To get a sense of the size of space, out to the edge of the observable universe, let's use a Three-Step Scale Model, something you can remember and tell other people. It starts with a one in 500 million scale of real space, taking the Earth down to the size of a walnut. On this scale, the moon is a pea at arm's-length. The Sun is a three meter ball about 300 meters away, and the entire solar system spans about 15 kilometers or 10 miles. It's so boring to realize that the sum of our space exploration involving humans has only taken us this arms length distance, from the Earth to the Moon. Especially when you realize that on this scale, the next nearest star, would be 50,000 kilometers away, not even on the Earth's surface in this scale model. That's the prodigious task awaiting us if we ever travel to the stars. This scale of reduction is not chosen accidentally. If we scale space this way, we also scale light-speed by the same factor, taking the fleet footed light traveling at 300,000 kilometers per second, down to a slow walk. Therefore, light traveling through the scale model moves at walking speed, and we can imagine that light would take about a second, to travel from the Earth to the Moon an arm span. You can remember the hiccuping conversations of the Apollo astronauts, due to the two and a half second time delay of voices traveling there and back. The sun would be an eight minute walk. The nearest star however would be years to get to, the solar system perhaps five hours across. These are light travel times in the solar system and to the next nearest star, still small fractions of a human lifespan. We have the solar system in view within the size of a city, but the nearest star is not even on our planet. So let's shrink the scale model by second scale factor, this time 10 million. With this reduction, the solar system shrinks such that the outer periphery of the planets would be the size of sand grain, about a millimeter. The sun at the center would be invisibly small, microscopic. With this second reduction of scale, the typical distance between stars in the Milky Way is about 10 meters. So in an average living room, there might be a couple of sand grains, representing adjacent stars. Space is vastly empty. On this scale, the Milky Way, our system of stars would be the size of a state like Massachusetts, or a country like Switzerland, and we can imagine billions of stars scattered across the state with 10 meter distances between them. That's our galaxy, but still we only have one galaxy in view, and the universe is a lot larger than that. So let's shrink the model even more, this time by a factor of a million. If you're keeping track, we've gone down nearly nine orders of magnitude, then seven, then six, a total of 22 orders of magnitude, or 1 in 5 times 10 to the 21 scale model. Reducing this third factor, the entire Milky Way reduces to about the size of a dinner plate, and we can imagine the disk of our galaxy that size. In the nearby region of our universe, the next nearest galaxy is perhaps five or 10 meters away, Andromeda, another dinner plate. Again, in a living room, perhaps only two plates representing spiral galaxies, and maybe a handful or a dozen cotton wool balls representing the dwarf galaxies scattered through that volume. On this scale, the visible universe is now the size of Massachusetts or Switzerland, but of course extending in three-dimensions, and it's scattered with about 100 billion dinner plate size galaxies. Now we have a sense of the visible universe, and Cosmology actually tells us that there may be space beyond that, that we cannot easily observe. It's useful to imagine these Powers of Ten, and see what structures are seen on different scales moving up from the human scale. What we notice is that there are scales where there are structure; humans or planets or perhaps stars themselves, and then there are whole orders of magnitude of scale where there's nothing. Emptiness. The emptiness between stars, the emptiness between galaxies. If we continue Powers of Ten down into the atom, something similar happens. The space between atoms is large, and the space within an atom before you get to the atomic nucleus, is also large and mostly empty. This alternating sequence of structure and emptiness, is typical of the physical universe, all the way from quarks to the cosmos. The picnic near the lakeside in Chicago is the start of a lazy afternoon, early one October. We begin with a scene one meter wide, which we view from just one meter away. Now, every 10 seconds, we will look from 10 times farther away, and our field of view will be 10 times wider. This square is 10 meters wide, and in 10 seconds, the next square will be 10 times as wide. Our picture will center on the picnickers, even after they've been lost to sight. One hundred meters wide, the distance a man can run in 10 seconds, cars crowd the highway, power boats lie at their docks. The colorful bleachers are Soldier's Field. This square's a kilometer wide, 1,000 meters, the distance a racing car can travel in 10 seconds, we see the great city on the lake shore. Ten to the fourth meters, 10 kilometers, the distance a supersonic airplane can travel in 10 seconds, we see first the rounded end of Lake Michigan, then the whole great lake. Ten to the fifth meters, the distance their orbiting satellite covers in 10 seconds, long parades of clouds -the day's weather in the Middle West. Ten to the sixth, a one with six zeros, a million meters, soon the Earth will show as a solid sphere. We are able to see the whole Earth now, just over minutes along the journey. The Earth diminishes into the distance, but those background stars are so much farther away, but they do not yet appear to move. A line extends at the true speed of light in one second that half crosses the tilted orbit of the moon. Now