If our Universe shrunk to the point where Earth became the size of the period at the end of a sentence, how big would it be? When I was a kid, questions like this fascinated me; so what harm can there be to revisit a few of them?
We have to string together about one-hundred dots the size of the period at the end of this sentence to make an inch. If we shrink the earth to the size of one of these dots, plug-in the numbers and calculate, we find that the observable universe shrinks to a diameter of about two light years.
Since a light year is about six-trillion miles, the universe is really big. Even at this reduced scale, the size of the universe remains pretty much incomprehensible.
At this scale the Sun shrinks to the size of a Ping-Pong ball. The dot-sized Earth revolves around it ten feet away. Neptune, the farthest planet, is smaller than a BB—a tiny ball of methane ice—almost one football field away (ninety-seven yards).
The distance light travels in a year shrinks to about one-hundred and twenty miles—a speed approaching one-quarter inch per second. The distance to Alpha Centauri—the nearest sun-like star—shrinks to five-hundred miles. Alpha Centauri itself shrinks to a ball only slightly larger than the Ping-Pong ball sized Sun.
Imagine two Ping-Pong balls separated by five-hundred miles. Imagine trying to commute between these balls when the top speed is less than one-quarter inch per second. Of course, we can’t travel at the speed of light. At speeds typical of spacecraft today, Alpha Centauri is 100,000 years away.
At this scale, where our Sun is the size of a Ping-Pong ball and our earth is a grain of sand, we might wonder what range of sizes other stars exhibit. It turns out, most suns (stars) in our universe range in size from a large grapefruit down to a good-sized pea. (Note: we are talking size here, not weight or mass.)
Of course, outliers exist, like Deneb, the blue-white supergiant visible in the Summer Triangle. At two-hundred times the size of our Sun, it shrinks to fifteen feet in diameter. Some supergiants—though rare—are even larger; some can be seventy-five feet in diameter or more at this scale. But in our own galaxy, the Milky Way, our Ping-Pong ball sized Sun is one of the larger stars.
Is there another way to grasp how large the universe is? The Milky Way Galaxy—our Sun orbits around its center in the space between two of its outermost spiral-arms—is 100,000 light-years across. If we reduced our galaxy to the diameter of a coin the size of a quarter, the visible universe (the universe we can see with our telescopes) would collapse into a sphere of space fifteen miles in diameter.
The larger galaxies become the size of frisbies—but outliers like the mammoth IC1101 take on the size of truck tires. The size of the smaller galaxies shrivel into mere grains of sand. Distances between galaxies diminish to a hundred feet or so, but variations are huge, because galaxies tend to cluster together to form groups, which are separated from one another by vast distances.
Some astrophysicists believe the galaxies we don’t or can’t see (because the space between us and them is expanding faster than the speed of light) would, at this reduced scale, make our entire universe (the visible and beyond) fifty miles in diameter or more. Light, believe it or not, seems to stand still at this scale. We would observe no movement at all of objects or light.
Even the faster-than-light expansion of the universe would be un-detectable. According to physicist, Stephen Hawking, it takes a billion years for the universe to expand by ten-percent. Five miles (ten-percent of fifty miles) during a period of a billion years is seven-billionths of an inch per day. That’s two-thousandths of an inch (less than half the width of a human hair) during a human lifetime. At the scale where the Milky Way Galaxy is the size of a quarter, our universe is frozen in time over the lifespan of any human observers.
What about tiny things? To examine the scale of the very small we can enlarge molecules—the building blocks of all things—to the size of the same period-sized dots. We might ask how tall an average person would be? After again plugging in the numbers and calculating, it turns out our stretched human grows to a height of one-thousand miles. The eye expands to an orb fifteen miles across.
Molecules are small. But at this imagined scale—a scale which none but our most sophisticated instruments are capable of discerning—the individual molecules become visible. They look like little dots separated by distances only a little larger than the molecules themselves. Sadly, we can’t see the individual atoms which make up the molecules. Even at this scale, they are too small.
No instruments or microscopes have ever been constructed which will allow us to see atoms. We believe atoms are real, because we see the evidence they leave behind as they or their parts move through the detection mediums of cyclotrons and other machines. But models of atoms we study in science class are invented to help make sense of the results of many experiments. They are fanciful.
As for living cells, the basic building blocks of all biology, we are able to see them, because every cell is built up from many billions of molecules. (Some human cells have trillions.) The size of a typical cell, at this scale, is about sixty feet across.
The gulf between the very large and the very small strains credulity, but science says it’s real. When thinking about it, I am overcome by wonder and the despair of not knowing why or how.
Theoretical physicist, Nema Arkani-Hamed, has said that the gulf between the very large and the very small is required to balance the force of gravity against electrical forces in celestial objects like planets. In fact, he has pointed out, the ratio of the surface area of a typical atom verses the surface area of a typical planet matches the difference (that is, the ratio) between the two forces of gravity and electricity. The huge difference between the force of gravity and the force of electricity makes the gap between the very large and the very small essential in a universe that works like ours; the difference in scale is inevitable, he says.
If the ratio moves too far away from this balance—if the surface area of an object gets too big—gravity can overwhelm the electrical forces that hold the atoms apart just enough to cause the object to light up from a process called fusion, leaving behind a star; a very large object can collapse completely to become a black hole.
Why is the gap between the force of gravity and the electrical force as vast as the difference in size (that is, the difference in surface area) between a typical planet like Earth and a hydrogen atom? No one knows. The values of the forces seem to be finely tuned; they appear almost arbitrary. Arkani-Hamed and others are working on it.
The other big question: why is the universe so big? Even Arkani-Hamed admits he doesn’t have the answer just yet. Perhaps the answer lies in the geometry of spheres, which is the basis of the Billy Lee Conjecture discussed in my essay, Conscious Life.
Speaking of spheres, everyone knows how smooth a polished billiard ball can be. Someone once said that the earth—shrunk to the size of a pool ball—is even smoother, less blemished and more perfectly round. If someone breathed on that polished earth ball, the mist which formed would be deeper than the deepest ocean. I did the math. It’s true.
As a child my earliest nightmare was an image of a huge whale crushing a small flower. A psychologist once told me the whale was my parents, and I was the flower. Maybe. But the universe captures my nightmare. It is so big, and we are so small.