by Katie Mack
For a while, sure, the more distant things are smaller. The Sun and the Moon look the same size to us because even though the Sun is vastly bigger, it’s also a heck of a lot farther away. And for many billions of light-years, the more distant the galaxy is, the smaller it looks. As you would expect. But somewhere in the vicinity of the Hubble radius, that relationship reverses. Beyond that distance, the farther away something is, the larger it appears! This is super convenient for us astronomers, of course, as it allows us to see structure and details in galaxies that are extremely distant from us, and that in a sensible universe would look like infinitesimal points. But if we think about it too much, it still seems like an utterly unreasonable way for geometry to work.
Figure 12: The apparent size of distant galaxies (assuming the same physical size) as a function of distance from us. Out to a certain distance, a faraway galaxy will appear to be smaller, but at some point, this turns around, and a more distant galaxy will look bigger in the sky. The dotted line indicates how the apparent size would relate to distance in a static universe.
The reason for this reversal is related to the reason we can see things that are currently moving away from us faster than light. In the past, when the light was emitted, they were closer. So close, in fact, that they covered more of the sky. Even though they’re much farther away now, the “snapshot” they’ve sent us has been traveling all that time, and is just reaching us now, showing us the ghostly image of a much closer thing. And the farther back in time you go, the smaller the universe was. So beyond a certain point, the balance between “the universe was smaller in the past” and “light takes a certain amount of time to get here” is such that a galaxy that is more distant than another galaxy now might have actually been closer when its light was emitted.
Look, I warned you it would be weird.
Anyway, if this is all deeply confusing and mind-boggling, that’s totally okay and normal. Maybe try drawing some sketches on napkins, and then stretch out the napkins in every direction while on some kind of infinite treadmill running at an extreme speed over the course of billions of years, and hopefully it’ll make sense then. Meanwhile, we should get back to what this all means for the future of existence. Because it really isn’t good.
THE SLOW FADE TO BLACK
The assertion that “dark energy ruins everything” is not an overstatement. A universe whose expansion is accelerating is, paradoxically, one in which the influence exerted by the things in it is shrinking. Distant galaxies being dragged out of the Hubble radius by cosmic expansion will become lost to us. Galaxies whose distant past we can see now will slowly fade into darkness like ancient decaying photographs. In our own cosmic neighborhood, after the Milky Way and Andromeda merge, our little Local Group of galaxies will become more and more isolated, surrounded by darkness and the dying primordial light. All across the cosmos, invisible to us, other groups and clusters of galaxies will merge to form giant elliptical clumps of stars, burning brightly in the initial violence of the collisions but fading eventually to embers, whose glow will never reach beyond their own pool of expanding, emptying space.
Eventually, each new, dying supergalaxy will be utterly alone. Nothing will again approach to bring in a fresh supply of gas to fuel new stars. The stars already shining will burn out, exploding as supernovae or, more often, sloughing off outer layers to become slow-burning relics, gradually cooling for billions or trillions of years. Black holes will grow, for a time. Some will engulf galaxies’ worth of dead stellar remnants; some will stall in their growth, with no new matter approaching close enough to be consumed.
When the stars have all faded to darkness, the ultimate decay sets in.
Black holes begin to evaporate.
It was originally thought that black holes were eternal—capable of growing by consuming other matter but incapable of ever losing any mass. It makes sense that something defined by the fact that not even light can escape it would be a one-way, bottomless pit. But Stephen Hawking calculated in the 1970s that quantum effects on a black hole’s horizon cause it to glow, faintly. The glow carries away energy—or, equivalently, mass—and the black hole shrinks. This process goes slowly at first, and then faster and brighter and hotter until a final explosion and disappearance at the end. Even the supermassive black holes at the centers of galaxies, with masses millions or billions of times that of the Sun, are destined to eventually fade and disappear.
Ordinary matter—the stuff making up stars and planets and gas and dust—suffers a similar, if less dramatic fate.
Most particles of matter are known to be, at some level, unstable. If left alone long enough, they decay into other things, dropping in mass and energy in the process. A neutron, for example, will eventually decay into a proton, an electron, and an antineutrino. While we’ve never seen a proton decay experimentally, we have reason to believe that can happen too, if you’re willing to wait something like 1033 years. At that point even hydrogen atoms, which have been persisting as the most numerous atoms in the universe since the Big Bang itself, will finally cease to be.
The distant future of a universe governed by dark energy in the form of a cosmological constant is one of darkness, isolation, emptiness, and decay. But this slow fade is just the beginning of the ultimate end: the Heat Death.
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The name “Heat Death” might sound like a misnomer for a state of the cosmos that is colder and darker than anything else in the history of creation. But in this case, the term “heat” is a technical physics term, not meaning “warmth” but rather “disordered motion of particles or energy.” And it’s not the death of heat, but a death by heat. It’s the disorder in particular that kills us. Which is why we need to take a moment to talk about entropy.
