General Relativity - a Short Review
Seppo Nurmi · 2010
() . Moreover, if we have a peace of solid material, in order to give the tension force all over the material we need something more elaborate to express how the material responds to the force, and that in all directions, in all space dimensions. Such an elaborate thing is called a tensor, but it is merely only a generalization of the string constant. This I tell in order to demystify the tensor, because it is basically something very practical. It is not difficult to grasp what it is for, but it becomes mathematically intricate because it must cover all possible coordinate positions and directions of the force. A tensor has a multitude of components, arranged in certain way, and all the components are functions of the coordinates. Formally mathematically a tensor is often defined as a system of functions that transforms in a certain way under a coordinate transformation. Tensor algebra turned out to be a very potent tool, being able to express most complicated and general conditions in form of compact expressions. The compactness is much of the trouble, because tensors come with those many indices with an urge of practical training in the handiwork. The more technological kind of science, solid state physics, or with a more modern word, condensed state physics, curiously, has turned out to be an important source of ideas for the pure theoretical physicists, offering not only ideas, but also the mathematical tools. Not only general relativity, but also more modern theories such as quantum field theory with things like Higgs particles, has borrowed ideas from condensed state physics.