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# 1.28 A Scale Model of Space

Intuition is useless when it comes to scales of time and space that are far beyond human experience. Take a scale model: the state map you might have in your car has a scale of 1 inch to 10 miles or so, shrinking space by a factor of 500,000. The globe in a school or office shrinks space even further. We can shrink space by any factor; choosing 1:300,000,000 brings the Earth down to 4 cm — the size of a golf ball. At this scale, if the Earth were in front of you, the Moon would be at arm's length, and not much bigger than a pea.Mars would be the size of a gumball, 800 feet away at its closest approach. Jupiter would be a beach ball a mile and a half away. And the Sun would be an incandescent globe fourteen feet across at a distance of 1500 feet.

So far, it's fairly comforting. Golf balls, peas, and beach balls are familiar objects. The entire solar system is 12 miles across — the size of a small town. Notice how empty space is; this small town contains a star the size of a bus at the center, nine planets (none larger than a beach ball), asteroids and meteors that would be no bigger than specks of dust, and nothing else. Wait, we're just getting started. At a 1:300,000,000 scale, the nearest stars are 20,000 miles or more distant. In other words, if each solar system is a "town," space is so empty that the Earth's surface would contain only one town.

The scale we've chosen is not arbitrary. In this model, speed is also reduced by the same factor. Light, which moves so fast in everyday life that its departure and arrival cannot be distinguished, is slowed to a manageable 1 meter per second, a brisk walking speed. It takes eight minutes for light to stroll from the Earth to the Sun, and five hours to walk across the solar system. But if you set out for the nearest star at light speed, it's like walking around the Earth. If you took no rest breaks and had no oceans to stop you, it would take several years. We see the Sun as it was eight minutes ago, Pluto as it was five hours ago, and the nearest stars as they were several years ago. It makes no sense to ask what the universe is like "now" because light is the fastest messenger we know of. Also, we're limited in our vision by light's speed, only able to see regions from which light has been able to reach us in the age of the universe.

One huge factor of reduction doesn't bring most of the universe into view, so we apply a second factor of 300,000,000. Our scale is now 1:1019 or nineteen powers of ten of reduction. The Sun reduces to the size of an atom and other stars shrink to microscopic scales. The typical distance between them is 3mm. The Milky Way is a twisting spiral of stars about 100 feet across; the size of large house. Within this "house" are 400 billion stars. The nearest house is a mile away. Now we can visualize the extragalactic universe, where house-sized galaxies, each containing billions of stars, are sprinkled across a vast landscape with the separation of farmland villages on the Great Plains.

In this analogy, the observable universe is about the size of the Earth. But here the analogy breaks down. In our universe, we don't see the contents of the universe laid out before us at a snapshot in time. We see the outer edge of the Milky Way as it was 20,000 years ago. For example, if we ever received a signal from a species on the far side of the galaxy, it may already have gone extinct by the time we can reply. We see the nearest galaxies as they were 3 or 4 million years ago, and the most distant galaxies as they were 11 or 12 billion years ago. There are regions of the universe we've not yet seen and some we'll never see. We are bounded by time not space.Intuition is useless when it comes to scales of time and space that are far beyond human experience. Take a scale model: the state map you might have in your car has a scale of 1 inch to 10 miles or so, shrinking space by a factor of 500,000. The globe in a school or office shrinks space even further. We can shrink space by any factor; choosing 1:300,000,000 brings the Earth down to 4 cm — the size of a golf ball. At this scale, if the Earth were in front of you, the Moon would be at arm's length, and not much bigger than a pea.Mars would be the size of a gumball, 800 feet away at its closest approach. Jupiter would be a beach ball a mile and a half away. And the Sun would be an incandescent globe fourteen feet across at a distance of 1500 feet.

So far, it's fairly comforting. Golf balls, peas, and beach balls are familiar objects. The entire solar systemis 12 miles across — the size of a small town. Notice how empty space is; this small town contains a star the size of a bus at the center, nine planets (none larger than a beach ball), asteroids and meteors that would be no bigger than specks of dust, and nothing else. Wait, we're just getting started. At a 1:300,000,000 scale, the nearest stars are 20,000 miles or more distant. In other words, if each solar system is a "town," space is so empty that the Earth's surface would contain only one town.

The scale we've chosen is not arbitrary. In this model, speed is also reduced by the same factor. Light, which moves so fast in everyday life that its departure and arrival cannot be distinguished, is slowed to a manageable 1 meter per second, a brisk walking speed. It takes eight minutes for light to stroll from the Earth to the Sun, and five hours to walk across the solar system. But if you set out for the nearest star at light speed, it's like walking around the Earth. If you took no rest breaks and had no oceans to stop you, it would take several years. We see the Sun as it was eight minutes ago, Pluto as it was five hours ago, and the nearest stars as they were several years ago. It makes no sense to ask what the universe is like "now" because light is the fastest messenger we know of. Also, we're limited in our vision by light's speed, only able to see regions from which light has been able to reach us in the age of the universe.

One huge factor of reduction doesn't bring most of the universe into view, so we apply a second factor of 300,000,000. Our scale is now 1:1019 or nineteen powers of ten of reduction. The Sun reduces to the size of an atom and other stars shrink to microscopic scales. The typical distance between them is 3mm. The Milky Way is a twisting spiral of stars about 100 feet across; the size of large house. Within this "house" are 400 billion stars. The nearest house is a mile away. Now we can visualize the extragalactic universe, where house-sized galaxies, each containing billions of stars, are sprinkled across a vast landscape with the separation of farmland villages on the Great Plains.

In this analogy, the observable universe is about the size of the Earth. But here the analogy breaks down. In our universe, we don't see the contents of the universe laid out before us at a snapshot in time. We see the outer edge of the Milky Way as it was 20,000 years ago. For example, if we ever received a signal from a species on the far side of the galaxy, it may already have gone extinct by the time we can reply. We see the nearest galaxies as they were 3 or 4 million years ago, and the most distant galaxies as they were 11 or 12 billion years ago. There are regions of the universe we've not yet seen and some we'll never see. We are bounded by time not space.