by Katie Mack
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There are some caveats.
And to be clear, these are not caveats of the “well, technically there’s this small detail” sort, but caveats of the “OMG this changes everything” sort.
This time, the weirdness comes down to a part of physics called statistical mechanics. This is what we use when we need to talk about something like temperature, which is really just the amount of motion in a system of particles, without painstakingly describing the path of each and every particle individually. Statistical mechanics is where the Second Law really shines, since it lets you describe a big complicated system in terms of one important property: its entropy. But it also introduces a kind of “out.” That point about how it’s an inescapable law of the universe that the entropy always increases? That technically only applies on average over sufficiently large scales. On the quantum scale, or even on large scales if you wait long enough, unpredictable fluctuations will, from time to time, spontaneously shift some part of the system into a lower-entropy state at random. The larger the system, the less likely it is that fluctuations could do much of anything at all, but in a universe that is in an eternal expansion and contains only a cosmological constant, there’s a lot of time and space for waiting around, and even extremely low-probability events happen. It’s unlikely that a whale and a bowl of petunias could suddenly pop into existence in completely empty space, but, in principle, if you wait long enough, it could happen.
This might come in handy. If anything can spontaneously pop into existence after the Heat Death, why not another universe?
The idea isn’t as far-fetched as it sounds. There’s a principle of statistical mechanics that says that any arrangement a system of particles finds itself in can happen again, if you wait long enough. Let’s say you have a box filled with a gas of randomly moving molecules, and you take a snapshot of them at one moment and mark down what positions they’re in. If you watch the box for a very long time, eventually you’ll find the molecules in those positions again. The less likely the configuration, the longer it’ll take, so a very rare event like all the particles huddling up in the lower right-hand corner of the box will take a lot longer to appear again, but in principle, it’s just a matter of time. This is called Poincaré recurrence. If you have an infinite amount of time to work with, any state the system can be in is a state it WILL be in again, an infinite number of times, with a recurrence time determined by how rare or special that configuration is. In one rather arresting example, physicists Anthony Aguirre, Sean Carroll, and Matthew Johnson once calculated that if you were willing to wait something like a trillion trillion times the age of the universe, you could watch an entire piano spontaneously assemble itself in a seemingly empty box.
A post–Heat Death universe is, essentially, a very large, very slightly warmed box, with statistical mechanics stepping in to provide the random fluctuations. If the Big Bang is a state the universe has been in once, and the post–Heat Death universe is eternal (so eternal that, having lost the arrow of time, past and future are meaningless), there’s no reason a Big Bang can’t fluctuate out of the vacuum to start the universe anew.
Hold on, though. It gets even weirder. And more personal.
If every state the universe has ever been in could be revisited through random fluctuations, that means this moment right now could happen again, exactly the same in every detail. Not only could it happen again, it could happen again infinitely many times.
This possibility is of particular interest to cosmologist Andreas Albrecht, who has written about what he calls the de Sitter Equilibrium state. The basic idea of this equilibrium version of de Sitter space is that the origin of our universe and everything that happens in it can be thought of as the result of random fluctuations out of an eternally expanding universe containing only a cosmological constant. From time to time, a universe fluctuates out of the heat bath into a very low entropy starting state, and then evolves forward (with increasing entropy) until it gets to its own Heat Death, decaying back into the background de Sitter universe. And from time to time, the fluctuation doesn’t produce a Big Bang, it just re-creates last Tuesday—specifically, that moment when you stubbed your toe on the kitchen table and spilled an entire cup of coffee on the floor. That moment. And every other moment of your life. And everyone else’s.
If this sounds like a vaguely familiar image of dystopia, it’s probably because it’s disturbingly similar to a nightmare thought experiment first proposed by Friedrich Nietzsche in the late 1800s. In his book The Gay Science he writes the following:
What if some day or night a demon were to steal after you into your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence—even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!”
Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: “You are a god and never have I heard anything more divine.” If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, “Do you desire this once more and innumerable times more?” would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal?
Heavy.
For Nietzsche, the point of this proposal had nothing to do with thermodynamics and everything to do with an examination of the meaning, purpose, and experience of life as a human being. He likely never imagined such a scenario could be literally, physically true, as the de Sitter Equilibrium hypothesis proposes.
You could argue that these scenarios are not exactly the same thing. The quantum fluctuation that re-creates your experience of stubbing your toe might produce something that is exactly like you in every detail, but you, as an entity, would have been long dead by then. But this brings up questions of what it means to be you. Is the exact configuration of atoms you, or is there something ineffable and persistent about your consciousness that could never be re-created piece by piece? This is the same question that sparks heated debates among science fiction fans around teleportation and whether or not Captain Kirk was brutally murdered every time he stepped into a transporter beam, only to be replaced by a duplicate impostor that mistakenly believed itself to be him. We are unlikely to answer it here.
