### Matter, Acceleration, Time, and Existence

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From any point on the equator, for instance, the shortest path to the North Pole follows a curve — the geodesic corresponding to a meridian. If two people start out on such a trek, starting some distance apart, they pursue different curved meridians to the pole but grow closer together as they travel northward. As it turned out, some bending of light would have been expected even with Newtonian gravity, as Johann von Soldner had calculated unknown to Einstein more than a century earlier.

But Einstein predicted precisely twice as much bending as von Soldner had. Gravity deflects light just as general relativity requires. Gravitational lensing was first observed in , but Einstein had suspected its possibility in , even before his theory had been completed. But modern astronomical explorations proved the contrary.

Einstein was also ambivalent about other consequences of general relativity. In , for instance, he raised the possibility of gravitational radiation — waves rippling through spacetime after a massive body abruptly changes its motion, as when colliding with another mass. But later Einstein changed his mind. In , he and Nathan Rosen submitted a paper arguing that such waves did not exist after all.

## Dark matter | CERN

But their paper contained a mistake. Astronomers have already detected another offspring of general relativity, black holes, throughout the cosmos. Most of that shift could be explained by the gravitational effects exerted by other planets in the solar system. But 43 seconds of arc remained unexplained. For decades, astronomers sought a solution by searching for a postulated planet, called Vulcan, nearer to the sun than Mercury. But such a planet was never found. It was the first mathematical step toward describing black holes in space.

It was , two years after his special theory of relativity had rewritten textbook notions about time and motion. But in real life, objects and people move in all sorts of nonuniform ways. Let the air out of a balloon, for instance. Einstein wanted to extend relativity to all forms of accelerated motions.

## Dark matter exists: Observations disprove alternate explanations

Then his happy thought in the patent office raised hope. A person falling freely accelerates toward the ground because of gravity but feels no force until impact. Therefore, Einstein realized, gravity and acceleration are two sides of a coin. The upward thrust of an accelerating rocket ship pins the occupants to the floor just as the gravitational pull of the Earth keeps your feet on the ground.

At first progress was slow. In special relativity, measures of space or time differ for different observers. But Minkowski showed that space and time combined — spacetime — yielded a mathematical description of events that all observers could agree on. One of the first predictions of general relativity to be tested involved the bending of light. Because a massive body, such as a star, warps spacetime around it, a light beam passing nearby should be deflected from a straight-line path.

From Earth, light from a distant star passing near the sun would be bent in such a way as to alter the apparent position of the distant star. In , astronomers photographed stars near the sun during a solar eclipse. General relativity requires twice as much bending because the light ray is bent while passing through space already curved to begin with.

Establishing such coordinates requires a frame of reference, or origin point. Different observers will choose different origins. By , Einstein realized that his goal would require abandoning Euclidean geometry. Real space, he realized, could not conform to the idealized lines and angles of the textbooks. Gravity distorted the coordinates, just as a grid of straight lines on a rubber sheet would curve if you placed a heavy cannonball on it.

But Einstein did not possess the mathematical skills to cope with non-Euclidean geometry. Fortunately, his college friend Marcel Grossmann, an accomplished mathematician, was eager to help. It had one drawback, though — it worked for some coordinate systems, but not all possible systems. That made his original goal impossible. But Einstein seemed satisfied that he had done the best that nature would permit. It turned out that there actually was something more beautiful. But to find it, Einstein had to move to Berlin. Born in Ulm, Germany, in , he moved when an infant to Munich and then as a teenager to Milan, Italy, having dropped out of high school.

He went back to school in Switzerland, eventually graduating from college in Zurich.

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## Something’s wrong with gravity

During his years at the patent office, Einstein produced an explosive output of papers poking holes in traditional physics, including reports on his special theory of relativity and Nobel Prize—winning work on quantum physics. Eventually those papers led to sufficient recognition in the physics world to get a faculty appointment in Prague.

But at the first chance he returned to Zurich, where Grossmann now taught math. There Einstein and Grossmann developed the Entwurf theory. And then Berlin, the pinnacle of German and world physics, called. With help from his friend Marcel Grossmann, Einstein adopted further advances by the mathematicians Gregorio Ricci-Curbastro, Tullio Levi-Civita and Elwin Christoffel to describe spacetime geometry in terms of mathematical expressions called tensors.

Tensors are similar but can encompass more than just two components. Einstein used tensors to develop his equation describing the gravitational field, known as the Einstein field equation. On the left side of the equation is a tensor describing the geometry of spacetime — the gravitational field. On the right is the tensor describing the matter and energy density — the source of the gravitational field.

The equation shows that spacetime geometry equals mass-energy density when adjusted with the proper units and numerical constants.

Actually, the equation stands for a set of multiple equations owing to the complexity of tensors. So experts usually speak of the Einstein field equations, plural.

### A Physics Analysis of Tesla's Shattered Cybertruck Windows

When he applied this equation to the entire universe, Einstein found that the universe would be unstable, easily disturbed into a state in which spacetime would be either expanding or collapsing. So he added a term that came to be called the cosmological constant, symbolized by the Greek letter lambda.

It represents a constant amount of energy density throughout space that would supposedly keep the universe stable and changeless. Later, evidence that the universe was indeed expanding led Einstein to renounce lambda. Growing apart from Mileva, he pursued a relationship with his cousin Elsa. And Mileva did not relish the idea of life in Berlin.

During the following year his freedom nourished a fertile few months in which he saw a new path to success. In mid he saw that there was a way to make relativity truly general. Rather than imposing energy-momentum conservation on the equations, he worked on devising equations that would impose the conservation law on the universe.

### 35 Replies to “How Do We Know Dark Matter Exists?”

By November , Einstein sensed victory. On November 4, he submitted a paper on general relativity to the Prussian Academy, following up with an addendum November During the following week, he finally found the correct form for the equations describing the gravitational field, presenting his result on November General relativity worked. Einstein quickly realized or had known all along that his new theory of gravity was really a theory of the cosmos. In , he wrote a famous paper applying general relativity to the universe as a whole.

Today that paper stands as the foundation for modern cosmology. But at the time, Einstein was troubled — his equations implied an unstable universe, either growing or collapsing. The Swiss astronomer Fritz Zwicky discovered in the s that velocities in galaxy clusters were too high to account for how much matter we could see.

A similar phenomenon was described by several groups of astronomers, such as Vera Rubin and Kent Ford , when they studied the motion of stars at the far edges of the Andromeda Galaxy. The velocities of the stars far from its centre were expected to decrease, as they experience less gravitational force.

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