Einstein taught us mere mortals that energy is mass. Feel free to ignore the c in the famous equation E = mc2, since almost all theoretical physicists do anyway. It's just a constant, a number, floating around in the math. Here it serves as a conversion factor; it tells you how much energetic punch a given amount of matter can pack. When you remove that pesky term, Einstein's relation becomes a lot clearer—and a lot more awe-inspiring: Energy is mass. Mass is energy. They are equivalent. They are the same.
Once this fact settles into your bones the world becomes a lot stranger. You can disappear a particle without any magic tricks: if it has mass, it can convert to energy. And if you bunch enough energy together at a specific place, boom—you've made yourself a particle. We're actually much more used to this process than we think: every time you turn on a light, trillions upon trillions of photons—the particles that carry the electromagnetic force—are spontaneously born at the light source, leap across the room, and are immediately extinguished in a deposit of energy at your eye.
For photons, this creation/destruction process is pretty easy. They're massless, after all, and so don't take a lot of energy to get up and going. But if quantum field theory has taught us one thing, it's that what goes for electromagnetism goes for everybody. Thus electrons, quarks, W bosons, whatever-ons, can all be created in a flash and snuffed out just as easily as flicking a switch.
It's hard to visualize unless you have on your field glasses. But if particles are just vibrations in a field that stretches across all space-time, then of course they can be created or destroyed at will. It's just a matter of adding or subtracting vibrational energy to or from that field. Pluck a guitar string, make a note. Pluck a quantum field, make a particle.
The collisions and battles of the early universe take on a new light in this context. Just as a single field can populate a volume of space with a bunch of particles, the various fields can interact with each other—a vibration in one can translate to a vibration in another. This is how we understand particle transformations, how a photon can split into a particle-antiparticle pair or vice versa. The struggle of matter versus antimatter in the early universe was more about the relationship of fundamental quantum fields, vibrating against each other for dominance.
And just as the rules of quantum mechanics dictated a minimum energy level for electrons bound to an atomic nucleus, these fields that flit and float throughout the universe also get stuck with a minimum energy. A certain low-level buzzing, a humming that permeates the cosmos. This is usually described as the “quantum foam” and visualized as “virtual” particles constantly popping into and out of existence before you have a chance to notice. That's not an incorrect description, but (a) I'm not going to bother untangling the word “virtual” for you, and (b) I like the concept of a background hum better. It's more Keplerian.
This ground-state energy of the universe has a more formal name—vacuum energy. It's a real thing, and I'll turn to it in more filling yet ultimately unsatisfactory detail later.
The complete picture of our universe at the fundamental level, from the catalogs of particles to the wiggly-field nature of interactions, goes by the astoundingly boring name of “the standard model.” This (complicated) model categorizes the leptons and baryons, puts antimatter in its place, incorporates the Higgs boson, and provides a fully quantum picture of electromagnetism and the weak and strong nuclear forces.
As standard as it claims to be, this massive monument of modern physics isn't as complete as we'd like it to be. We know of some creatures in our universe that don't fit under our one-size-fits-all umbrella, and they'll get some attention in our discussion very soon.
Oh, and there's no explanation for gravity. At the current state of play in our understanding of the universe, gravity stands alone. The force that Newton identified as universal, the force that swung the planets in their orbits so regularly that Kepler could find a deep pattern in their motions—the force that, perhaps, we're most intimately familiar with—does not have a home in our quantum-backed view of the world.
As beautiful and complex and elegant as general relativity is, we know it's incomplete. It never got the quantum makeover that the other forces did. All attempts to unify it under a comprehensive picture (a “theory of everything”) or, failing that summit, to settle for a “just a theory of quantum gravity” base camp, have utterly failed.
It's a problem of infinities. Quantum field theory calculations are notoriously difficult; the mathematics have a tendency to blow up in unexpected and unwanted places, rendering further calculations (and any predictions) useless. For a long time it was thought that quantum field theory would be completely unusable as a physical theory. Then, in 1948, Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga showed a path forward, essentially by tucking away all the unpleasant infinities into a small collection of terms, then replacing those terms with known constants like the electron mass.