But it does bring up another wrinkle to the rebirth-by-quantum-fluctuation scenario—one that has as much to do with the transporter question as it does with the sperm whale and bowl of petunias, all wrapped up in a kind of quantum mechanical solipsism. It’s a problem called Boltzmann Brains.
The idea is that if it’s possible for the entire universe to quantum-mechanically fluctuate out of the vacuum, it’s much more likely for just a single galaxy to do it, because a single galaxy is less complicated and requires less stuff to suddenly appear. And if it’s more likely for a single galaxy to appear, it’s more likely for a single solar system, or a single planet. In fact, far more likely even than that is that the only thing that fluctuates out of the vacuum is a single human brain, one that contains all your memories and is in the process of imagining that it lives on a perfectly functional world and is currently sitting in a coffee shop typing the words to the fourth chapter of a book about the end of the cosmos.
The Boltzmann Brain problem is the assertion that this unfortunate brain, doomed to quantum-fluctuate back into the vacuum almost instantaneously after its creation, is so vastly more likely to occur than a whole universe that, if we want to use random fluctuations
to build our universe, we have to accept that we’re much more likely to be just imagining the whole thing.
This question is not yet settled. Despite being one of the first people to propose the Boltzmann Brain problem in this context, Albrecht now comes down on the side that it’s more likely for a de Sitter universe to create a very low-entropy state like the Big Bang than something small on the brink of reabsorption. The basic argument is that creating a low-entropy state might seem to take a lot of quantum fluctuation energy, but actually takes out only a little bit of total entropy from the system. Many cosmologists take the opposite approach and say that it’s easier to fluctuate to a still relatively high-entropy state than to create a pocket where the entropy is very, very low. Settling this question could give us a handle on one scenario for the origin of the entire cosmos, as well as lend us some peace of mind with respect to our possible fate of infinitely playing back our most cringe-worthy moments forever.
And for some cosmologists, understanding how we started with a low-entropy state in the early universe, and determining once and for all whether or not we have to worry about Boltzmann Brains or Poincaré recurrences, are questions that shake the very foundations of our cosmological model. Trying to find a way to set up a low-entropy initial state has prompted some to hypothesize entirely new cosmic histories (as we’ll discuss in Chapter 7), though the issue is very far from resolved. And the possibility of fluctuations is so disturbing to our picture of a sensible cosmos that it has been described by Sean Carroll as “cognitively unstable.” It’s not that it can’t be true, but that if it is, nothing makes sense, and we might as well give up on trying to understand the universe at all. The jury is still out on this one.
If you’re not too disturbed by the possibility of disembodied sentient brains popping into and out of existence, the possibility of rare random fluctuations can, in some sense, drag some order out of the Heat Death’s nihilistic disarray. But even in this most optimistic view, a universe dominated by a cosmological constant unquestionably spells doom for any beings living within it, as absolutely every coherent structure is destined for dark, lonely emptiness and decay. Before dark energy was discovered, physicists like Freeman Dyson came up with speculative proposals that a machine whose computation constantly slows can persist for an arbitrarily long time into the cosmic future.XII But even this ideal machine would be subject to entropic erosion via the Second Law, and would eventually disintegrate into waste heat in the face of the de Sitter horizon. The timescales for the achievement of maximum entropy—the true and timeless Heat Death—depend on estimates of the decay time of the proton, which are still uncertain. Nonetheless, we probably have a good 101000 years or so before we and all other thinking structures fade from the possibility of memory.
It could be worse.
As dark energy goes, a nice, steady, predictable cosmological constant is something of a best-case scenario. Other possibilities are not ruled out, and one of them, phantom dark energy, leads to something more dramatic, more immediate, and, in a sense, much more final: the Big Rip.
I. Weirdly, as of this writing, we are still not actually sure which of these is the main mechanism by which this happens. We just see the star go off and we know at least one white dwarf was involved.
II. As much as the rest of us physicists might find it frustrating to admit, the guy had a lot of pretty good ideas.
III. You can tell you’re in a demanding field when just SAVING THE UNIVERSE is not enough.
IV. If you were sitting in a different galaxy in a different part of the universe, you would also define your observable universe as being a sphere about 45 billion light-years in radius, centered on your own position. “Observable universe” is a subjective, literally self-centered, concept.
V. As we have seen in Chapter 2, defining “now” is tricky.
VI. The relative-size-increase factor of the universe is 1 plus the redshift, so something nearby, at redshift 0, is in a universe whose size is the same as ours.
VII. The Hubble radius is not technically a horizon, in the physics sense of the word. The particle horizon is; it’s a limit beyond which we cannot possibly obtain information about anything. The Hubble radius is just the radius at which the CURRENT expansion speed is the speed of light, but it changes over time, and, as we’ve just discussed, objects can cross into it. People sometimes call it a horizon, but many cosmologists will get very worked up if you use that term.
