12 Monkeys, Hartle-Hawking state, and the Fate of the Universe

It’s been quite some time since I wrote a blog post (turns out grad school is really time demanding), so I thought I’d get back to it by first telling you about some cool science advising I got to do, and combine it with explaining some of the science I worked on! I’ll break this post up into two parts: The first will be on the science I worked on for the TV show “12 Monkeys”, and the second will be the geometry and fate of the Universe. That way, you get to learn about this cool thing I got to do, and get to read about physics as well!

12 Monkeys and the Hartle-Hawking State

Last year, I was contacted by the co-creator and showrunner of the TV show “12 Monkeys“, Terry Matalas. He was looking for someone to help make some seriously mind-bending science work in the show’s upcoming storyline that would usher in the coolest, most daring time-travel storyline I’ve ever come across. Naturally, I jumped at the chance, and became the show’s science advisor to bring something really brilliant to scientific life: the Hartle-Hawking state! You can read a really cool article by Emily Rome of Inverse that Terry and I were interviewed for, as well as watch a 2-minute-video where I talk about the Hartle-Hawking state (!!), here.*
*Note that in the video, when I say observations tell us we live in an “open” Universe, I really meant “flat”; I was so focused on the fate of the Universe (which is the same for open and flat Universes) that I swapped the two.

The Hartle-Hawking state is really complicated stuff. It combines the physics of the very big with the physics of the very small to arrive at a description of the Universe. James Hartle and Stephen Hawking worked out this theory together in 1983, which is essentially a wavefunction of the Universe. In quantum mechanics, a wavefunction describes a particle’s motion and evolution through time (or space), and having one for the Universe would mean we would know just about everything there is to know about it at any point in time (or space). But, the Universe is really big, so writing out a wavefunction for it would be really (and I mean really) hard. However, let’s look at what happens to the Universe as time progresses: dark energy keeps stretching spacetime apart at an accelerating rate, so that as time passes, the more the Universe is being “stretched” apart! Now, let’s look at this process in reverse: if we go backwards in time, the Universe must shrink. So if we go really far back to almost the very beginning, the Universe would be this really small and dense thing, small enough for quantum effects to begin to matter. That’s what Hartle and Hawking did: they found a wavefunction for the Universe in its infancy.

This wavefunction, called the Hartle-Hawking state, predicts something really weird happens to time at the very beginning, before the Planck era: spacetime splits apart, so that space and time are separate. (The Planck era is about 10^-44 seconds after the Big Bang; almost instantaneous, but not quite.) That effectively means that during that period, time doesn’t exist for space, so that if you could get to that point in the Universe’s history (and you really would not want to do that, it would be a super dense and incredibly hot mess of stuff I can’t even describe), time would not exist for you… Weird, right? And this worked perfectly for the 4th season (and final) of 12 Monkeys (which you’ll understand if you’re watching the show. And you are watching, right?! Because you should be watching).

The problem with the Hartle-Hawking state is that it also makes a prediction that contradicts our observations: it predicts that we live in a closed Universe, while observations tell us, to really good accuracy, that we live in a flat Universe. If our observations are correct, then in its current state, the Hartle-Hawking state does not work for our Universe… So, we still have work to do to find a wavefunction for the Universe. But hey, that’s what physics is about!

The Geometry and Resulting Fate of the Universe

Okay, so the Hartle-Hawking state predicts the Universe is closed. But what is a “closed”, or “open”, Universe? The answer lies in the geometry of the Universe, and its geometry in turn determines the fate of the Universe. There are three types of geometries universes can have: positive curvature, which corresponds to a closed Universe, negative curvature, which is what we call an open universe, and finally, flat, with no curvature at all. Let’s talk about each to get an idea of how to visualize these types of universes, and what each of these mean for how the Universe will meet its end.

