| This dissertation elucidates conceptual and mathematical roots of Albert Einstein's special theory of relativity of 1905 by analyzing its emergence in light of the history of kinematics, the science of motion. In the first volume, I trace the development of kinematics, mainly during the nineteenth century, to show how physicists came to regard it as the fundamental branch of physics. I discuss physicists' dissatisfaction with traditional algebraic methods, and their consequent efforts to develop vector algebra as a more suitable mode of physical representation. I explain how physicists reformulated basic kinematic concepts owing to arguments based on experience, measurement procedures, and mathematical refinements such as the distinction between vectors and scalars. In the second volume, I analyze the emergence of Einstein's special theory in relation to the conceptual and mathematical developments discussed. I trace the relation of Einstein's concepts to those developed earlier by other theorists, especially those with whose writings Einstein was acquainted. I reconstruct in detail Einstein's first derivation of the key equations of his theory, the Lorentz transformation equations, and explain that ambiguities in his derivation constituted obstacles in other physicists' attempts to understand his work. I then analyze Einstein's use of algebra to show how it deviated from kinematic concepts of vector theory. Einstein sought to solve problems in electrodynamics by clarifying underlying concepts of kinematics, but his kinematic analysis imported deep ambiguities from traditional algebra. Finally, I demonstrate that mathematical asymmetries that led to the creation of the Lorentz transformations stemmed partly from the particular kinematic interpretation given by physicists to algebraic terms in the equations of electromagnetism and optics. |
