Cosmic Curvature: The Efforts of Gauss and Lobachevsky to Understand the Universe

Carl Friedrich Gauss was so intrigued by the possibility of the universe being curved that in the 1820s and 1830s, he attempted to determine whether there was any curvature in space by measuring large triangles drawn between the peaks of the Hohenhagen, Inselberg, and Brocken mountains using data from geodetic maps. However, the fact that these mountains are located on Earth's curved surface indicated that the two-dimensional curvature of this surface could affect measurements intended to study the curvature of the three-dimensional space in which Earth resides. Gauss was clearly aware of this, and he likely aimed to eliminate the impact of this two-dimensional curvature on the measurements to determine if the remaining curvature provided any clues about the general structure of space.

The first person to attempt to measure the curvature of space directly was the Russian mathematician Nikolay Ivanovich Lobachevsky. Unlike Gauss, Lobachevsky was one of two mathematicians who boldly proposed the existence of curved geometries, known as "hyperbolic," where parallel lines could converge. Interestingly, Lobachevsky published his work on hyperbolic geometry, which we now call "negatively curved" or "open" universes, in 1830. Shortly thereafter, he began exploring whether the three-dimensional structure of our universe could also be hyperbolic. He suggested that to experimentally solve this question, one could examine a triangle formed by stars. As Earth moves in its orbit around the Sun, Lobachevsky proposed observing the bright star Sirius six months apart to study the curvature of the universe. His observations led him to conclude that the curvature of our universe must be at least 166,000 times greater than the radius of Earth's orbit. While this may seem like a large number, it is quite small on a cosmic scale. Although Lobachevsky's idea was correct, the technological limitations of his time prevented his measurements from being precise enough. However, about one hundred and fifty years later, the discovery of the Cosmic Microwave Background Radiation began to change the situation.

The Cosmic Microwave Background Radiation is the oldest radiation remaining in the universe after the Big Bang. This radiation contains information carried from the early stages of the universe to the present day and provides direct evidence that the Big Bang actually occurred. Through it, we can directly observe the early universe and gain insights into its structure. The discovery of the Cosmic Microwave Background Radiation is particularly interesting because it was found by two scientists in New Jersey who didn’t even know what they were looking for. Moreover, this radiation went unnoticed for decades. In fact, you may have unknowingly seen the effects of this radiation; if you remember the static that appeared on old televisions when channels stopped broadcasting at night, you should know that 1% of that static is from the Big Bang.

The source of the Cosmic Microwave Background Radiation is quite straightforward. Due to the finite age of the universe (about 13.72 billion years), the farther away an object is, the further back in time we look (because it takes a long time for light from these objects to reach us). If we look far enough, we might think we could even see the Big Bang itself. While this is theoretically possible, in practice, there is a kind of "wall" between this early period and us. Although this wall is not a physical barrier, its effects are just as significant.