Flat Universes

Let’s start with a flat universe*, because it is the simplest to understand, and we can build off the definition of a flat universe to describe the rest. How do we picture what a flat universe is? Well, because our brains can’t really think in three dimensions, we are essentially stuck to two-dimensional visualizations. A good one for a flat universe is a flat sheet, like the one in the figure above. (See how the grid isn’t warped, because the sheet is flat?) This means that the triangle in red, which you should assume to be drawn on a cosmic scale, has angles that add up to 180 degrees. (If this seems obvious to you right now, you’ll see later why it was important to point this out). It also follows that cosmic lines remain straight right through a flat universe, meaning that if you had two laser pointers that were powerful enough to shoot across the Universe, if they begin parallel to each other, they’ll end up parallel to each other as well; things change when you add curvature to a universe!
*Notice how I sometimes capitalize “universe”, and sometimes don’t? This isn’t an accident: when we talk about this Universe, the one we live in, we capitalize it, while if we talk about some universe, or universes, that aren’t our Universe in particular, then we don’t capitalize.

A really important property of a flat universe is that the density of the stuff it contains is exactly equal to the critical density, which can be described mathematically as Ω₀ = ρ/ρ_crit = 1, and that’s what the Ω₀ in the figure stands for (understanding the math doesn’t matter much, but in case you’re interested, that’s what it looks like). This basically means a flat universe is one where the expansion will slow down, yet its expansion will never stop and reverse either. In other words, the pull of gravity matches the stretch of the expansion in a universe with a density that is equal to the critical density, which means it can never collapse on itself (for more detail on the critical density, check out my previous blog post, here).

A flat universe’s end could be really chilly: things just keep cooling down until they reach absolute zero, resulting in a Big Freeze… ouch. But what could also happen is it could suffer what’s called a Heat Death, which is due to entropy reaching a maximum. In nature, entropy, which is a measure of the amount of disorder in an isolated system, increases with time, so that things get more and more disordered with time. But, if this happens for a really long time (about a hundred orders of magnitude longer than the age of the Universe—that’s really long, since the Universe is about 13.8 billion years old!), disorder reaches homogeneity, so that it can’t be any more disordered than it has already become—the Universe, all of it, reaches complete and total equilibrium. Once this happens, work can no longer be produced, leaving the Universe a dead place of nothingness… eek.

Now, let’s introduce a positive cosmological constant, or dark energy, like the one stretching our Universe apart at an accelerating rate. This case further ensures that one of the above scenarios will be the ultimate fate of a flat universe. …unless dark energy isn’t a constant, but rather, its density increases with time: phantom dark energy. If dark energy is of the phantom type, then it would stretch its universe apart so tremendously that it would eventually tear everything in it to shreds—galaxies, stars, your favorite t-shirt—all of it, so that all that’s left are elementary particles that cannot come together to form new matter, and thus would be its end.

Positively Curved Universes

A closed universe, or a universe with positive curvature (like the one the Hartle-Hawking state predicts our Universe to be), can be visualized as a sphere. But we can do a little better than that. In a positively curved universe, unlike the flat universe described above, the angles of a triangle add up to greater than 180 degrees, so that it looks kinda like an inflated triangle, like the triangle that’s drawn in red on the sphere above. Then in a positively curved universe, if you were to point two lasers out to a cosmic distance, parallel to each other, instead of remaining parallel all the way through like they do in a flat universe, they would eventually converge*. That’s kinda how you can visualize what a positively curved universe would look like.

<span style=”font-size: 14px !important;”>*Keep in mind that, because we’re talking about cosmic scales, the triangles you draw out on a piece of paper would still have angles that add up to 180 degrees, and parallel lines on small scales would not cross.</span>

In a closed universe, the density of the universe is greater than the critical density: Ω₀ = ρ/ρ_crit > 1. So, in this type of universe, there is enough stuff, or enough gravity, to cause the expansion to halt and reverse in the distant future, so that its fate is ultimately what we call a Big Crunch, so that that universe would end up collapsing in on itself. And the cool thing is that it’s possible that a universe like this would just form a new one after collapsing in on itself by starting a whole new Big Bang! Of course, that’s cool for that new universe, but it wouldn’t be cool for ours.