Entropy is perhaps one of the most essential, versatile, and tragically obscure topics in all of science. It shows up everywhere—not just in the physics of everything from balloons to black holes, but also computer science, statistics, and even economics and neuroscience. Entropy is usually explained in terms of disorder. The more disordered a system, the higher its entropy. A pile of puzzle pieces has higher entropy than a completed puzzle; a scrambled egg has higher entropy than an intact one. In cases where “disorder” is not an immediately obvious property, you can think of entropy as a measure of how free or unconstrained the elements of the system are. To be concrete, a completed puzzle has low entropy because there’s only one way for all the pieces to be arranged to make the puzzle whole, whereas a pile of pieces can be in any of a number of configurations and still successfully constitute a pile.
Though it’s not so obvious in these examples, higher entropy is also linked to higher temperature. This makes sense if you think of the difference between a block of ice and a cloud of steam. In order to be ice, the water molecules have to be arranged in a crystal structure, whereas the particles in steam are free to move around in three dimensions. But even just cooling the steam a bit reduces its entropy because the particles are moving less: they’re more constrained, or less disordered.
The important thing about entropy, in cosmic terms, is that over time it goes up. The Second Law of ThermodynamicsIX states that in any isolated system, the total entropy can only increase, not decrease. In other words, order does not spontaneously appear out of nowhere, and if you leave something alone long enough, it will inevitably decay into disorder. Anyone who has tried to keep their desk tidy will understand this, the universe’s most intuitive and maddening natural law.
Whether or not the universe itself counts as an isolated system can be a matter of some discussion, but taking it to be one leads us to the conclusion that the future of the cosmos is one of inevitably increasing disarray and decay. In fact, the Second Law is considered to be so inescapable and fundamental, it’s been blamed for the passage of time itself.
The laws of physics generally have no regard for the direction of time; in most situations, reversing the equations in time makes no difference to the physics. The onl
y part of physics that seems to care at all about which direction time is going is entropy. In fact, it’s possible that the only reason we can remember the past and not the future is that “things can only get worse” is a truth so universal that it shapes reality as we know it.
“But wait!” you might say, “I completed the jigsaw puzzle! I created order! Did I just reverse the arrow of time?!”
Not exactly. The puzzle is not an isolated system, and neither are you. Technically, any local increase in entropy can be reversed with enough effort. It would be massively difficult, but you could unscramble an egg if you put in enough time and some incredibly sophisticated laboratory equipment. But the total entropy will always go up. In the case of the puzzle, the effort it takes you to put the pieces together requires an expenditure of energy, which means that you’re breaking down food chemicals and releasing heat and waste products (like, you know, carbon dioxide) into your environment. That heats up the room, creates particulate waste, and probably wrinkles your shirt while you’re at it. I don’t know what an egg-unscrambling machine would do to its surroundings, but I’m pretty sure I wouldn’t want to be in a closed room with it when it’s running.
This, incidentally, is why leaving your refrigerator door open will ultimately make the whole kitchen hotter, and why air conditioners can contribute to global warming. Every attempt to bend some part of the world to our will creates disorder somewhere else, often in the form of heat.
As much as this has interesting applications for eggs and fridges and air conditioners, it all gets much weirder when we throw black holes into the mix.
Back in the 1970s, physicists were talking a lot about entropy and how the entropy of the whole universe must be increasing over time, and what the implications of that might be. At the same time, a young, not-quite-famous-yet Stephen Hawking and even younger postdoctoral researcher Jacob Bekenstein were thinking about black holes and wondering if these bizarre, inescapable, spacetime garbage disposals might wreak havoc on the Second Law of Thermodynamics. What if, for example, you used your egg-unscrambler to unscramble the egg, and then pocketed the egg while throwing the whole messy hot unscrambler lab into the nearest black hole? Would you have decreased the overall entropy of the universe by putting the egg back together and getting rid of all the entropy you created in the process? After all, a black hole is defined as something that not even light can escape from, an object so massive and compact that its gravity turns outgoing light rays right around to send them diving back toward the central singularity. Beyond the event horizon of a black hole, the gravitational point of no return, nothing—not light, not information, not heat—can escape once it’s gone in. Could hiding entropy behind black hole event horizons be the perfect crime?
Whatever other part of physics you have to break, don’t bet against the Second Law of Thermodynamics. The solution to the entropy problem of black holes turned out to change everything we thought we knew about black holes and absolutely nothing about entropy. You can’t hide entropy in black holes, because they have entropy of their own. Which means they have a temperature (they create heat). Which means they are not black at all.
What Bekenstein and Hawking eventually concluded about black holes is that a black hole has to have an entropy associated with it, to exist in accordance with the Second Law. Since that entropy should increase every time it swallows something, it makes sense that the entropy is connected to the size of the black hole itself—specifically, it’s related to the total surface area of the event horizon. Throw a refrigerator into a black hole, and the mass increases by the mass of the refrigerator, which increases the horizon size and therefore the surface area.X
The fact that you can’t have entropy without having a temperature means that black holes have to be radiating something (particles and radiation, specifically). And the only place they can radiate from is at or just outside the event horizon, since we still can’t have anything coming out once it’s gone in. So something weird has to be happening around there.
