Space Time Matter by Hermann Weyl

Author:Hermann Weyl
Language: eng
Format: epub
Publisher: Dover Publications

that is, the projection has a true affine character; this means that in the minor space affine geometry holds, of which the dimensions are less by one than those of the original “complete” space.

If the space is metrical in the Euclidean sense, that is, if it is based on a non-degenerate quadratic form which is its metrical groundform, Q(x) = (xx),—to simplify the picture of the process we shall keep the case for which Q is definitely positive in view, but the line of proof is applicable generally,—then we shall obviously ascribe to the two points of the minor space, which two straight lines parallel to e appear to be, when we look into the space in the direction of e, a distance equal to the perpendicular distance between the two straight lines. Let us formulate this analytically. The assumption is that (ee) = e ≠ 0. Every displacement x may be split up uniquely into two summands

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