It was, as usual, an ugly hack, but it worked, and the entire standard model eventually flowed from these methods. But gravity remained resistant. Including a dynamic space-time in the calculations of fundamental particle interactions adds too many infinities to package up; it's ten gallons of infinities in a five-gallon bucket.
This is why the initial moments of the big bang are so fascinating. Not just because, hey, we like to know stuff about the universe, but also because this is the era when quantum gravity actually mattered. We could never find a solution for bringing gravity into the quantum fold, and doing so wouldn't affect our daily lives one bit. But if we're trying to build a complete picture of the universe, which we have been since the days of Kepler and Galileo, then we need to crack the gravitational puzzle to unlock those first moments.
Our universe was born in mystery, but that doesn't mean that puzzling specters don't still haunt the modern-day cosmos. By the 1960s we had firmly established both the big bang and beginnings of the standard model. We knew the universe both inside and out. That would perhaps be the last time we would feel so assured in our knowledge.
Let's just go ahead and assume that you're a little confused. Don't worry, I won't judge. We've all been there. Trust me. Answers cosmological don't come easy—it's not like our brains were hardwired for pondering the expansion of a universe billions of light-years across, so there's bound to be some poor connections made between the mathematics that we use to describe our reality and the words that I'm using to describe the mathematics. So let's take a little break from our breakneck race through cosmology and cosmological history to settle some old scores, once and for all.
Like the good teacher I pretend to be, I've tried to anticipate some of your questions:
WHAT DOES IT MEAN FOR THE UNIVERSE TO “EXPAND”?
Although the analogies come in handy in some limited cases, I want you to stop thinking of balloons inflating, bread rising in the oven, or anything else. Just simply absorb this bare-naked observational statement: on average, at large scales, all galaxies in our universe are moving away from each other. Take a snapshot of all the galaxies in the universe and record the distances between them. Wait a while. How long? It depends—how long is your ruler? Take another snapshot and repeat your distance measurements. The second set will be bigger numbers than the first set. And there it is: the expansion of the universe.
WHERE IS THE CENTER?
It's right here, where you're standing. Surprised? I thought we junked that whole Earth-centered business. The new wrinkle is that “You're the center of the universe” is now a meaningless statement. From any perspective, anywhere, on any planet in any galaxy, they will view themselves to be the center. Since every galaxy moves away from every other galaxy, the “center” is arbitrary. From our perspective, it looks like everybody is fleeing from the Milky Way. From Andromeda, same story. Pick the farthest, dimmest galaxy you can spot. If there are aliens in the galaxy, they'll come to the same conclusions: the universe is expanding from them. “Center” doesn't have any meaning in an expanding u
niverse.
WHERE DID THE BIG BANG HAPPEN?
You really won't let this go, will you? The universe has no center. The big bang didn't happen somewhere over there. It happened everywhere. It happened in the room you're sitting in, in the distant galaxies, and in all the voids between. There's no place in the sky you can vaguely gesture to and say, “It happened roughly over there.” The big bang wasn't an explosion in space, it was an explosion of space. It happened everywhere simultaneously. It was a distinct moment in time that sits in the finite past of everything in the universe, not a point in space that everyone can, er, point to.
WHERE IS THE EDGE OF THE UNIVERSE?
Just as it has no center, it has no edge. I know, I know, it's very hard to imagine something with structure but without any outside. Look, if the universe had an edge, like a wall, separating universe from not-universe, then the not-universe would be a thing, and since by definition the universe is all the things, we would have to include it in the definition, and we'd be right back to where we started. If the universe is infinite, then we don't even have to think about it anymore. If the universe is finite, it gets a little harder to contemplate, since we're not used to the concept of objects having limited spatial extent but no boundary.
CAN I GET A METAPHOR, PLEASE?
