Is Infinity Real?

Some philosophers believe in the concept of infinity as a logical, sensible outgrowth of thought, and some do not. Mathematicians handle it with style and grace. But does infinity exist in the physical sense? Is it a real thing about which you and I should be concerned?

Until recently, the universe was thought to be an endless expanse. The prevailing theory told of an even, infinite distribution of stars. It was incomprehensible that there could be an end, a boundary, a place beyond which there was nothing, past which nothing could exist.

This idea has intuitive appeal because it is simple. A cosmos with unlimited space ought also to have unlimited time, no beginning and no end. This satisfies human desire for immortality. Even in prayer, some declare, "World without end. Amen." This would mean not a million generations, nor a quadrillion, nor an octillion, but infinitely many.

Modern science tells us something different.

If the human species survives for a long enough time, it will face a hostile sun. Astronomers say that in several billion years, the hydrogen fuel that powers our parent star will begin to run out, and the temper of the sun will change. There will be, as astronomer Carl Sagan puts it, a "last perfect day," and then the sun will start to bloat, and the earth will get hotter. The seas will boil and all life will be exterminated. Some say that the red giant sun will finally swallow and vaporize the earth. Thereafter, the sun will shrink to a white dwarf and cool down slowly until it dies. Human beings will no longer inhabit the solar system.

Although this will not occur for a long time, it will take place; even the sun has a finite lifespan. On a much greater time scale, every star visible today must die. It is not known whether the universe will perish in cold and darkness, coasting forever outward into an infinite black void, or if it will collapse under its own weight in a burst of heat and light.

Early in the twentieth century, Edwin Hubble and other astronomers saw that all the galaxies in the universe appear to be flying away from each other. This means that they once were much more closely packed than they are now. Extrapolating far back in time, they must have been literally on top of one another. Why didn't gravity cause them all to collapse into a black hole? Could it be that they really are falling inward, not flying apart as they seem to be, and we are seeing time in reverse? Is it possible that "backward time" and "forward time" are only illusions, and that in the grandest of grand schemes, there is no difference between them?

According to the current conventional wisdom, about 15,000,000,000 years ago all the matter and energy in the cosmos was compressed into an unimaginably hot, bright, dense particle called ylem. This "primordial atom" exploded, congealing into all the different particles known today, and forming galaxies, stars, planets, and living things. There must have been, and perhaps still is, a great repelling force, capable of tearing apart what would otherwise be an absolutely unbreakable particle. Without this force, the attraction of gravity would have been so great as to prevent anything ever happening.

The weak but persistent attraction of gravity is pulling on every atom in every galaxy in the universe, trying to bring all the matter back together again. Is it strong enough? This depends on the density of the universe, and astronomers aren't yet certain if it is great enough to cause collapse.

The fastest ejected matter was catapulted from the primeval atom at almost the speed of light. In 15,000,000,000 years, it has gone 90,000,000,000,000,000,000,000 miles. But that is not infinity far. It is no closer to infinity than the distance across your home town, or across your desk, or between the legs of a fly, or from one side of a proton to the other.

So, then, what is infinity?

In the mathematical sense, infinity is the number of numbers. In physics, the term infinity has a different meaning, more difficult to grasp. The mathematician G.H. Hardy once said that mathematics is more real than physics. This might seem an inside-out view, until you confront infinity. When you try to touch it, infinity runs away. It is the density of a star compressed into a point. It is the time from now until the thirty-first of never. Even the whole universe, if the Big Bang theory is to be believed, isn't that big. Maybe, in the material world, there is no place for infinity.

Finiteness does not necessarily impose limits on space and time. Albert Einstein, among others, pointed this out while working on his General Theory of Relativity. It might at first seem impossible that something could have no boundaries, and yet be finite in extent. But the idea becomes clear at once, upon realizing that the surface of the earth is an example of it. Einstein postulated that the universe is a four-dimensional sphere, with the three spatial dimensions comprising its surface. He envisioned that gravitation, on a large scale, bends space into this shape, so that it contains a finite number of cubic miles, but does not have a boundary.

Still another haunting theory, believed by some since antiquity, holds that time and space are both finite yet unbounded. The four-sphere universe might oscillate in and out, periodically cleansed by big bangs, with each cycle of events identical to the one before it, and the one before that, and the one before that. In this way, time would have no limits, and yet there would be only a finite number of seconds in the lifespan of the universe. You and I would live infinitely long, but would only be able to experience a finite number of things. Maybe that is where deja vu comes from. We really were here before.

Perhaps the question "Is infinity real?" is one of those mysteries that humankind can never unravel. Should you or I be concerned about it? Probably not, from a practical standpoint. But there is no law that says we always have to be practical -- is there? Oh, I suppose some practical politician will introduce a bill to that effect. But I would venture to say that the universe is a decidedly impractical contrivance, that all of us could stand to be impractical a lot more often than we are, and that ultimately, if we do not become impractical by choice, we will be forced into the mode by powers greater than ourselves.

Copyright 1998, 1999, 2000 by Francisco Carrera.