Your Place in the Universe

by Paul M. Sutter

  Kepler was right—it is more accurate to think of the solar system as just that, solar—but for all the wrong reasons. And his legacy survived not on its scientific merits but on its astrological usefulness. Scholarly discourse slowly abandoned the concept of heavenly crystal spheres in the decades following Kepler's input. There simply wasn't a need: it was much easier to talk about the universe as if the sun hung at the center and the planets zoomed along on their little elliptical racetracks.

  But his story serves as an object lesson for this book. The universe is far, far messier than we would prefer it to be. Wouldn't it be great if a few simple circles (and heck, let's be generous and toss in a few epicycles too) were enough to completely describe the cosmos?

  Unfortunately, Mother Nature isn't that kind to us. Ellipses are more complicated than circles, for sure, but to Kepler that was a boon rather than a curse. With this much more rich information, he had enough clues to perceive an orderly pattern. He didn't fully understand the causes or physical implications of his third law, but he did discern it.

  And that's why Kepler, as nutty as he was, even in the eyes of his peers, was onto something good.

  Oh, right, Galileo. He was kind of a big deal, operating at the same time as Kepler, living in Italy in the shadow of his frenemy the Catholic Church. He was the astronomer's astronomer and the curmudgeon's curmudgeon. A rude dude who straight up called his boss an idiot (pro tip for the Renaissance scientist: don't tick off the pope, who also happens to wield supreme temporal power over your land). I'm not saying the church was in the right putting him under house arrest for arguing against the orthodoxy, but Galileo didn't exactly do himself any favors. The full story of Galileo is wonderful and convoluted and wonderfully convoluted, and also the subject of another book.13

  Instead, I want to focus on what Galileo saw with his newfangled telescope. The instrument itself is deceptively simple. On paper it looks so easy a kindergartener could assemble it: a couple of curved lenses and a tube. The physics of optics does all the rest. And while Galileo didn't invent the telescope per se, he certainly invented the astronomical telescope, which is what we usually think of when we use the word “telescope.”

  The device had been developed within Galileo's lifetime, and, people being people, I'm sure somebody somewhere pointed it up at the night sky to see what he could see. Unfortunately, that person couldn't see much; the trick to telescopes isn't in their construction but in their finishing. You have to polish the lens to an extremely high level of precision so the path of light gets bent in just the right way, or you get a smudgy mess on the other end.

  A telescope does two things. First, it's just a bucket for light. Your pupil can only cram so much light into it at a time, and that sets a limit to the dimmest thing you can see (I'm, uh, glossing over some biological details here, but you get the idea). A wider telescope is like a wider eyeball: it can soak up photons that would normally just hit the rest of your face.

  The second thing a telescope does is magnify. It takes all that collected light and focuses it down to a smaller area so that it can fit in your eye. That operation turns small separations into big separations, so a minuscule dot on the horizon can be recognized as, say, a ship.

  “Hey, guys, there's a ship on the horizon…I think” was the current gold standard for telescopes until Galileo took a crack at it. With uncommon dedication, he made a lens so smooth, so flawless, that the celestial realm completely changed its character.14

  The moon, thought to be a smooth globe of marble, was instead a loose collection of jagged rocks. Jupiter was not alone—it was joined by four small moons that were obviously orbiting it. Saturn had two lumps on either side of it that, over the course of Galileo's repeated observations, shrank to thin slivers and disappeared—before reappearing again.

  The sun had spots that, after a little geometrical legwork, were shown to be attached to its surface. And that surface was spinning. Fast.

  Venus had phases. Phases. Like the moon. Since phases are a trick of perspective—the light from the sun illuminates only one side of an object at a time, and that side can be different from the one we view—the only way to make that work was for the sun to be at the center of the solar system.

  The universe that Galileo revealed was frightfully messy. With this joining Brahe's earlier discovery of a new star appearing and his demonstration that comets were not confined to our atmosphere,15 scholars (at this early stage, I hesitate to call them scientists in the sense we're used to) were quickly realizing that our home is a strange place indeed.

  What got Galileo into trouble (well, one of the things) was his insistence on circular orbits. He saw, right through the lens of his telescope, direct evidence for a sun-centered cosmos. He must have been aware of Kepler's work—Johannes wrote to him like an eager fanboy—but he either missed the memo on elliptical orbits or outright ignored it because it was caught up in mystic mumbo jumbo.

  It's interesting that Kepler and Galileo were tackling the same problem (the structure and contents of the universe) using different techniques (Kepler digging deep into mathematics and Galileo producing literal volumes of observations) and arriving at conclusions that seem at odds. But on closer inspection, their results were two sides of the same coin.

  Galileo saw firsthand a messy universe but insisted on simple, orderly circles to explain the orbits of the planets. Kepler found elegant geometric order in the chaos but argued that the universe was directly connected to our everyday lives. I can't think of better prototypical experimentalists and theorists.

  Put them together and you have the picture that modern cosmology—the study of the cosmos—brings us: we live in a simple universe that is connected to our daily lives.

