Whereas space and time were formerly con ceived as completely independent dimensions, the present attitude of physics is that a body in unaccelerated motion carries with it, as it were, a space which is essentially distinct from the space with reference to which it is in motion and that distances are not the same when measured with reference to two sets of axes in relative motion. In other words, the system of reference of modern physics cannot be divided into independent spatial and tem poral parts, but constitutes an essentially homo geneous spatial-temporal manifold, which is a Euclidean four-dimensional space with real minimal lines. See ANALYTICAL METRICS.
The problems of the infinitude and the in finite divisibility of space and of unoccupied space are again matters of scientific convenience. It is far simpler for the scientist to have a system of reference which does not depend on the entities which are referred to this system than to be continually hemmed in by the limi tations of matter and the construction of a system without lacuna from a system which possesses them is no very difficult logical task. Consequently, the space of science is physically independent of its occupation by matter.
The problem of the extension of the world forms the subject matter of one of Kant's antinomies; that of its infinite divisibility is the subject matter of another. Both of these antinomies or paradoxes have a double aspect. Mathematically, they involve the motions of infinite collections and dense series, which have only received a satisfactory logical treatment within the last half-century. The infinitude of space and its infinite divisibility are again merely the results of the scientist's protest against the complications brought into his work by the supposition of a limited space or a space which offers obstacles to repeated division. Thus Kant is both right and wrong when he solves these antinomies by making space and time forms of perceptive experience, not things in themselves. He is right in so far as the infinitude and infinite divisibility of space emanates from ourselves and not from the object, but wrong in that he believes that in finitude and infinite divisibility involve un oidable contradictions. (See ASSEMBLAGES,