we mark a small part of the path, in which the Earth moves about the Sun. Now the orbital paths of the neighbor planets: Venus, and Mars, then Mercury. Entering our field of view is the glowing center of our solar system, the Sun, followed by the massive outer planets, swinging wide in their big orbits. That odd orbit belongs to Pluto: a fringe of a myriad comets too faint to see, completes the solar system. Ten to the 14th. As the solar system shrinks to one bright point in the distance, our sun is plainly now only one among the stars. Looking back from here we note four Southern constellations still much as they appear from the far side of the earth. This square is 10_16 meters. One light-year, not yet out to the next star. Our last 10-second step took us 10 light-years further, the next will be a hundred. Our perspective changes so much in each step now that even the background stars will appear to converge. At last, we pass the bright star Arcturus, and some stars of the Dipper. Normal but quite unfamiliar, stars and clouds of gas surround us as we traverse the Milky Way galaxy. Giant steps carry us into the outskirts of the galaxy. As we pull away, we begin to see the great flat spiral facing us. The time and path we chose to leave Chicago has brought us out of the galaxy along a course nearly perpendicular to its disk. The two little satellite galaxies of our own are the Clouds of Magellan, 10_22 power, a million light-years. Groups of galaxies bring a new level of structure to the scene. Glowing points are no longer single stars, but whole galaxies of stars seen as one. We pass the big Virgo cluster of galaxies among many others. A hundred million light-years out, as we approach the limit of our vision, we pause to start back home. This lonely scene, the galaxies like dust is what most of space looks like. This emptiness is normal. The richness of our own neighborhood is the exception. The trip back to the picnic on the lakefront will be a sped-up version reducing the distance to the earth's surface by 1 power of 10 every two seconds. In each two seconds, it will appear to cover 90 percent the remaining distance back to Earth. Notice the alternation between great activity and relative inactivity. A rhythm that will continue all the way into our next goal, a proton in the nucleus of a carbon atom beneath the skin on the hand of a sleeping man at the picnic. Ten to the nine meters, 10_8, 7, 6, 5, 4, 3, 2, 1, we are back at our starting point. We slow-up at one meter, 10_0 power. Now, we reduce the distance to our final destination by 90 percent every 10 seconds. Each step much smaller than the one before. At 10_-2, one one-hundreth of a meter, one centimeter, we approach the surface of the hand. In a few seconds, we'll be entering the skin, crossing layer-after-layer from the outermost dead cells into a tiny blood vessel within. Skin layers vanish in turn, an outer layer of cells, fealty collagen. A capillary containing red blood cells and a roughly lymphocyte. We enter the white cell. Among its vital organelles, the porous wall of the cell nucleus appears. The nucleus within holds the heredity of the man in the coiled coils of DNA. As we close in, we come to the double helix itself, a molecule like a long twisted ladder whose rungs of paired bases spell out twice in an alphabet of four letters, the words of a powerful genetic message. At the atomic scale, the interplay of form and motion becomes more visible. We focus on one commonplace group of three hydrogen atoms bonded by electrical forces to a carbon atom. Four electrons make up the outer shell of the carbon itself. They appear in quantum motion as a swarm of shimmering points. At 10 to the minus 10 meters, one angstrom, we find ourselves right among those outer electrons. Now, we come upon the two inner electrons held in a tighter swarm. As we draw toward the atom's attracting center, we enter upon a vast inner space. At last the carbon nucleus. So massive and so small, this carbon nucleus is made up of six protons and six neutrons. We are in the domain of universal modules. There are protons and neutrons in every nucleus, electrons in every atom. Atoms bonded into every molecule out to the farthest galaxy. As a single proton fills our seen, reached the edge of present understanding, are these some quirks that intends interaction? Our journey has taken us through 40 powers of 10. If now the field is one unit, then when we saw many clusters of galaxies together, it was 10_40 or one and 40 zeros. To get a sense of the emptiness of space, let's compare a typical chunk of the universe to the air we're breathing. A typical one-inch cube of the air you're breathing holds about 10_22 atoms, 10,000 billion, billion atoms. A typical one-inch cube of the universe doesn't even hold a single atom. It's vastly pure vacuum with almost no matter in it, and very little radiation either. In fact, if you wanted to directly compare these two situations, you'd have to take that one inch cube of the air you're breathing and stretch the top end of it all the way to the Andromeda Galaxy, M31, two-and-a-quarter million light years before the vacuum was as good as the vacuum of intergalactic space. The span of the visible universe is about 92 billion light-years, 46 billion light-years in any direction. It's a phenomenal number and hard to comprehend. We can approach it with a three-step scale model, wherein 23 orders of magnitude of reduction, we take the earth first down to the size of a walnut, and then shrink another eight orders of magnitude, such that the solar system is a grain of sand, and then shrink another eight orders of magnitude until a galaxy is like a plate, and the visible universe is the size of the continental United States. It takes analogies like this and scale models to get a sense of the vastness of the universe.
