Spacetime Continuum

The mathematician Hermann Minkowski, in his groundbreaking 1908 paper “Space and Time,” stated that “henceforth space by itself, and time [Page 1183]by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” Minkowski's insight referred to the fact that until the late 19th century, space and time in physics were treated as two separate entities. This was because traditional approaches used different ways of describing space and time, which again was a heritage of the dualistic ontology of the modern era.

Such ontology can be found especially in the work of René Descartes, who identified space with the outer realm and objects as matter (res extensa) in opposition to the rational interior (res cogitans). To Descartes the outer world furthermore was characterized as a plenum, which means that in his opinion there is no void, but that anything is of a certain substance: Anything that exists in the object world occupies space, because it is extended. The concept of plenum is not equal to space itself, but to the continuity of matter, which fills space. Descartes thus adheres to an antique notion of substance that can be found as early as Aristotle and the nonatomis-tic philosophies, which denied the existence of the void.

After Descartes, in Isaac Newton's physics, the concept of “absolute space” no longer implied a materialistic concept of space. Newton conceived of (absolute) space as the frame for any possible description of movement (in space), and as such the void is just as continuous as the plenum of Descartes. Furthermore, “absolute time,” according to Newton, can also be continuous in the sense that there is the theoretical possibility of an endless movementnot limited by either space or time. Here the concepts of space and time include the continuity of each one, but not a continuity of both of them together.

Subsequently, Immanuel Kant, with the most serious consequences, combined Newton's physics with Cartesian dualism and defined space as the condition of the possibility (spatiality) of any perception or construction of things present to the outer senses by means of uniformity and, in opposition to that, time as the condition of the possibility (temporality) of any perception or construction of things changing shape or placethat is, the concept of movement. For more than 200 years after Newton and Kant, not only were space and time treated as separate entities, but space became identified with the unchangeable and was even attributed as “dead,” whereas time, as the specific mode of inner perception, became identified with the principle of life; as such it can be found in Henri Bergson's concept of the élan vital and the notion of time as durée (duration).

Minkowski's enterprise therefore was neither purely mathematical nor physical; it thereby aimed at the heart of the predominant worldview, according to which time and space are strictly separated entities. Minkowski's student Albert Einstein interpreted this in a chiefly psychological respect: In his view, time and space are both forms of lifeworld abstractions from physical instances, as can been seen in the concept of space as a container (three-dimensional) or time as a line (fourth dimension). But the possibility of describing these abstractions in respect to space (volume) or time (interval) suggests a false understanding of matter, which is always spatially situated and is always moving. To overthrow this misinterpretation Einstein suggested defining space as something that is of a certain “age” as well as to define time as something that is extended. Therefore not only time and space are continuous in themselves, but they together form a space-time continuum: Each location in the universe therefore is a single manifold, which is qualified by the impact of gravity. In consequence the description of a manifold is no longer relative to an observer but is defined as a (four-dimensional) reality in its own, which has no gaps but rather is a “smooth” space. Any object moving in spacetime can thus be depicted according to a “world line” that is describing its unique path through the universe in respect to time as well as to space, whereby the three dimensions of space are condensed to one. Hence, in a two-dimensional diagram, all four dimensions can be represented.

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