Understanding Gravitational Waves and Their Impact on Modern Physics

All Around Us

A lot of things around us are curved! A piece of wire, a mug, the Earth we live on, and even this whole universe. From a distance, it would be easy to perceive the curvature of the universe if we were observing the universe. However, this fact would be much harder to grasp for an ant.

Riemann

German mathematician Bernhard Riemann was the first to devise a way to think of curvature as an intrinsic quantity in all dimensions. The distances and angles between nearby points in curved spaces differ from those in flat spaces. As a result, shortest paths, or “geodesics,” and parallelism do not behave the same.

When Geometry Breaks the Rules

Oddly enough, the angles of a geodesic triangle may not always add up to 180 degrees, and parallel lines may not remain parallel after traveling around a loop. Using these methods, it is possible for an ant on a ball to discover that the world it lives in is curved.

Einstein

Six decades after Riemann’s breakthrough, making extensive use of his theory, Albert Einstein published what is now known as general relativity. According to this theory, the distribution of matter, energy, and force across the universe bends space and time. Objects, when undisturbed, simply follow geodesics in curved spacetime, creating the illusion of gravitational force.

Gravitational Waves

More than a century after Einstein proposed general relativity, its predictions were finally confirmed in a dramatic way. In 2015, scientists detected gravitational waves—tiny ripples in spacetime produced by the collision of massive black holes billions of years ago. Using an experiment that split laser beams and sent them down miles-long tunnels, researchers measured changes smaller than the width of a proton. These minuscule vibrations revealed that spacetime itself can stretch and compress, providing direct evidence that the universe is dynamic and curved, just as Einstein had predicted.

Our understanding of curvature has transformed the way we see the universe. What once seemed flat and unchanging is now known to be shaped by matter, energy, and motion. From an ant discovering the curvature of its world to scientists detecting ripples across the cosmos, these ideas show how mathematics and observation work together to uncover hidden truths. By studying curvature, we learn not only about space and time, but also about the power of human curiosity to explore realities far beyond what we can see!

Work Cited

American Physical Society. “1854: Riemann’s Classic Lecture on Curved Space.” APS News, 1 June 2013, www.aps.org/apsnews/2013/06/riemanns-curved-space.

Encyclopaedia Britannica. “Curvature.” Encyclopaedia Britannica, n.d., www.britannica.com/science/curvature. Accessed 24 Jan. 2026.

NASA. “100 Years of General Relativity.” NASA Blueshift, 25 Nov. 2015, asd.gsfc.nasa.gov/blueshift/index.php/2015/11/25/100-years-of-general-relativity/.

Einstein Online. “Gravity: from Weightlessness to Curvature.” Einstein-Online, n.d., www.einstein-online.info/en/spotlight/geometry_force/. Accessed 24 Jan. 2026.

LIGO Laboratory. “Gravitational Waves Detected 100 Years After Einstein’s Prediction.” LIGO Lab | Caltech, 11 Feb. 2016, www.ligo.caltech.edu/news/ligo20160211.

Abbott, B. P., et al. “Observation of Gravitational Waves from a Binary Black Hole Merger.” Physical Review Letters, vol. 116, no. 6, 2016, link.aps.org/doi/10.1103/PhysRevLett.116.061102.

NRICH. “When the Angles of a Triangle Don’t Add Up to 180 Degrees.” NRICH, 1 Feb. 2011, nrich.maths.org/articles/when-angles-triangle-dont-add-180-degrees.