Notes on Chapter 10: Space-Time Curvature
First Solvay Conference (1911) – The first Solvay Conference, held in Brussels, brought together many of the leading physicists of the time to grapple with emerging questions in quantum theory. Good accounts can be found in [Clark] and [Isaacson-1]. During this gathering, Einstein met Marie Curie, and the two formed a deep and lasting friendship based on mutual scientific respect and personal warmth.
Einstein’s essay on the war – In 1915, as World War I raged, Einstein published an essay titled My Opinion on the War [Einstein,1915]. In it, he argued that the roots of war lie in the aggressive, biologically ingrained instincts of human beings, particularly men. He critiqued nationalism and patriotism as emotional forces that often cloud rational judgment and perpetuate conflict—a theme that would continue to shape his later activism.
“Entwurf” paper – In 1913, Einstein collaborated with his old friend Marcel Grossmann to publish the so-called “Entwurf” paper (Outline of a Generalized Theory of Relativity and Gravitation) [Einstein, 1913]. Although it marked a major step forward in his quest to generalize relativity, the mathematical framework in this work was flawed. Einstein would later abandon it, but the collaboration with Grossmann helped clarify the essential role of advanced mathematics in the final theory.
Competition with Hilbert – In late 1915, a dramatic intellectual race unfolded between Einstein and David Hilbert, one of the foremost mathematicians of the time. Both men were striving to formulate the gravitational field equations for a general theory of relativity. Their letters to each other—many of which are preserved in [Princeton Papers]—reveal a complex mixture of rivalry and mutual respect. Historical evidence confirms that Einstein independently completed and published the correct covariant equations first [Isaacson-1].
Einstein’s breakthrough and emotional aftermath – In a letter to Arnold Sommerfeld [L-Einstein, 1915], Einstein described the shock of discovering flaws in his “Entwurf” theory. As noted in [Pais], this breakthrough—culminating in the correct formulation of general relativity—was the most powerful emotional moment of Einstein’s scientific career. Writing to Paul Ehrenfest later [L-Einstein, 1916], he exulted, “Imagine my delight at realizing that general covariance was feasible and at finding the equations yield Mercury’s perihelion motion correctly. I was beside myself with joy and excitement for days.”
The four lectures that changed physics – In November 1915, Einstein delivered four lectures at the Prussian Academy of Sciences outlining his final breakthroughs [Einstein, 1915a-d]. After the first two, his equations were still incomplete. In an extraordinary feat of intellectual effort, he worked frantically between the second and third lectures, successfully deriving the equations that explained Mercury’s anomalous orbit. By the fourth lecture, Einstein was able to unveil the full general theory of relativity with its elegant covariant equations, arguably one of the greatest achievements in the history of human thought.
