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Is the universe infinite, Aristotle asked in 350 BCE, “or is this an impossibility? The decision … is … all-important to our search for the truth.” The Greek philosopher opined that “the heavens” (meaning the moon, planets, sun and other stars) travel around the Earth in circles, and that a “body which moves in a circle is not endless or infinite, but has its limit.” Moreover, he assumed that Earth sits at the center of the universe. In that case, the universe must be finite, Aristotle reasoned, for otherwise it could not have a center. With that, he’d apparently resolved an issue that had confounded both his predecessors and his contemporaries.
Glen Starkman, a leader of the Compact collaboration, is mapping the signals that a universe with an interesting shape would produce.
(photo: David Hintz/Case Western Reserve University)
Circular as Aristotle’s logic was, his conclusion could still be correct. More than two millennia later, we still can’t be sure if the universe is finite or infinite. The universe could be boundless, continuing in all directions without end, or it could be sealed up in a compact shape such as a sphere or doughnut.
Of course, modern scientists have wondered about this issue as well. They’ve devised strategies to investigate the universe’s overall topology, using methods more rigorous than Aristotle’s. The first tests, conducted about two decades ago, linked a range of possible topologies to signals that might have been spotted in astronomical data. Efforts to find those signals have come up short, but hope may be on the horizon.
Recently, a group of about 15 scientists from seven countries known as the Compact collaboration has devised a new way of finding topological clues. They’re taking advantage of computational capabilities that weren’t available a decade ago, buoyed by the conviction — as they wrote in Physical Review Letters in April 2024 — that “prior searches for topology have far from exhausted the potentially significant possibilities. Much more can be done to discover, or constrain, the topology of space.”
“The size and shape of the universe is absolutely one of the most basic and important questions we could ask,” said Neil Cornish, a Montana State University astrophysicist who is not part of Compact. Given that a substantial amount of relevant data is already available, he said, “it makes sense to expend the effort to do the most complete analysis possible.”
Circles in the Sky
The Compact collaboration builds on work from more than 25 years ago. In 1998, Cornish, Glenn Starkman, a theoretical physicist at Case Western Reserve University who unofficially leads Compact, and David Spergel, who at the time was at Princeton University1, published “Circles in the Sky,” a road map for probing our cosmic topology.
The technique that the three researchers introduced would work if a few assumptions fell into place. Most important, the universe’s topology would have to allow light, traveling for almost the entire age of the universe, to take two totally different routes to get to us, in much the same way that an airplane traveling from Spain to New Zealand can fly either east across Asia or west over the Americas.
The surface of the Earth is like a sphere, but other shapes are possible for the universe as a whole. Consider, for instance, a doughnut-like torus. In this case, there are multiple ways for a light ray to travel around the surface of the torus and return to the same point. The light can loop around the outside of the doughnut, or loop through the central hole. Either way, it makes it back to where it started from.
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