Whereas Einstein's theory claims that non-Euclidean geometry should hold in the presence of a strong gravitational field, "the bending of a light path" is meaningful only when we presuppose the classical Euclidean space. This situation shows that there is a kind of measurement problem of general relativity. The present author discusses this problem and underscores the point that the revolutionary character of general relativity consists in its prediction of some phenomena which can be observed but cannot be explained without ad hoc hypothesis in terms of classical standpoints concerning space-time. Furthermore, the present author analyses the concept of 4-dimensional neighborhood of relativity physics. We must drastically change the classical concept of neighborhood of space and time. The objectively valid definition of the neighbourhood of an event is the 4-dimensional space-time region of |ds|<ε, and neither of |dt|<ε nor of |dl|<ε. The so-called light cone (|ds|=0) acquires an intuitive meaning of the realm of presentational immediacy as a three dimensional space with a temporal depth.
