![]() ![]() Klein’s work with Bohr had opened his eyes to the possibilities of quantum theory, and he shifted his research interest away from physical chemistry. At Kramer’s invitation, Klein traveled to Copenhagen and worked for a year with Kramers and Bohr before returning to defend his doctoral thesis in 1921 in the field of physical chemistry. Returning to Sweden, he enlisted in military service from 1915 to 1916 and then joined Arrhenius’ group at the Nobel Institute where he met Hendrick Kramers-Bohr’s direct assistant at Copenhagen at that time. It was arranged for him to work in France and Germany in 1914, but he was caught in Paris at the onset of World War I. He began as a student in physical chemistry working in Stockholm under the famous Arrhenius. Oskar Klein was a Swedish physicist who was in the “second wave” of quantum physicists just a few years behind the titans Heisenberg and Schrödinger and Pauli. The person who took the step to make five-dimensional space-time into a quantum field theory was Oskar Klein. Yet Kaluza’s theory was fully classical-if a fifth dimension can be called that-because it made no connection to the rapidly developing field of quantum mechanics. He later launched his own effort to explore such unified field theories more deeply. ![]() But Einstein finally sent it to be published in the proceedings of the Prussian Academy of Sciences. Einstein, to whom Kaluza communicated his theory, was intrigued but hesitant to forward Kaluza’s paper for publication. Here was a five-dimensional theory that seemed to unify E&M with gravity-a first unified theory of physics. In addition to electro-magnetism, something akin to Einstein’s field equation of gravitation emerges. It was more than just an exercise in mathematics-adding a fifth dimension to relativistic dynamics adds new degrees of freedom that allow the dynamical 5-dimensional theory to include more than merely relativistic massive particles and the electric field they generate. In 1919 Theodore Kaluza of the University of Königsberg in Prussia extended Einstein’s theory of gravitation to a fifth spatial dimension, and physics had its first true parallel dimension. ![]() It is this pseudo-metric that allows space-time distances to be negative as easily as positive. ![]() Even so, Minkowski’s time dimension was not on an equal footing with the three spatial dimensions-the four dimensions were entwined, but time had a different characteristic, what is known as pseudo-Riemannian metric. Nonetheless, the three spatial dimensions we enjoy in our daily lives remained the only true physical space until Hermann Minkowski re-expressed Einstein’s theory of relativity in 4-dimensional space time. Riemann laid out a program of study that included physics problems solved in multiple dimensions, but it was Rudolph Lipschitz twenty years later who first composed a rigorous view of physics as trajectories in many dimensions. The idea of parallel dimensions in physics has a long history dating back to Bernhard Riemann’s famous 1954 lecture on the foundations of geometry that he gave as a requirement to attain a teaching position at the University of Göttingen. ![]()
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