  Wait, no, that's not right. It's the other combination: we live in a messy universe that doesn't care about us.

  That's it.

  You know, it's really hard to start the story of our universe at the place it should—the start of the universe—because strictly speaking, the universe doesn't have a beginning. Or maybe it does.

  It's complicated.

  Here's the problem. We live in an expanding universe. Every second of every day, galaxies are generally getting farther away from each other. Run the clock backward, and you quickly realize that in the past, galaxies were closer together. This is pretty straightforward logic, I suppose.

  Run the clock back further, and there aren't galaxies anymore—all the matter is too smooshed together. There's just a bunch of junk filling up the universe. Keep going, and eventually the entire universe, as big as it appears today, shrinks and shrinks to an infinitely small point. That is precisely what general relativity, our mathematical tool for understanding the evolution of the universe over these almost incomprehensible timescales, tells us: that at a finite time in the past (spoiler alert for later chapters: around 13.8 billion years ago), the universe was compressed into a singularity, a point of infinite density.

  Of course, that's wrong. Nature doesn't like infinities. But we have to separate what nature actually does from how we model it. Physics is a mathematical description of the world around us. And that mathematics provides a wonderful tool. For one, math compacts vague natural-language sentences into precise, meaning-filled equations. You could go on and on about how a wave of electromagnetic radiation propagates (and in fact I'm probably going to do that later) without getting all the details right, simply because English isn't really equipped to describe it. But a couple of neat equations can do all the work for us, summarizing and describing in one elegant go.1

  Math also forces logical consistency, which is handy when a physicist wants to make predictions. “If we assume this is true based on the evidence, then that must happen” is a soothing statement that calms us during bouts of midnight existential dread.

  But it does have its shortcomings. We can only provide approximate descriptions of nature, because we are fundamentally limited by uncertainties in measurement. Sometimes those approximations
are really really (really) good, so we don't care about the discrepancy anymore. But sometimes the math is so broken, so dysfunctional, that we can't use it to piece together what Mother Nature is whispering to us at all.

  And that's the case with singularities. When a singularity appears in a description, it's the mathematics itself telling you that you've gone too far—your fancy equations are no good here. It means you're doing something wrong, and the math wants no part of your shenanigans.

  Singularities are actually pretty common, at least in mathematics. If I model the force provided by a simple spring, I can use Hooke's law: The more I compress the spring, the harder it will push back on me. But if I were to compress it all the way, so that the spring was a single point, the force pushing back on me would be infinite. That seems like a dumb thing to say, but that's what Hooke's mathematics tells us.

  But duh, you can only compress a spring just so far until some other force takes over—like, say, the electric repulsion of the atoms in the metal, preventing them from squeezing down to infinity. The singularity appears in the math, but nature knows better.

  Now take this example and replace Hooke's law with general relativity, and the spring with the entire universe. Welcome to the cosmologist's nightmare.

  Einstein's theory of general relativity is fantastically easy to state: we all live embedded in space-time. The presence of mass or energy distorts space-time “underneath” it (in a three-dimensional sense, but there aren't any good English words for it), and that distortion tells other matter how to move. Put two kids on a trampoline: they can affect the motion of each other without touching. Now imagine that in four dimensions, and you have gravity.

  It's almost funny how a somewhat benign statement like the one above masks such a horrible snake pit of mathematics. General relativity itself is a set of ten complicated, interwoven equations describing the detailed relationship between space-time and matter and energy, plus some more equations governing how objects move. Heavy stuff.

  General relativity is the story of gravity, and at the very largest scales (i.e., bigger than galaxies), gravity is the only force with enough oomph. It's incredibly weak but affects all matter and energy across infinite range, and it's that staying power that provides its dominance at large scales. On balance the universe is neutral, so the electromagnetic force cancels out. The strong nuclear force peters out past an atomic nucleus, and the weak nuclear force is, well, weak. When it comes to cosmology, only gravity matters.

  Except when it doesn't, like in the earliest fraction of a fraction of second into the existence of the universe as we know it.

  Cosmology is the story of gravity at large scales, and general relativity is just fine and dandy for describing that gravity—giving us the very history of our cosmos. But there are singularities lurking within Einstein's greatest hit. We use general relativity to understand the evolution of our universe, and those mathematics say—and logic tells us—if we live in an expanding universe (and we do!), then at one time in the past, everything was crammed into an infinitely dense point.

  Unless something got in the way. Unless something prevented or replaced the inevitable collapse, stopping the universe from becoming infinitely dense—just significantly or even stupendously dense. Anything but infinite and we can handle it. And in fact, something must prevent it. We know that singularities don't actually appear in nature; they are flaws in our model of reality.

  So general relativity draws a line in the sand: we could mine the entire universe for information, extract every single bit of useful data from our observations, but we will never, ever understand the earliest moments of the universe unless we try some other tool in our mathematical toolbox. When it comes to the first 10−43 seconds, we simply have no idea what's going.

