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Einstein and General Relativity

A 1914 sketch by Einstein on how the Sun’s mass might cause light to bend. Photo Credit: American Institute of Physics
Photo Credit: American Institute of Physics

A 1914 sketch by Einstein on how the Sun’s mass might cause light to bend.

Einstein’s theory of special relativity ensured his place among the greatest physicists of all time, but Einstein himself wasn’t satisfied. He knew there was a piece missing, and he spent the next decade hammering out the details of a more general theory of relativity that could incorporate acceleration, which was ignored by special relativity.

Even Einstein’s close friend, Max Planck, felt that his younger colleague had taken on a well-nigh impossible task. "As an older friend, I must advise you against it, for in the first place you will not succeed; and even if you succeed, no one will believe you," Planck wrote. But Einstein persevered. And he found the key to general relativity in an elevator analogy in 1907. He realized that someone riding in an elevator couldn’t tell the difference between gravity and acceleration, and he elevated this insight to a general principle, which he called the Principle of Equivalence: the laws of nature in an accelerating frame were equivalent to the laws in a gravitational field.

Furthermore, gravitational "force" could be explained by pure geometry. In the seventeenth century, Isaac Newton had considered gravity to be an instantaneous interaction between two separate bodies, and that view had persisted during the intervening centuries. Instead, Einstein chose to envision gravity as arising from the geometric curvature of space-time caused by massive celestial objects. But he initially lacked the mathematical formalism he needed to express his physical principle. He struggled with the problem for three long years, writing to his close friend, Marcel Grossmann, "Grossmann, you must help me or else I’ll go crazy."

Grossmann came through for his friend. He alerted Einstein to the work of the 19th century German mathematician, Georg Friedrich Bernhard Riemann, who, in a famous 1854 lecture, had developed a generalization of Euclidean geometry that now bears the name Riemannian geometry. Central to the discussion was the metric tensor, which, in four dimensions, has ten independent components and which describes the coordinate-invariant distance between two nearby points. From the metric tensor one can compute the local curvature and any other quantities of geometrical interest.

Treating the metric tensor as a dynamical field analogous to the electromagnetic potential in Maxwell’s equations, Einstein found he could incorporate the entire body of Riemann’s work into a field theory of gravity. This turned into general relativity, which Nobel laureate Subrahmanyan Chandrasekhar once called "the most beautiful theory that ever was." Einstein completed the formulation of the theory in late 1915 and early 1916.

Every new theory must have its predictions experimentally tested and verified. As Einstein showed, general relativity could account for a hitherto unexplained piece of the precession of the perihelion of the planet Mercury. In addition, as Einstein had noted years earlier, it is a direct consequence of the principle of equivalence that light emanating from a massive body should be redshifted. This effect was first observed as a terrestrial effect many years later, in 1960, by Pound and Rebka.

A 1919 photo of the solar eclipse that confirmed Einstein’s predictions. Photo Credit: American Institute of Physics
Photo Credit: American Institute of Physics

A 1919 photo of the solar eclipse that confirmed Einstein’s predictions.

Finally, according to general relativity, when a ray of light passes near a massive body, the ray should be bent. For example, starlight passing near the sun should be slightly deflected by gravity. This deflection could be measured when the sun’s own light was blocked during an eclipse. Einstein predicted a specific amount of deflection, and the prediction spurred British astronomers to try to observe a total eclipse in May 1919. Feverish preparations began as World War I ended. Two expeditions, one to an island off West Africa and the other to Brazil, succeeded in photographing stars near the eclipsed sun. The starlight had been deflected just as Einstein had predicted.

Announcement of the eclipse results caused a sensation, and not only among scientists. It brought home to the public a transformation of physics, by Einstein and others, that was overturning established views of time, space, matter, and energy. Einstein became the world’s symbol of the new physics.

It is an interesting footnote to this story that, if one uses only special relativity, one obtains a deflection that is half the full amount predicted by general relativity. Einstein had suggested this experiment in 1913, but with the wrong numerical prediction. If war had not intervened, delaying the observation until 1919, the agreement between theory and observation would have been much less dramatic. Timing and luck cannot be discounted as factors in shaping the history of physics.
Sources:
AIP exhibit: http://www.aip.org/history/einstein/ Kaku, Michio. Hyperspace.



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