Fine. Imagine the surface of the Earth. Just the surface, nothing else. Every location on the surface can be perfectly described by two numbers: latitude and longitude. Where is the center of the surface of the Earth? Notice I did not say “the center of the Earth.” I'll ask again to really make it clear: where is the center of the two-dimensional surface of the Earth? There isn't one. Where's the edge of the surface of the Earth? There isn't one (in two dimensions). Does the surface of the Earth have finite size? Yeah, 196.9 million square miles. Does it have a boundary? No.
ARE YOU SAYING THAT THE UNIVERSE IS CURVED LIKE THE EARTH?
Yes, but no. The universe may be curved at very large scales, but it doesn't matter. The point is that finite structures don't need to have a boundary in order to be a thing. Sure, we can easily visualize the surface of the Earth by imagining it embedded in a higher three-dimensional setting, but it's a mistake to think that everything must be embedded like that. The three-dimensional universe (ahem, four-dimensional, but let's focus on just space right now) could be embedded in a four-dimensional spatial structure, but it doesn't have to be for all the math to work out. It's just one of these weird things where the math is totally chill about it, but it's hard to express in English, let alone paint a picture in our brains. We're just not wired to conjure up images of three-dimensional, expanding, finite things. Sorry.
I THOUGHT YOU SAID THE UNIVERSE WAS FLAT.
One, that's not a question, and two, you're skipping ahead in the book.
SO WHAT IS IT EXPANDING INTO?
OK, I can't be too hard on you for not cracking this nut. The answer isn't “nothing” or even “something else.” The universe has no outside, and no edge. This is the real kicker: this question doesn't even make sense when it comes to the universe. There simply isn't an answer, but not because we don't know, but because the question can't be formulated. “What color is a cat's meow?” has all the correct English words and grammatical structure, but it's not a question we can answer. There is simply no such thing as an outside to the universe.
HOW BIG IS THE UNIVERSE?
Current estimates (which are very good, thank you very much) pin the whole observable universe to be a sphere about ninety-three billion light-years across. That's a big universe.
HOLD ON A SEC, WHAT DO YOU MEAN BY “UNIVERSE”?
I'll admit it, I've been playing a little fast and loose with my definitions. In one chapter I say that the universe is impossibly large—due to inflation—or maybe even infinitely big, but here I just gave it a size. When people (like me) refer to the size of the universe, we usually mean the observable universe, the limit of what we can see based on the age of the universe. It's the distance to the “horizon,” which, like a horizon on Earth, is…the limit of what you can see. The cosmic microwave background sits juuuust inside this horizon, and so for all practical purposes, it is the farthest thing we can see. But there is much more universe that we can't see—more galaxies, stars, solar systems, farm fields. That's the whole entire universe, but since it's completely inaccessible to us, can never affect us, and frankly doesn't care much for us, it doesn't matter. At all, so just ignore it.
UH, OK. WELL, HOW OLD IS THE UNIVERSE?
13,799,000,000 years, plus or minus 21 million years “since” the big bang. Yes, we know it that precisely,1 and yes, we're very proud of ourselves.
DOESN'T THAT MEAN THE UNIVERSE EXPANDS FASTER THAN LIGHT?
Well, yeah. The radius of the universe is bigger than 13.8 billion light-years. So superluminal expansion is a thing, especially during inflation (that was kind of the point). And even now! In an expanding universe, the farther you go from the Milky Way, the faster the rate of recession. Double the distance, double the speed. Eventually you'll come upon a distance that gives a speed faster than light. What's the big deal? Oh, you think that's a problem with special relativity, which set a universal speed limit? Haven't we, like, tested that or something?
Come here, child; let me share a secret with you. Special relativity is a local law of physics. The quantity we call “speed” is really only something you can measure nearby: you'll never measure the speed of a rocket blasting in front of your face to be greater than light. But a galaxy on the distant edge of the universe? It can have any “speed” it wants—if its redshift implies that it's going faster than light, it just means that the expansion of the universe is carrying it away so fast that you'll never, ever catch up to it. Even if you really want to.