  It's here where speculation reigns. We have a relatively firm grasp of the history of the universe, but not its origins. Or even if origins is the right word. We haven't (yet) developed the mathematical language to describe these initial moments. Or even if initial is the right word.

  Maybe there's more “universe” happening before what we call the big bang (as you can see, this term is meant to describe not the birth of our universe but its very early history). Maybe the very concepts of space and time break down. Maybe there's no such thing as “before” the universe. There are a lot of speculative ideas beyond our known physical laws floating around in the minds of physicists and their arcane academic journals. Maybe string theory has an answer here, or was it loop quantum gravity? Who knows?2

  The singularity draws the eye of the theoretical physicist because it's an unambiguous signpost that there's more to be learned here. For all other times and scales in the universe, we have at least some guidance on how to proceed. But in this moment, when the universe has a temperature of more than 1032 Kelvin and is no bigger than 10−35 meters across, we don't have much to guide us.

  To give you a sense of the extremity of the tininess of this epoch—called the Planck era, by the way—hold out your hands as far as they can reach. Go ahead, you could use the stretch. The scale difference between the width of the observable universe today (about ninety-three billion light-years) and your outstretched hands is about the same as the scale difference between your outstretched hands and the size of the universe at this newborn state—if the universe were about a billion times wider back then.

  In other words, imagine how long it would take to stretch out your arms so wide that you could hug the present-day universe. The Planck-era universe would have to do that a billion times over to give you a friendly squeeze.

  I'm sorry—there just aren't a lot of useful analogies for these sorts of situations. The temperatures, densities, and length scales in operation at the early stages of our universe aren't something we normally come in contact with, so we don't have handy metaphors or explanatory tools at the ready. Usually in these situations we can instead appeal to the mathematics to guide us, like a distant lighthouse in a storm of nonsense, but even here the light is gone out.

  We don't understand the Planck era because we don't understand physics at those scales, but it is at least reassuring to know where our laws break down. And that Planck era, with its characteristic energy and length scales, isn't just pulled out of the Random Number Jar to sound impressive—there's a reason our understanding goes so haywire at numbers so small.

  Let's say you have to pick your top five most important physical constants that appear in our descriptions of the universe. Actually, skip that; I'll just tell you what they are. You have the familiar speed of light, which appears in electromagnetism and special relativity, and you need to include Newton's classic gravitational constant. You might not recognize the Coulomb constant, which is like the gravitational constant but for electricity, but it's important too. Plus you need to toss in the Boltzmann constant, which for gases connects things we can easily measure (like temperature) to things we can't (like energy of the gas particles).

  Last but certainly not least is the Planck constant itself, warily introduced by Max Planck in the early 1900s.3 Originally shoehorned into his math to help him understand the behavior of light (and one of its uses is to define the relationship between the wavelength of light and the amount of energy it carries), it quickly grew to become the numerical ambassador for quantum mechanics itself. I'll get into that story more later.

  All these constants help us relate one thing to another. If I have this much charge, how strong will its electric force be? Coulomb can tell us. If I start waving around some electric and magnetic fields, how fast will they move? Speed of light. How much mass do I need to hold down my coffee? Newton's got your back.

  These constants are like little governors for their respective domains of physics. What's really fun is when we start combining physics, and the relationships between these constants tell us when and where multiple areas of physics get together and start partying. To find out, we combine the governing constants in interesting ways, known as the Planck units.


  Take the Planck length, which combines Newton's constant, the speed of light, and the original Planck constant (sorry that his name keeps popping up in confusing ways; he was kind of smart and kind of important). That number comes out to about 1.6 × 10−35 meters…hey, wait a minute, that's the size of the universe where our physical theories break down!

  Now we can see why: the Planck constant tells us about where we need to care about quantum mechanics, and Newton's constant tells us the same for gravity. The Planck length is a scale where both gravity and quantum mechanics matter. It's not like the universe magically transforms into something weird and wonderful at those scales, but since the Planck length is constructed from other useful numbers, when you're trying to play the gravity-quantum matchmaking game, those same numbers are going to crop up. So think of the Planck length as a warning sign: here be dragons.

  And those are quantum gravity dragons. We do not, at the time of the writing of this book and most likely also at the time of your reading, have a quantum description of gravity. Why not? That's a long story, and probably a tale for another book.4 For our purposes, we simply don't have a single mathematical language that incorporates gravity into our quantum worldview. And it's that lack of language that prevents us from fully understanding those first moments in the universe, and especially what might come “before.”

  I'm purposely not spending a lot of time discussing what some speculative ideas might be for combining gravity with quantum mechanics and for the origins of the universe. Things like colliding branes and collapsing universal wave functions sound super awesome, but at this point they're one step away from pure fantasy. Not that such hypotheticals shouldn't be explored—far from it. We need creative ideas to move forward. But we're so far out on the ledge that it's hard to tell a good idea from a bad one. I would hate to waste your precious time describing in detail a concept that a year from now will be ruled out by experiment (or, more likely, go out of fashion), especially when there's so much more cool stuff to talk about.