Welcome to the Universe

An Astrophysical Tour

Neil deGrasse Tyson, Michael A. Strauss, J. Richard Gott

• Publisher: Princeton University Press
• Year: 2016
• ISBN:
  9781400883226
• Topic: Scienze fisiche
• Subtopic: Astronomia e astrofisica

The New York Times bestselling tour of the cosmos from three of today's leading astrophysicists Welcome to the Universe is a personal guided tour of the cosmos by three of today's leading astrophysicists. Inspired by the enormously popular introductory astronomy course that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton, this book covers it all—from planets, stars, and galaxies to black holes, wormholes, and time travel.Describing the latest discoveries in astrophysics, the informative and entertaining narrative propels you from our home solar system to the outermost frontiers of space. How do stars live and die? Why did Pluto lose its planetary status? What are the prospects of intelligent life elsewhere in the universe? How did the universe begin? Why is it expanding and why is its expansion accelerating? Is our universe alone or part of an infinite multiverse? Answering these and many other questions, the authors open your eyes to the wonders of the cosmos, sharing their knowledge of how the universe works.Breathtaking in scope and stunningly illustrated throughout, Welcome to the Universe is for those who hunger for insights into our evolving universe that only world-class astrophysicists can provide.

1

THE SIZE AND SCALE
OF THE UNIVERSE

NEIL DEGRASSE TYSON

We begin with the stars, then ascend up and away out to the galaxy, the universe, and beyond. What did Buzz Lightyear say in Toy Story? “To Infinity and Beyond!”

It’s a big universe. I want to introduce you to the size and scale of the cosmos, which is bigger than you think. It’s hotter than you think. It is denser than you think. It’s more rarified than you think. Everything you think about the universe is less exotic than it actually is. Let’s get some machinery together before we begin. I want to take you on a tour of numbers small and large, just so we can loosen up our vocabulary, loosen up our sense of the sizes of things in the universe. Let me just start out with the number 1. You’ve seen this number before. There are no zeros in it. If we wrote this in exponential notation, it is ten to the zero power, 10⁰. The number 1 has no zeros to the right of that 1, as indicated by the zero exponent. Of course, 10 can be written as 10 to the first power, 10¹. Let’s go to a thousand—10³. What’s the metric prefix for a thousand? Kilo- kilogram—a thousand grams; kilometer—a thousand meters. Let’s go up another 3 zeros, to a million, 10⁶, whose prefix is mega-. Maybe this is the highest they had learned how to count at the time they invented the megaphone; perhaps if they had known about a billion, by appending three more zeroes, giving 10⁹, they would have called them “gigaphones.” If you study file sizes on your computer, then you’re familiar with these two words, “megabytes” and “gigabytes.” A gigabyte is a billion bytes.1 I’m not convinced you know how big a billion actually is. Let’s look around the world and ask what kinds of things come in billions.

First, there are 7 billion people in the world.

Bill Gates? What’s he up to? Last I checked, he’s up to about 80 billion dollars. He’s the patron saint of geeks; for the first time, geeks actually control the world. For most of human history that was not the case. Times have changed. Where have you seen 100 billion? Well, not quite 100 billion. McDonald’s. “Over 99 Billion Served.” That’s the biggest number you ever see in the street. I remember when they started counting. My childhood McDonald’s proudly displayed “Over 8 Billion Served.” The McDonald’s sign never displayed 100 billion, because they allocated only two numerical slots for their burger count, and so, they just stopped at 99 billion. Then they pulled a Carl Sagan on us all and now say, “billions and billions served.”

Take 100 billion hamburgers, and lay them end to end. Start at New York City, and go west. Will you get to Chicago? Of course. Will you get to California? Yes, of course. Find some way to float them. This calculation works for the diameter of the bun (4 inches), because the burger itself is somewhat smaller than the bun. So for this calculation, it’s all about the bun. Now float them across the ocean, along a great circle route, and you will cross the Pacific, pass Australia, Africa, and come back across the Atlantic Ocean, finally arriving back in New York City with your 100 billion hamburgers. That’s a lot of hamburgers. But in fact you have some left over after you have circled the circumference of Earth. Do you know what you do with what you have left over? You make the trip all over again, 215 more times! Now you still have some left over. You’re bored going around Earth, so what do you do? You stack them. So after you’ve gone around Earth 216 times, then you stack them. How high do you go? You’ll go to the Moon, and back, with stacked hamburgers (each 2 inches tall) after you’ve already been around the world 216 times, and only then will you have used your 100 billion hamburgers. That’s why cows are scared of McDonald’s. By comparison, the Milky Way galaxy has about 300 billion stars. So McDonald’s is gearing up for the cosmos.

When you are 31 years, 7 months, 9 hours, 4 minutes, and 20 seconds old, you’ve lived your billionth second. I celebrated with a bottle of champagne when I reached that age. It was a tiny bottle. You don’t encounter a billion very often.

Let’s keep going. What’s the next one up? A trillion: 10¹². We have a metric prefix for that: tera-. You can’t count to a trillion. Of course you could try. But if you counted one number every second, it would take you a thousand times 31 years—31,000 years, which is why I don’t recommend doing this, even at home. A trillion seconds ago, cave dwellers—troglodytes—were drawing pictures on their living room walls.