Fortunately, if we need weirdness in physics, we can always rely on the quantum realm to serve us up something good. In this case, Hawking made use of the quantum weirdness of virtual particles—pairs of positive- and negative-energy particles popping into and out of existence from the vacuum of space itself.XI The idea is that this spacetime popcorn is happening all the time, everywhere, but usually it has no effect on anything because the two particles will appear and immediately annihilate against one another, both going back to being nothing again. But, Hawking said, near a black hole, you could have a situation where the negative-energy virtual particle falls past the horizon, leaving the positive-energy virtual particle so bereft that it becomes real and wanders away. The mass of the black hole would reduce a little as it absorbs that bit of negative energy, and the same amount of positive energy would appear to radiate off the black hole’s horizon. Because these virtual particles are always popping up everywhere in space, any black hole that’s not actively pulling in matter from its environment should be gradually bleeding off mass through this evaporation process all the time.
As complicated as this might sound, it’s still a vastly simplified picture, meant to capture just the basic idea without getting too technical, and it’s an explanation that’s used all the time. But it has never been particularly satisfying to me, since it seems to require the negative-energy particles to preferentially fall toward the hole, and the positive-energy ones to be traveling away from the black hole with enough energy to escape. It turns out that despite talking in these terms for popular audiences, Hawking never really wanted this explanation to be taken literally, and the real explanation involves calculating wave functions and the scattering that the waves experience in the vicinity of a black hole. I can’t really get into it without a massive amount of math and a level of physics exposition that would probably require weekly lectures for two or three semesters, but I’m telling you about it because if it bugged me, it might bug you too, and I wanted to assure you that despite the inadequacy of the popular analogy the full calculation does make sense if you do it all rigorously, using general relativity and quantum field theory.
The point of this diversion was to say that we can safely assume that when facing the Heat Death, black holes do indeed evaporate away, leaving nothing but a bit of radiation spreading out through an increasingly empty universe. I hope that helps.
Also, aside from ultimately dooming all the black holes, the ability of horizons to radiate, and to account for the entropy of the things they contain, is actually an essential part of the Heat Death. Because our observable universe has a horizon too, and we’re inside it.
MAXIMUM ENTROPY
A universe in the thrall of a cosmological constant is a universe that is evolving inexorably toward darkness and emptiness. As the expansion accelerates, there’s more empty space, and thus more dark energy, causing more expansion, ad infinitum. Eventually, when the stars have burned out and the particles have decayed and the black holes have all evaporated, the universe is basically empty space with only a cosmological constant in it, expanding exponentially. We call this de Sitter space, and it evolves in the same way we think the very early cosmos did during inflation. Only, inflation eventually stopped. If dark energy really is a cosmological constant, the expansion can’t stop and the cosmos will instead continue expanding, exponentially, forever.
So does a universe like this truly end, if it just keeps expanding? To answer that, we have to dig deeper into entropy, and the arrow of time.
Every time a star burns out or a particle decays or a black hole evaporates, it converts more matter into free radiation, which spreads through the universe as heat: pure disordered energy. Reducing something to heat radiation is dialing up its entropy to the maximum, because there are now no restrictions on the flow of energy. As the universe gets even emptier, that radiation gets more diluted, so you might think that the total entropy should drop as the temperature does. But that doesn’t happen.
The way it works is this: when the universe reaches a state of steady exponential expansion, you can define a radius (from wherever you are) beyond which the rest of the cosmos is forever hidden. It’s a true horizon in the sense that nothing beyond it could ever reach you. It turns out that this horizon, like a black hole’s horizon, also has an entropy associated with it, and thus a temperature. The difference is that instead of the heat going out like it does with a black hole, it goes in. The temperature is very small—something like 10-40 degrees above absolute zero—but when everything else has decayed, this radiation is all that’s left to contain all the entropy of the universe. When the universe gets to this pure de Sitter state, it is a maximum entropy universe. From that point on, there is no way for the universe’s total entropy to increase, which means, in a very real sense, the arrow of time is… gone.
Figure 13: Density of matter, radiation, and cosmological constant over time. Because the density of dark energy (in the form of a cosmological constant) doesn’t change as the universe expands, while everything else dilutes, it comes to dominate the energy density of the universe. Today, dark energy makes up around 70 percent of the universe, while matter is around 30 percent and radiation is a tiny amount.
I should just reiterate here that the arrow of time and the Second Law of Thermodynamics are so integral to the functioning of the universe that if there’s no way for entropy to go up, nothing can happen. It is no longer possible for any organized structures to exist, for any evolution to happen, for any meaningful processes of any kind to occur. A necessary part of anything really happening is energy moving from one place to another. If entropy can’t go up, then energy can’t flow from one place to another without immediately flowing back, erasing anything that might have just, by chance, appeared to occur. Energy gradients are the basis of life, but also of any other structure or machine that performs any kind of work. Energy gradients can’t exist in a universe that is just one giant (but very cold) heat bath. Heat is useless. Heat is death.