Roczniki Filozoficzne

Volume 15, Issue 3, 1967

Geometry and Physical Space

The paper discusses the problem that Euclidean geometry is only one of a number of possible geometries. Generally speaking three types of these can be distinguished: elliptic, parabolic and hyperbolic. The Euclidean axiom: through a point not in a straight line one and only one straight line may be drawn parallel to the given line, is denied by Lobatchevsky’s system in which an infinite number of straight lines may be drawn through that point. Although different geometries are contradictory, each of them is logically consistent in the same sense as Euclidean geometry is. The case being such, the question arises which geometry describes our physical world, which one applies to our physical space. Experience alone can answer the question but we lack as yet adequate data to solve the problem. It is worth remarking that we should not expect Euclid to, be confirmed by experience. In fact his geometry is, as it were, a limitary case of non-Euclidean geometries, between elliptic geometry and the hyperbolic one. Now experience, which makes use of approximate estimations, cannot distinguish the limit case from its sufficiently close approximation. That is why experience may decide only as far as non-Euclidean systems are concerned. The acceptance of the general theory of relativity logically implies a non-Euclidean space. This is, however, a theoretical approach to the problem, not an experimental one. Every experimental proof of the general theory of relativity may be regarded as confirming the assumption that physical space is non-Euclidean.