HOW CAN WE ALL AGREE ON THE AGE? ISN'T TIME RELATIVE?
Yes, time is relative and not all clocks tick at the same tock…in special relativity. But the game of cosmology is played with general relativity, which is, you guessed it, more general. While usually time and space are all mixed together in a single cotton-poly blend of a fabric, in a homogeneous, isotropic universe (like the one we live in), time splits off from the spatial dimensions and ticks away comfortably at its own preferred rate. Due to the way the cosmic microwave background was emitted (across the entire universe at about the same time in about the same way), you can use that to find the heart of the cosmological clock. No matter your motion through the universe, once you measure the CMB, you can compute a frame of reference that is, at rest, relative to the universe. Once you know that, you can measure the universally common time (called the conformal time if you're feeling fancy) since the big bang.
IS MORE SPACE BEING CREATED, OR DOES THE EXISTING SPACE STRETCH?
Does it matter?
HOW CAN GRAVITY MAKE THINGS EXPAND?
It's not that gravity is, per se, making everything expand. It's that the behavior of the universe writ large is determined by its initial conditions and its contents. In the framework of general relativity, the universe found itself in an expanding state, and so that's what it's going to do unless somebody tells it otherwise.
IF THE EARLY UNIVERSE WAS SO DENSE, WHY DIDN'T IT COLLAPSE INTO A BLACK HOLE?
Remember that black holes, those infinitely dense bastards of the cosmos, are things in space. It's hard for all of space (i.e., the universe) to be a black hole: it's a different setup. The catastrophic, unstoppable gravitational collapse that leads to the formation of a black hole is driven by differences in density from place to place. But the extremely early universe was equally extremely uniform: despite its overall global density, there wasn't much difference within the cosmos at the time. It's only later that contrast arises.
IF BOTH SOLUTIONS ARE POSSIBLE, WHY IS THE UNIVERSE EXPANDING RATHER THAN CONTRACTING?
Now that's a good question.
Have you ever played one of those games where you look at a super-zoomed-in image of a common household object and try to guess what it is? It's unre
al. Below the threshold of normal human vision, everything just looks so freaky. What appears to be alien landscapes or monsters from your worst nightmares turns out to be shoelaces or stains on a coffee mug. When the micro is brought into the macro, when structures usually hidden beneath detection come into the realm of normal experience, it's unsettling.
A few hundred thousand years in, our universe needed a little unsettling. After the release of what would become the cosmic microwave background, the light was free; the universe quickly became dark. With the inevitable cosmic expansion that dictates so much of the physics of this story, the light that once so brilliantly flooded the universe shifted down from the intense white-hot energy of its initial release to a smoldering red, eventually slipping out of the visible altogether. For the first time in its exotic, strange journey, the universe experienced true coldness.
As the universe celebrated its one-millionth birthday, it was practically geriatric. Nothing substantial or worthy of note had happened to it since the flash of recombination. No radical phase transitions. No battles between competing forces. Matter had finally dominated over all other forms of energy density—it was now the big cheese in the universe, but it inherited a bleak, featureless landscape.
It seemed as though the universe, before it even had a chance to really get going, was locked into a grim, boring fate. Like when you're stuck watching a movie you don't really care for, it resigned itself to sit back and maybe at least catch a nap. Cooling and expansion—that's it. That's all that is left for the universe to do. You can't fight gravity, after all, and it's the dictates of general relativity that put the universe in this state.
The expansion is even slowing down—unbelievable! With matter in charge, a slowdown is inevitable. The expansion rate of the universe is intimately wedded to the proportion of the various contents within it, and with radiation not just losing dominance but rapidly plunging to essentially insignificant levels of background annoyance, the expansion has to listen to the voice of matter and matter alone. And that matter is self-gravitating: it pulls on itself and everything around it.
Your Place in the Universe Page 14