When a physicist refers to curvature of space he at once falls under suspicion of talking metaphysics. Yet space is a prominent feature of the physical world; and measurement of space—lengths, distances, volumes —is part of the normal occupation of a physicist. Indeed it is rare to find any quantitative physical observation which does not ultimately reduce to measuring distances. Is it surprising that the precise investigation of physical space should have brought to light a new property which our crude sensory perception of space has passed over?

Space-curvature is a purely physical characteristic which we may find in a region by suitable experiments and measurements, just as we may find a magnetic field. In curved space the measured distances and angles fit together in a way different from that with which we are familiar in the geometry of flat space; for example, the three angles of a triangle do not add up to two right angles. It seems rather hard on the physicist, who conscientiously measures the three angles of a triangle, that he should be told that if the sum comes to two right angles his work is sound physics, but if it differs to the slightest extent he is straying into metaphysical quagmires.

In using the name “curvature” for this characteristic of space, there is no metaphysical implication.