Abstract
At this point it is of great advantage to use the language of tensors applied to the 4-dimensional Minkowski spacetime. Tensors are mathematical objects, described by their components in a given coordinate system, which separate true geometric and physical properties from properties that are specific to certain coordinate systems and only valid there. The formalism of tensors is constructed by studying how tensorial quantities transform under coordinate changes and, since Special Relativity is based on changes of inertial frame (the Lorentz transformations) which are coordinate changes, it is natural to use 4-tensors to formulate Special Relativity. The formalism of tensors, however, is not specific to Special Relativity; it is used in many other areas of physics. For example, tensors occur in the study of the Newtonian mechanics of rigid bodies, fluids, elasticity, electromagnetism, and diffusion. This chapter is quite general and does not refer specifically to tensors in Special Relativity. The adaptation of the formalism to Minkowski spacetime and to spacetime quantities will be discussed in the next chapter.
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