At New York City’s Rose Center of Earth and Space, we display a timeline spiral of the Universe that begins at the Big Bang and unfolds 13.8 billion years. Uncurled, it’s the length of a football field. Every step you take spans 50 million years. You get to the end of the ramp, and you ask, where are we? Where is the history of our human species? The entire period of time, from a trillion seconds ago to today, from graffiti-prone cave dwellers until now, occupies only the thickness of a single strand of human hair, which we have mounted at the end of that timeline. You think we live long lives, you think civilizations last a long time, but not from the view of the cosmos itself.

What’s next? 10¹⁵. That’s a quadrillion, with the metric prefix peta-. It’s one of my favorite numbers. Between 1 and 10 quadrillion ants live on (and in) Earth, according to ant expert E. O. Wilson.

What’s next? 10¹⁸, a quintillion, with metric prefix exa-. That’s the estimated number of grains of sand on 10 large beaches. The most famous beach in the world is Copacabana Beach in Rio de Janeiro. It is 4.2 kilometers long, and was 55 meters wide before they widened it to 140 meters by dumping 3.5 million cubic meters of sand on it. The median size of grains of sand on Copacabana Beach at sea level is 1/3 of a millimeter. That’s 27 grains of sand per cubic millimeter, so 3.5 million cubic meters of that kind of sand is about 10¹⁷ grains of sand. That’s most of the sand there today. So about 10 Copacabana beaches should have about 10¹⁸ grains of sand on them.

Up another factor of a thousand and we arrive at 10²¹, a sextillion. We have ascended from kilometers to megaphones to McDonald’s hamburgers to Cro-Magnon artists to ants to grains of sand on beaches until finally arriving here: 10 sextillion—

the number of stars in the observable universe.

There are people, who walk around every day, asserting that we are alone in this cosmos. They simply have no concept of large numbers, no concept of the size of the cosmos. Later, we’ll learn more about what we mean by the observable universe, the part of the universe we can see.

While we’re at it, let me jump beyond this. Let’s take a number much larger than 1 sextillion—how about 10⁸¹? As far as I know, this number has no name. It’s the number of atoms in the observable universe. Why then would you ever need a number bigger than that? What “on Earth” could you be counting? How about 10¹⁰⁰, a nice round-looking number. This is called a googol. Not to be confused with Google, the internet company that misspelled “googol” on purpose.

There are no objects to count in the observable universe to apply a googol to. It is just a fun number. We can write it as 10¹⁰⁰, or if you don’t have superscripts, this works too: 10^100. But you can still use such big numbers for some situations: don’t count things, but instead count the ways things can happen. For example, how many possible chess games can be played? A game can be declared a draw by either player after a triple repetition of a position, or when each has made 50 moves in a row without a pawn move or a capture, or when there are not enough pieces left to produce a checkmate. If we say that one of the two players must take advantage of this rule in every game where it comes up, then we can calculate the number of possible chess games. Rich Gott did this and found the answer was a number less than 10^(10^4.4). That’s a lot bigger than a googol, which is 10^(10^2). You’re not counting things, but you are counting possible ways to do something. In that way, numbers can get very large.

I have a number still bigger than this. If a googol is 1 followed by 100 zeros, then how about 10 to the googol power? That has a name too: a googolplex. It is 1, with a googol of zeroes after it. Can you even write out this number? Nope. Because it has a googol of zeroes, and a googol is larger than the number of atoms in the universe. So you’re stuck writing it this way: 10^googol, or 10^{10^100} or 10^(10^100). If you were so motivated, I suppose you could attempt to write 10¹⁹ zeros, on every atom in the universe. But you surely have better things to do.

I’m not doing this just to waste your time. I’ve got a number that’s bigger than a googolplex. Jacob Bekenstein invented a formula allowing us to estimate the maximum number of different quantum states that could have a mass and size comparable to our observable universe. Given the quantum fuzziness we observe, that would be the maximum number of distinct observable universes like ours. It’s 10^(10^124), a number that has 10²⁴ times as many zeros as a googolplex. These 10^(10^124) universes range from ones that are scary, filled with mostly black holes, to ones that are exactly like ours but where your nostril is missing one oxygen molecule and some space alien’s nostril has one more.

So, in fact, we do have some uses for some very large numbers. I know of no utility for numbers larger than this one, but mathematicians surely do. A theorem once contained the badass number 10^(10^(10^34)). It’s called Skewe’s number. Mathematicians derive pleasure from thinking far beyond physical realities.

Let me give you a sense of other extremes in the universe.

How about density? You intuitively know what density is, but let’s think about density in the cosmos. First, explore the air around us. You’re breathing 2.5 × 10¹⁹ molecules per cubic centimeter—78% nitrogen and 21% oxygen.

A density of 2.5 × 10¹⁹ molecules per cubic centimeter is likely higher than you thought. But let’s look at our best laboratory vacuums. We do pretty well today, bringing the density down to about 100 molecules per cubic centimeter. How about interplanetary space? The solar wind at Earth’s distance from the Sun has about 10 protons per cubic centimeter. When I talk about density here, I’m referencing the number of molecules, atoms, or free particles that compose the gas. How about interstellar space, between the stars? Its density fluctuates, depending on where you’re hanging out, but regions in which the density falls to 1 atom per cubic centimeter are not uncommon. In intergalactic space, that number is going to be much less: 1 per cubic meter.

We can’t get vacuums that empty in our best laboratories. There is an old saying, “Nature abhors a vacuum.” The people who said that never left Earth’s surface. In fact, N...