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Einstein himself considered the introduction of the cosmological constant in his 1917 paper founding cosmology as a "blunder". [3] The theory of general relativity predicted an expanding or contracting universe, but Einstein wanted a static universe which is an unchanging three-dimensional sphere, like the surface of a three-dimensional ball in four dimensions.
1. At 16 years old and a student at the Gymnasium in Aarau, Einstein would have had the thought experiment in late 1895 to early 1896. But various sources note that Einstein did not learn Maxwell's theory until 1898, in university. [7] [8] 2. A 19th century aether theorist would have had no difficulties with the thought experiment. Einstein's ...
Einstein excelled at physics and mathematics from an early age, and soon acquired the mathematical expertise normally only found in a child several years his senior. He began teaching himself algebra, calculus and Euclidean geometry when he was twelve; he made such rapid progress that he discovered an original proof of the Pythagorean theorem ...
Einstein remarked, "I never failed in mathematics.... Before I was fifteen I had mastered differential and integral calculus." [67] Einstein did, however, fail his first entrance exam into the Swiss Federal Polytechnic School (ETH) in 1895, when he was two years younger than his fellow students, but scored exceedingly well in the mathematics ...
Although this theory was founded on a very different kinematical model, it was experimentally indistinguishable from the aether theory of Lorentz and Poincaré, since both theories satisfy the relativity principle of Poincaré and Einstein, and both employ the Lorentz transformations.
Albert Einstein was a physicist, who taught himself algebra, Euclidean geometry, and calculus when he was 12. [73] He also independently discovered his own original proof of the Pythagorean theorem , [ 74 ] and he had worked through a geometry textbook he was given by his family tutor, Max Talmud . [ 75 ]
Einstein explained his goal in the preface of the book's German edition by stating he "wanted to summarize the principal thoughts and mathematical methods of relativity theory" and that his "principal aim was to let the fundamentals in the entire train of thought of the theory emerge clearly". [1]
When studying and formulating Albert Einstein's theory of general relativity, various mathematical structures and techniques are utilized. The main tools used in this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics of general ...