Is that the only fate possible for a positively curved universe? Not necessarily; throw enough dark energy into that universe that it counters the halt and reversal of the expansion, and you have a universe that expands forever as well. So, yet again, you could have the upper scenarios occur here, too. But you’d need a lot of dark energy, or the type of dark energy that has a density that increases with time so that it becomes enough to counter the collapse. Otherwise, CRUNCH.

Negatively Curved Universes

The final type of geometry we have left to discuss is the negatively curved, or open, universe. This one kinda looks like a saddle, or even better, like a Pringles chip:

This type of universe is one where a cosmic triangle looks deflated, so that the sum of its angles is less than 180 degrees. The triangle drawn on the saddle figure doesn’t really show what that looks like, so I drew it out on my whiteboard, along with how parallel lines would diverge in a negatively curved universe (as well as the other types):

In an open universe, cosmic triangles look squished, and cosmic lasers that begin parallel, end up diverging. And, in this type of universe, the density of its contents is less than the critical density, so that Ω₀ = ρ/ρ_crit < 1. What does this mean? Well, there’s simply not enough stuff in it for gravity to be able to take effect and halt/reverse its expansion—this type of universe expands forever, whether or not it contains dark energy.

You probably guessed that there’s no way this type of universe would ever end in a Big Crunch, and you’d be right. Rather, this type of universe most likely ends in a Big Freeze or Heat Death, or possibly a Big Rip if dark energy is weirder than we thought and its density increases with time. No Big Crunch leading to new Big Bangs here.

Vacuum Decay (?!)

The above scenarios for the demise of the Universe aren’t the only ones—there’s also vacuum decay, which is really cool (well, not so good for the universe it happens to). I read about this one in an article written by my friend and favorite theoretical astrophysicist Katie Mack, and thought I really need to tell you all about it, too, and it has to do with the Higgs field: the potential of the Higgs field tells us if the Universe is in its lowest energy vacuum state (called the true vacuum, think of the bottom of a hill), or if it isn’t quite in its lowest energy, but seems as though it is (the false vacuum, like at the center of a hilltop).

If the Universe is in its lowest energy vacuum state, then we have no problems; if, however, it’s in a false vacuum, something could happen that would shove the Universe into the true vacuum state (like a ball on a hilltop getting nudged and rolling down to the bottom of the hill), which would change everything in the Universe at once, probably making it inhospitable for us and everything else.

If our Universe undergoes vacuum decay… yikes. Vacuum decay is so frightening and so cool and I cannot do it justice, so you really need to check out Katie’s article, here. She does a great job of explaining it, and how catastrophic it would be if our Universe suffered vacuum decay, and much more! Also, keep an eye out for her book, where you’ll get to learn tons about the ways the Universe could meet its demise, and who wouldn’t want to read about that?!

What about Our Universe?

The shape of the Universe affects things like its fate, but this isn’t something you’d directly notice in your everyday life. Adding curvature, positive or negative, does make a cosmologist’s life a big more complicated, since the equations aren’t as nice as they are if the Universe is flat. Luckily for us, observations tell us that we, to a good degree of certainty, live in a flat Universe. And while this is really nice for working with the theory, it’s kinda weird: the Universe just happens to sit on this really fine line between too much or too little density for the expansion to continue or halt—this is something we call the “flatness problem”, and you can read all about it in my previous blog post, here.

So our Universe is flat, and not closed, like the Hartle-Hawking state predicts. What else does that mean, other than making the theory a bit nicer? Well, the Universe probably isn’t ending in a Big Crunch; instead, it might end in a Big Freeze, or a nice Heat Death. Unless the Universe has expanded so much that we can’t see any curvature because we’re limited by our particle horizon (which defines the extent of our observable Universe; read about it in my previous blog, here), and we might not be seeing enough of the Universe to really know what its curvature is… And there’s always good old vacuum decay! Plenty of possibilities for how the Universe meets its demise. But we have lots of time, many orders of magnitude more time than the age of the Universe, before any one of these possibilities happens. So don’t worry, you’re not losing your favorite t-shirt anytime soon.

Featured image credit: NASA, ESA, and S. Beckwith (STScI) and the HUDF Team