Examine the question more closely. I suppose that the straight line possesses in Euclidean space any two properties which I shall call _A_ and _B_; that in non-Euclidean space it still possesses the property _A_, but no longer has the property _B_; finally I suppose that in both Euclidean and non-Euclidean space the straight line is the only line having the property _A_.
If this were so, experience would be capable of deciding between the hypothesis of Euclid and that of Lobachevski. It would be ascertained that a definite concrete object, accessible to experiment, for example, a pencil of rays of light, possesses the property _A_; we should conclude that it is rectilinear, and then investigate whether or not it has the property _B_.
But _this is not so_; no property exists which, like this property _A_, can be an absolute criterion enabling us to recognize the straight line and to distinguish it from every other line.
Shall we say, for instance: "the following is such a property: the straight line is a line such that a figure of which this line forms a part can be moved without the mutual distances of its points varying and so that all points of this line remain fixed"?
This, in fact, is a property which, in Euclidean or non-Euclidean space, belongs to the straight and belongs only to it. But how shall we ascertain experimentally whether it belongs to this or that concrete object? It will be necessary to measure distances, and how shall one know that any concrete magnitude which I have measured with my material instrument really represents the abstract distance?
In reality the property just enunciated is not a property of the straight line alone, it is a property of the straight line and distance. For it to serve as absolute criterion, we should have to be able to establish not only that it does not also belong to a line other than the straight and to distance, but in addition that it does not belong to a line other than the straight and to a magnitude other than distance. Now this is not true.
It is therefore impossible to imagine a concrete experiment which can be interpreted in the Euclidean system and not in the Lobachevskian system, so that I may conclude:
No experience will ever be in contradiction to Euclid's postulate; nor, on the other hand, will any experience ever contradict the postulate of Lobachevski.