Celebrating the Poetry of Imagination Without Boundaries

By Lawrence M. Krauss


hot air balloon

This article first appeared on June 6, 2000 in The New York Times. Reprinted by permission of the author.



This is a geometric concept. Einstein's general theory of relativity tells us that light rays bend in a gravitational field because space is "curved" in the presence of such a field, meaning that the standard Euclidean rules of geometry taught in high school need not always apply. The recent observations, however, imply that when crossing the entire visible universe, light seems to travel in straight lines.











I remember progressing from graduate student to professor during this time, as we in the "flat-universe trenches" began to win the day, and others in the field and out began to come around. The argument seemed so compelling that it appeared that nature would have had no choice but to adopt it, even if there was always a slight equivocation that what seemed natural to us might not be so natural for the universe.


When I ponder these developments, I remain amazed that we have come to understand the universe so intimately that we may have suspected in advance that it should be flat. We are, after all, confined to the immediate proximity of our spinning globe on the outskirts of the Milky Way galaxy.

No one could guess by simply peering with a naked eye at the night sky that our galaxy is one of 100 billion or so in the visible universe, or that the universe is expanding, much less that space on large scales might be curved. Fortune indeed favors the prepared mind, and it is hard to over-emphasize the intellectual journey required before the very question of the naturalness of a flat universe could even be discussed.

But this essay is written in praise of cosmology, not cosmologists. I have made it sound as if the universe willingly followed the demands of human reason. Nothing could be further from the truth. The models we invented in the 1980's to try to bring a flat universe into accord with the observations at the time are clearly wrong. Much to our surprise the energy that dominates in the expanding universe is not associated matter of any sort, pedestrian or exotic.

Rather, it appears that our universe is only flat because empty space is endowed with some sort of funny energy, whose origin we can only begin to imagine at the present time. Although Einstein had been the first to speculate about such a possibility by introducing what became known as a cosmological constant (in order to explain why an apparently static universe might not collapse of its own gravity) he later found it so abhorrent that he dismissed it as his greatest blunder.

It is fair to say that if observations had not driven us to this precipice, no one would have traveled there in advance or later revisited it. Indeed, theoretical a priori arguments suggest that a cosmological constant tuned to produce a flat universe today is as unnatural on fundamental grounds as a flat universe now seems natural.

It gets worse. We were driven to determine whether the universe is flat or not with one main goal in mind: to constrain eternity. The classical arguments in pre-1995 cosmology books, mine included, stressed that if we could determine the geometry of the universe, we would know its ultimate destiny. How very marvelous to imagine that in our lifetimes we might determine, for certain, whether the universe would end with a bang or a whimper.

But the universe has outsmarted us once again. The realization that empty space might in fact provide the dominant source of energy in the universe has again changed everything. We now recognize that any universe, open, closed or flat, can collapse or expand forever, depending upon the magnitude of this new form of energy. Geometry and destiny have been disentangled.

Indeed, my colleague Michael Turner and I have argued that there will never be any finite set of astronomical measurements made over a finite time that will allow us to determine the ultimate fate of our universe. Some things, it seems, may be forever shrouded in mystery.

So we find ourselves at the dawn of the 21st century strangely self-satisfied and at the same time confused. A flat universe doesn't matter a tinker's damn, an expression my wife likes to use, in the everyday course of human events. Yet the lessons that arise from these discoveries can leave us with a completely new perspective of our place in the cosmos. That is what the progress of culture is all about. Ultimately this, not technology, may be the greatest legacy of science.

Finally, we learn that the universe is a stranger and more interesting place than human imagination alone can ever foretell. If we stop looking outward, we are likely to end up going nowhere.


Dr. Lawrence M. Krauss is a professor of physics at Case Western Reserve University. 

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