Probable Impossibilities: Musings on Beginnings and Endings

by Alan Lightman

Every atom in your body except for hydrogen and helium was made in stars long ago and blown into space when those stars exploded—much later to be tossed into the air and soil and oceans of Earth and eventually incorporated into your body.

The whole visible world is only an imperceptible atom in the ample bosom of nature…We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison to the reality of things. It is an infinite sphere, the center of which is everywhere, the circumference nowhere…What is man in the infinite? But to show him another prodigy equally astonishing, let him examine the most delicate things that he knows.

The Planck world is a ghost world. It is a world without “time” and without “space.” Just as Pascal suggested, we find ourselves at the abyss between nothingness and infinity.

How many times should the size of a human body be halved to reach the size of an atom (a size unknown until the twentieth century)? The answer is about 33. Going in the opposite direction, one can ask how many times the size of the human body should be doubled to reach the size of a typical star, like our Sun, the largest object known by Pascal. The answer is 30. Thus, counting in doublings, the size of a human being is nearly halfway between an atom and a star—certainly

Einstein once wrote, “The most beautiful experience we can have is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science.”

In particular, the forward direction of time is determined by the movement of order to disorder.

What we call the “future” is the condition of increasing mess; what we call the “past” is increasing tidiness.

“Two-Headed Time.” In this theory, time has existed forever. But unlike in the static models of Aristotle and Newton and Einstein, the universe changes as the eons go by. Furthermore, the evolution of the cosmos is symmetric in time, with the behavior of the universe before the Big Bang a nearly mirror image of its behavior after the Big Bang. Until fourteen billion years ago, the universe was contracting. It reached a minimum size at the Big Bang (which we call t = 0) and has been expanding ever since, like a Slinky that falls to the floor, reaches a maximum compression upon impact, and then bounces back to larger dimensions.

When Vilenkin talks about “quantum tunneling,” he is referring to the spooky phenomenon in quantum physics in which objects can perform such magic feats as passing through a mountain and suddenly appearing on the other side, without ever going over the top. That mystifying ability, which has been verified in the laboratory, follows from the fact that subatomic particles behave as if they could be in many places at once. Quantum tunneling is common in the tiny world of the atom but totally negligible in our human world—explaining why the phenomenon seems so absurd.

For to understand anything, as Aristotle argued, we must understand what it is not.

Atoms protected us from the whimsy of the gods, said Democritus and Lucretius, because atoms could not be created or destroyed. Even the gods had to obey atoms.

In fact, 99.9999999999999 percent of the volume of an atom is empty space, except for the haze of nearly weightless electrons. Since we and everything else are made of atoms, it is literally a fact that we are mostly empty space.

The philosophers of ancient Greece developed a terrifying view of the world called Zeno’s Paradox. Suppose you want to walk 15 feet across a room. Before you travel that distance of 15 feet, however, you must go halfway, which is 7.5 feet. And before you go that 7.5 feet, you must travel half of that distance, 3.75 feet. And before you go that 3.75 feet…And so on. In their minds, the philosophers kept chopping space into halves, into smaller and smaller dimensions ad infinitum, as did Pascal centuries later. The indivisible was pitted against the divisible. The ultimate conclusion of this intellectual exercise is that you cannot cross the room. In fact, you cannot move even an inch. You are frozen in a metaphysical conundrum. You are trapped by the infinity of the small.

In the last forty years, physicists have proposed objects far smaller than quarks, called “strings.” Instead of being point particles, like electrons, strings are extremely tiny one-dimensional “strings” of energy. Their sizes would be the Planck length, where gravity and quantum physics are joined. (See the earlier chapter “Between Nothingness and Infinity.”) An important property of strings is that they occupy a space of nine or ten dimensions, instead of the familiar three.

I’ve always been struck by the fact that the number of neurons in our brain is about equal to the number of stars in a galaxy: one hundred billion.

We can play games with infinity, but we cannot visualize infinity. By contrast, we can visualize flying horses. We’ve seen horses, and we’ve seen birds, so we can mentally implant wings on a horse and send it aloft. Not so with infinity. The unvisualizability of infinity is part of its mystique.

Indeed, one of the many intriguing properties of infinity is that you can’t get there from here.

DEEEEEEEP!!!

Indeed, Linde’s theory requires that we redefine what we mean by “universe.” Some physicists now take the word to mean a region of space that will be quarantined into the infinite future. This region may have been in contact with other parts of the cosmos in the past but can never communicate with the rest of the cosmos in the future.