# The spacetime has a curvature without matter

## Spacetime

Spacetime plays an active role in general relativity: its curvature influences matter - and vice versa.

From then on, space for itself and time for itself should completely sink into shadows, and only a kind of union between the two should preserve independence. ”In 1908, the Russian physicist Hermann Minkowski described space-time so beautifully. He himself defined the four-dimensional space in which Albert Einstein's special theory of relativity (drawn up in 1905) can be formulated: It is called the Minkowski space. In it there are four independent directions, three are spatial, one corresponds to time. However, the direction of time is not - as in Newton's theory - unambiguous. This manifests itself in the fact that time passes differently in systems that move relative to one another.

The “union” of space and time has often been described as counterintuitive, it is not necessarily so. "In language there are no two areas that are more closely connected than space and time", writes the linguist Guy Deutscher: We say "from Monday to Friday" like "from Berlin to Paris" and "through the year" like " through the jungle ”. The obvious difference in experience - that time passes in contrast to space, that it cannot be reversed, at least in a macroscopic way - the theory of relativity does not explain either; for the insight that the arrow of time points in the direction of increasing entropy, we need thermodynamics.

Space-time, in which the general theory of relativity (GTR) is at home, is far more counter-intuitive. In contrast to the Minkowski room, it is not flat, but can be curved. The curvature of a four- or even three-dimensional space cannot be vividly imagined, but that of a two-dimensional space, i.e. a surface, can. If you roll a sheet of paper into a cylinder, it is just an external curvature: triangles drawn on the sheet still have an angle sum of 180 degrees, parallel lines still do not intersect. It is different with a spherical surface: it also has an inner curvature, it cannot be rolled out on one plane. This type of curvature is essential in the GTR, it is caused by mass or energy - and in turn acts on this.

Has ART also influenced what philosophers can say about space and time? In a lecture at the Academy of Sciences, the physicist and philosopher Claus Beisbart pleaded for a clear yes: The ART strengthens the substantialism (represented by Newton), according to which space and time could also exist empty, without objects - in contrast to (von Leibniz championed) relationalism, according to which they are only relationships between objects. Kant's solution, that space and time are projected out of our heads into the world, is in any case obsolete according to the ART.

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("Die Presse", print edition, November 22, 2015)