Dark Energy Revealed: Chasing the Legacy of Einstein’s Constant

Steve Nadis is the author of Discover Magazines and Staff Writers Quanta.

Qiu Chengtong is a professor of mathematics at Tsinghua University and an honorary professor at Harvard University. Winner of the Fields Medal, National Medal of Science, and MacArthur Fellowship.

Below, co-authors Steve and Shing-Tung share five key insights from their new book: Math’s Gravity: How Geometry Rules the Universe. Listen to the audio version read by Steve in the Next Big Idea app.

1. Gravity is geometry.

To be clear, this was not the idea that Qiu and I came up with. This is something Albert Einstein discovered over 100 years ago, and it was probably not the discovery he expected when he set out to create a new theory of gravity in 1905. The popular theory of gravity proposed by Isaac Newton in the mid to late 1600s breaks down when objects move very fast (nearly the speed of light) and when gravitational fields are very strong. Einstein sought a law that was not subject to these same constraints.

Einstein believed that although Newton’s laws worked well under ordinary, non-extreme circumstances, the picture they painted was wrong. Newton believed that gravity was the attraction between two or more massive objects. Einstein envisioned something very different. He said a massive object like the Sun would bend the fabric of space and time around it, much like a bowling ball placed in the middle would deform a stretched sheet of rubber. For example, the deformation caused by the sun keeps smaller objects, such as the planets in the solar system, within the sun’s gravitational field.

In other words, a huge object causes the surface to curve or buckle. The curved surface in Einstein’s theory is a combination of space and time, called spacetime. The effect we call gravity arises directly from the curvature of space-time. But the shape and curvature of any surface are closely related to its geometry. This is why we can say that gravity is geometric in nature.

2. While Einstein was undoubtedly a genius, he was not a lone genius in developing his theory of gravity.

As Einstein became more deeply involved in this decade-long endeavor, the theory became increasingly mathematical, and mathematics was not his strong suit. As a student and young scientist, he had little interest in the subject and thus paid little attention to it.

But when he realized that his theory of gravity would rely heavily on curved space, involving a geometry with which he was unfamiliar, he turned to a friend, a former college classmate named Marcel Grossmann, for help. Specialized in geometry. Grossmann introduced Einstein to the work of Bernhard Riemann, who in the 1850s invented a new branch of geometry focused on higher-dimensional curved spaces. It turned out that this was exactly what Einstein needed.

“When he realized that his theory of gravity would rely heavily on curved space, involving a geometry with which he was unfamiliar, he turned to friends for help.”

In 1913, Einstein and Grossmann published a paper proposing a first draft of the gravitational equations (also known as the field equations of general relativity). Einstein wrote the physics portion; Grossman wrote the mathematics. The paper almost got it right, but it had some fatal flaws that took Einstein another two years to fix. During those years, he received help from other leading mathematicians, including Tulio Levi-Civita and David Hilbert. Although Einstein did not work entirely alone, his achievements are still remarkable.

3. Einstein proposed a revolutionary theory of gravity, but he was conservative about its implications.

Einstein’s equation for gravity, published in November 1915, had only a few terms and could be fit to a straight line. They look deceptively simple, but are actually quite complex. He wasn’t sure he could find an exact solution. As it turns out, he didn’t have to wait long.

About a month later, Einstein received the first of two letters from Karl Schwarzschild, an astrophysicist who was at the time of the First World War. Fighting for Germany in the Great War. Schwarzschild demonstrated that if the interior of a star contained enough mass within a small enough radius, the pressure and density at the center of the star would approach infinity. In other words, he described what 50 years later would be called a black hole.

Although the strange stars imagined by Schwarzschild derived directly from Einstein’s equations, Einstein did not believe that such objects could actually exist. He claimed that if the results were true, it would be a real disaster. His colleague Arthur Eddington insisted that there should be a natural law that prevented stars from committing such ridiculous acts. But on the contrary, all the evidence points to the fact that some celebrities behave in such ridiculous ways.

4. Einstein proposed the concept of gravitational waves, but he doubted their physical reality.

In 1916, Einstein used his general theory of relativity to predict that massive objects accelerating through space-time would cause ripples to form. Gravity waves are similar to those created by a motorboat traveling at high speed over a once-calm pond, except these waves propagate in all directions. It was a prescient idea that took a century to be confirmed. Einstein once again doubted the power of his theory.

In 1936, twenty years after his original prediction, Einstein was preparing to deliver a lecture at Princeton University on the nonexistence of gravitational waves. However, his stance softened when a colleague pointed out an error in the paper Einstein planned to build on. So he took a softer stance in his speech, saying, If you ask me whether gravity waves exist, I have to say I don’t know. But this is a very interesting question.

“An international study suggests there may be a permanent background of gravitational waves reverberating throughout the universe.”

It turns out that’s a better way to put it. In 2015, the LIGO observatory detected gravitational waves for the first time. Since then, there have been about 100 other detections related to collisions between two black holes, two neutron stars, and even black hole-neutron star collisions. Just last year, an international study suggested that there may be a permanent background of gravitational waves reverberating throughout the universe.

It seems Einstein got it right the first time.

5. What Einstein said was his greatest mistake—the cosmological constant, now thought to govern our universe.

In 1917, Einstein had what could be called an epiphany. His theory of gravity applied not only to the motion of the planets in the solar system or the motion of the stars in the Milky Way. It can be applied to the behavior of the entire universe.

Einstein realized that the universe could expand or contract unless he added a term to his equation called the cosmological constant, a calming influence that would keep things the way they are, which he and others subsequently The shared view of a calm, unchanging universe is consistent.

But Einstein never liked the word because it messed up his otherwise elegant equations. “I couldn’t believe something so ugly could happen in nature,” he said. It turns out that he was right to insert the word, even though he did so for the wrong reasons.

In 1998, it was discovered that the expansion of the universe is accelerating, stimulated by dark energy. The cosmological constant that Einstein long agonized over is now thought to be dark energy. Dark energy is an invisible energy field that pervades space and is thought to account for 70% of the total mass and energy of the universe. Furthermore, this proportion is growing steadily.

The mathematical development of general relativity did not end in 1915. Mathematical relativity remains a rich, active, and growing field. May gravity be with you.

To listen to the audio version read by co-author Steve Nadis, download the Next Big Idea app now: