevor, if you do not accept that the probability is zero of any particular state, I can use your reasoning to show that the hotel example works even if the receptionist does not enforce any rule about room numbers. If the rooms are filled at random and there is no rule about what room a guest receives, you would say that there is a non-zero probability that the first room is not taken (since this is not prohibited by any law in this new example). There are an infinite number of arrangements of guests in which the first room is not taken. Therefore you cannot argue that all rooms must be taken (or all states must occur) just because there are an infinite number of guests (or an infinite amount of time in the universe). I think Sean’s statement that “eventually, the thing we’re waiting for will come to pass” is not true.

  • Neal

    @Lou:

    “Mathematicians spend an inordinal amount of time in this hotel when they think about infinity.”

    I see what you did there.

  • http://www.rohanmedia.co.uk Rohan

    Sweet. Every girl that ever dumped me is inevitably going to desperately claw her way to get me back. Can’t wait! :D

  • http://www.loujost.com Lou Jost

    Neal, I am impressed. I didn’t expect anybody would notice….it was just my very lame attempt at mathematical humor….

  • http://www.loujost.com Lou Jost

    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.

  • http://j.mp/drb123p Dr. Dennis Bogdan

    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! :)

  • JimV

    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.

  • http://www.loujost.com Lou Jost

    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.

  • gnome

    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.

  • http://j.mp/drb123p Dr. Dennis Bogdan

    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! :)

  • greg

    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.

  • gnome

    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.

  • http://j.mp/drb123p Dr. Dennis Bogdan

    @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! :)

  • Fireworks Below 1TeV

    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?

  • Fireworks Below 1TeV

    Speaking of confusion, why is Lou Jost so confused about infinity?

  • http://www.loujost.com Lou Jost

    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.

  • Lili Mendoza

    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.

  • http://autodynamicslborg.blogspot.com/ Lucy Haye

    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

  • Fireworks Below iTeV

    @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?

  • http://www.loujost.com Lou Jost

    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.

  • http://www.loujost.com Lou Jost

    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.

  • Dan

    @ 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

  • Fireworks Below 1TeV

    @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.

  • http://www.loujost.com Lou Jost

    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.

  • http://skepticsplay.blogspot.com miller

    @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.

  • http://www.loujost.com Lou Jost

    @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.

  • http://skepticsplay.blogspot.com miller

    @Lou
    Yes, I have a different interpretation of the same statement. *shrugs*

  • http://www.loujost.com Lou Jost

    @Miller, how did you interpret the statement about the ice cube reforming if we wait long enough?

  • mikeL

    There is no infinite amount of time for the ice cube to eventually reform. Protons decay and the O and H will decompose in a finite amount of time.
    @Lou, there must be an infinite number of paths that do not ever cover all points in an unbounded state space?
    The question of retracing backwards through time, or time reversal/entropy decreasing and passing through everything, including ourselves, eggs uncooking, broken glass reforming, ice cubes refreezing, etc., is not even worth considering. The probability of any one possible path reversing all events approaches zero as the number of possible paths approaches infinity(!?); the statistical likelyhood is an infinitely regressing series whose limiting factor is zero, or one over infinity for any one path. And as Lou stated(and I agree), even an infinite number of scenarios may not, almost certainly will not, follow the path of time/entropy reversal, which still doesn’t even consider the infinite number of reversals possible, of which just one would obtain where the ‘movie’ of existence is played backwards.

    In any event(lol), I want to add that the universe, or even the possibility of the universe, arising out of ‘nothing’, is itself impossible as ‘nothing’ means the lack of everything – including possibilities.
    I’m not sure that a state of nothingness is even theoretically possible as there is no such thing as time(or the possibility of it) for the state of nothingness to ‘exist’.
    Now, ‘nothing’ can only exist instantaneously, ie. for zero time. There is no causal relationship possible without time. There is no such place as ‘the beginning’ to extrapolate backwards to, nor ‘the end,’ with zero entropy, to extrapolate forwards to.
    The universe is inevitably proceeding to a state of equilibrium, maximum entropy, chaos. We intuitively know that when things get too chaotic, that is when all hell breaks loose. There is confusion, upset, noise, and then, Bang! The universe just doesn’t know when to quit, does it?

  • Sam flynn

    Scientists……this theory proves you right and wrong at the same time:

    http://www.godlikeproductions.com/forum1/message1616159/pg1

    Trust me…..you read that….you humans will understand….

    :)

  • Sam flynn

    Human history will be changed by that document, if people read it.

  • Sam flynn

    It basically unites hawkings variance theory…..with Chris langans ctmu theory….

    Chaos and entropy leads to order…and ordercor rule based systems are unstable. By design so they evolve Into higher order omplexity, or intelligence…

    Read that document guys…..You will never see the world the same again.

  • Sam flynn

    I would be interested in seeing what Dr. Hawking has to say about this. the tautological fractal reality.

    Your awreness is increasing by the day. Good progress.

  • Sam flynn

    Nonesense…there are no laws…with sufficient awareness…there are always tricks….you can implement as the programmer..,by “confusing” reality at the extremes.

  • Sam flynn

    You are neo human, fly.

  • Sam flynn

    Someone make hawking read this thread. He’s got to read it.

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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] cosmicvariance.com .

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