VIII. Not literally, obviously. That would be both impossible and extremely inadvisable.
IX. The other laws are somewhat less exciting, though they do start with zero, just to be weird. Briefly, they are: 0) If one thing is in thermal equilibrium with another thing, and a third thing is in equilibrium with that, they’re all in equilibrium with each other. 1) Energy is conserved and perpetual motion machines are impossible (sorry). 3) As something approaches absolute zero temperature, its entropy approaches a constant value.
X. This isn’t a tangible surface, but rather a sphere in space defined by the distance from the black hole’s center to the Schwarzschild radius, which is what we call the distance from the singularity out to the horizon. The Schwarzschild radius is directly related to the black hole’s mass.
XI. Real particles can’t have negative energy, but these are virtual particles, which are just a totally different kind of beast, and are not to be confused with negatively charged particles like electrons.
XII. You may recognize Dyson’s name from the sci-fi concept of a “Dyson sphere”—a monumentally huge sphere built around a star to capture 100 percent of its radiation for the purposes of powering an advanced alien civilization. Observational surveys for Dyson spheres, which look for the waste heat expected to be emitted by them in the infrared, have so far come up empty.
CHAPTER 5: Big Rip
I keep thinking about this river somewhere, with the water moving really fast. And these two people in the water, trying to hold onto each other, holding on as hard as they can, but in the end it’s just too much. The current’s too strong. They’ve got to let go, drift apart. That’s how it is with us.
Kazuo Ishiguro, Never Let Me Go
For a cosmic phenomenon that is arguably the most important thing in the universe, dark energy is surprisingly difficult to study. As far as we can tell, it exists everywhere in the universe, completely uniformly, woven into the fabric of space itself, and its only effect is to stretch space out so gradually that it has no detectable impact on any scale smaller than the vast expanses between distant galaxies. Dark matter physicists have it much easier—despite being just as invisible as dark energy, dark matter makes its presence very known by clumping around virtually every galaxy or cluster of galaxies we’ve ever seen, dominating the gravitational field, bending light, and altering the course of cosmic history from the very beginning. Dark energy, on the other hand, just… expands.
This doesn’t completely prevent us from studying it. There are essentially two handles we have on dark energy: the expansion history of the universe and the way that galaxies and clusters of galaxies have grown over time. For both of these, we’re peering into the distance and the past, tracing out the evolution of the cosmos over time. But no matter how we look, we’re trying to tease out small effects using faint signals and statistics.
As challenging as these kinds of studies are, it’s worth putting in the effort, since dark energy is both the dominant component of the cosmos and a sure sign of some new physics beyond our current understanding.
That, and the fact that depending on what dark energy turns out to be, it might violently and inescapably destroy the universe, much sooner than anyone ever imagined. Why wait for the slow fade of a Heat Death, if you can have a dark energy apocalypse as sudden and dramatic as the appropriately named Big Rip? Not only would it be a kind of destruction from which there is no escape, quantum-mechanical fluctuation or not, it would be one that could tear apart the very fabric of reality, rendering any thinking creatures in the c
osmos helpless as they watch their universe being ripped open around them.
This alarming possibility is hardly an outlandish fringe idea. In fact, the best cosmological data we have not only fails to rule it out, but, from some perspectives, slightly prefers it. So it’s worth spending a bit of time exploring what, exactly, it would do to us.
A COSMOLOGICAL NONCONSTANT
Dark energy is often assumed to be a cosmological constant that stretches space out, accelerating cosmic expansion by imbuing the universe with some inherent inclination for swelling. On large scales, this is a pretty good description. But within galaxies, solar systems, or in the close vicinity of organized matter generally, a cosmological constant has no effect. It can be more properly thought of as a force for isolation—if two galaxies are already distant from one another, they get more distant, and individual galaxies, clusters, or groups of galaxies find themselves more and more alone as time goes on. They also form a bit more slowly in the presence of a cosmological constant than they otherwise would. What the cosmological constant cannot do is break apart anything that is already, in any sense, a coherent structure. What therefore gravity hath joined together, let not a cosmological constant put asunder.
The reason for this small mercy of the cosmological constant (which, to be fair, does still destroy the whole universe eventually) lies in the “constant” part of the story. If dark energy is a cosmological constant, its defining feature is that the density of dark energy in any given part of space is constant over time, even as space expands. The expansion rate isn’t constant, just the density of the stuff itself, in any given volume of space. This makes sense in a way, if every bit of space is automatically assigned a set amount of dark energy within it, but it’s still super weird, because it means that as space gets bigger, the amount of dark energy increases to keep the density constant. It also means that if you draw a sphere of a given size anywhere in the universe and measure the amount of dark energy inside the sphere, and then do the same at some future time, you’ll always get the same number, regardless of how much the outside universe has expanded in the meantime. If your original sphere contains a cluster of galaxies and some quantity of dark energy, in a billion years the amount of dark energy in that region will still be the same, so if it wasn’t enough to mess up the galaxy cluster before, it won’t be in the future. The balance between matter and dark energy in that sphere does not significantly change even as the rest of the cosmos seems to inexorably empty out.
