SCALE

The visible universe is really big. Most scientists believe the invisible universe—the universe we can’t see—is much bigger.

If the 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 these fascinated me; so what harm can there be to revisit a few of them?

About one-hundred dots the size of the period at the end of this sentence must be strung together to make an inch. If we shrink the earth to the size of one of these dots, plug-in the numbers and calculate, we discover 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 distant (ninety-seven yards).

The distance light travels in a year shrinks to 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.

Think about 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, nothing travels at the speed of light. At speeds typical of spacecraft today, it will take 100,000 years to reach Alpha Centauri.

At this scale one might wonder what is the range of sizes that other stars exhibit. It turns out, most suns (stars) in the universe range in size from a large grapefruit down to a good-sized pea. (Note: we are talking about size, 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 the sun, it shrinks to fifteen feet in diameter. Some supergiants, though rare, are even larger; some are seventy-five feet in diameter or more at this scale. But in our own galaxy, the Milky Way, the 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—the sun orbits its center in the space between two of its outermost spiral-arms—is 100,000 light-years across. If the galaxy were reduced in size to the diameter of a coin the size of a quarter, the visible universe (the universe that can be seen with telescopes) would collapse into a sphere of space fifteen miles in diameter.

Large galaxies become the size of frisbies—but outliers like the mammoth IC1101 take on the size of truck tires. The smallest 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 that 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 the entire universe (the visible and beyond) fifty miles in diameter or more. Light, believe it or not, stands still at this scale. No one could detect any movement at all of objects or light.

Even the faster-than-light expansion of the universe would be unobservable. According to physicist, Stephen Hawking, it takes a billion years for the universe to expand by ten-percent. Five miles (ten-percent of fifty) during a period of one billion years is seven-billionths of an inch per day. During a human lifetime it adds to two-thousandths of an inch (less than half the width of a hair). At the scale where the Milky Way Galaxy is the size of a quarter, the entire universe looks to be frozen solid during a human lifespan.

What about tiny things? To examine the scale of the very small we can imagine enlarging molecules—the building blocks of all things—to the size of the same period-sized dots. How tall might an average person be? After again plugging in the numbers and calculating, it turns out that a human stretches 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 the most sophisticated instruments can discern—individual molecules become visible. They look like little dots separated by distances only a bit larger than the molecules themselves. Sadly, no one can 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 to enable anyone to see atoms. Physicists believe atoms are real, because they see the evidence left behind as their debris moves through the detection mediums of cyclotrons and other machines. But models of atoms studied 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 thembecause 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. He has pointed out that the ratio of the surface area of a typical atom and the surface area of a typical planet matches the difference between the two forces. 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 from this balance—if the surface area of an object gets too big—gravity can overwhelm the electrical forces that hold the atoms apart enough to cause the object to light up from a process called fusion, which can leave behind a shining 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 surface area between a typical planet and a hydrogen atom? No one knows. The value of the forces seem as finely tuned as they are 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—not yet, anyway. Perhaps the answer lies in the geometry of spheres, which is the basis of the Billy Lee Conjecture discussed in the essay, Conscious Life.

Speaking of spheres, everyone knows how smoothly polished a billiard ball can be. Someone said that the earth—shrunk to the size of a pool ball—is smoother, less blemished, and more perfectly round. If anyone exhaled 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 an enormous whale crushing a tiny flower. A psychologist once told me that the whale was my parents, and I was the flower. Maybe. But the universe captures my nightmare. It’s really big, and I am so very, very small.

Billy Lee