Breaking in the 4-Vectors: The Four-Dimensional Movement in Gravitation, 1905–1910

  • Scott Walter
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 250)

In July, 1905, Henri Poincaré (1854–1912) proposed two laws of gravitational attraction compatible with the principle of relativity and all astronomical observations explained by Newton’s law. Two years later, in the fall of 1907, Albert Einstein (1879–1955) began to investigate the consequences of the principle of equivalence for the behavior of light rays in a gravitational field. The following year, Hermann Minkowski (1864–1909), Einstein’s former mathematics instructor, borrowed Poincaré’s notion of a four-dimensional vector space for his new matrix calculus, in which he expressed a novel theory of the electrodynamics of moving media, a spacetime mechanics, and two laws of gravitational attraction. Following another two-year hiatus, Arnold Sommerfeld (1868–1951) characterized the relationship between the laws proposed by Poincaré and Minkowski, calling for this purpose both on spacetime diagrams and a new 4-vector formalism.


World Line Gravitational Attraction Spacetime Diagram Kinematic Invariant Passive Mass 
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